The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal (...) almost disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : [email protected] : https://arxiv.org/abs/1810.09680. (shrink)

Let A and B be subsets of the reals. Say that A κ ≥ B, if there is a real a such that the relation "x ∈ B" is uniformly Δ 1 (a, A) in L[ ω x,a,A 1 , x,a,A]. This reducibility induces an equivalence relation $\equiv_\kappa$ on the sets of reals; the $\equiv_\kappa$ -equivalence class of a set is called its Kleene degree. Let K be the structure that consists of the Kleene degrees and the induced partial order (...) K ≥. A substructure of K that is of interest is P, the Kleene degrees of the Π 1 1 sets of reals. If sharps exist, then there is not much to P, as Steel [9] has shown that the existence of sharps implies that P has only two elements: the degree of the empty set and the degree of the complete Π 1 1 set. Legrand [4] used the hypothesis that there is a real whose sharp does not exist to show that there are incomparable elements in P; in the context of V = L, Hrbacek has shown that P is dense and has no minimal pairs. The Hrbacek results led Simpson [6] to make the following conjecture: if V = L, then p forms a universal homogeneous upper semilattice with 0 and 1. Simpson's conjecture is shown to be false by showing that if V = L, then Godel's maximal thin Π 1 1 set is the infimum of two strictly larger elements of P. The second main result deals with the notion of jump in K. Let A' be the complete Kleene enumerable set relative to A. Say that A is low-n if A (n) has the same degree as $\varnothing^{(n)}$ , and A is high-n if A (n) has the same degree as $\varnothing^{(n + 1)}$ . Simpson and Weitkamp [7] have shown that there is a high (high-1) incomplete Π 1 1 set in L. They have also shown that various other Π 1 1 sets are neither high nor low in L. Legrand [5] extended their results by showing that, if there is a real x such that x # does not exist, then there is an element of P that, for all n, is neither low-n nor high-n. In § 2, ZFC is used to show that, for all n, if A is Π 1 1 and low-n then A is Borel. The proof uses a strengthened version of Jensen's theorem on sequences of admissible ordinals that appears in [7, Simpson-Weitkamp]. (shrink)

continent. 2.1 (2012): 6–21. The French philosopher and novelist Tristan Garcia was born in Toulouse in 1981. This makes him rather young to have written such an imaginative work of systematic philosophy as Forme et objet , 1 the latest entry in the MétaphysiqueS series at Presses universitaires de France. But this reference to Garcia’s youthfulness is not a form of condescension: by publishing a complete system of philosophy in the grand style, he has already done what none of us (...) in the older generation of speculative realists has done so far. His book is sophisticated, erudite, rigorous, imaginatively rich, and abundant in worldly wisdom– despite the author’s conclusion that wisdom does not exist. The quality and scope of Forme et objet took few observers by surprise, since Garcia has been treated as an emerging philosopher to watch across half a decade of Parisian oral tradition. But Garcia was not just the subject of rumor, being already well known to the French public as a writer of fiction. His debut novel, La meilleure part des hommes , 2 was awarded the 2008 Prix de Flore 3 and has already appeared in English as Hate: A Romance . 4 His follow-up novel, Mémoires de la jungle , 5 made clever use of a chimpanzee narrator. Nor was Garcia only published as a novelist before last November: his philosophical study L’Image 6 had already appeared when the author was just twenty-six, a year before he was crowned by the muses at the historic Café de Flore. And then in 2011, just months before the appearance of Forme et objet , Garcia published a widely distributed work entitled Nous, animaux et humains , 7 with its focus on Jeremy Bentham’s ideas about animals. Given this prolific and versatile track record, an optimistic scenario might envisage the young Garcia as one of those combined literary/philosophical talents who appear intermittently in France across the centuries: Jean-Paul Sartre is merely the most famous recent case. While more time is needed to see how Garcia will channel his impressive mental energies, Forme et objet displays such breadth of insight that its author has a good chance to emerge as one of the leading philosophers of his generation. If we accept Aristotle’s dictum that the peak mental age is fifty-one, then to read Garcia’s massive book is to gain some idea of what European philosophy might look like in the futuristic-sounding 2030’s. The present article is confined to Forme et objet . At 486 pages, the work is obviously daunting in size. Indeed, it is even longer than it sounds, given that many of its early sections are printed in a smaller typeface to designate them as supplemental commentary to the main flow of the argument. But while the length of the book reportedly led to delays in French publication, and will probably slow the inevitable appearance of an English translation, the length of the book should not deter interested readers– much of it results from Garcia’s teacherly writing style. Whereas Quentin Meillassoux’s prose displays an arctic economy of means, Garcia’s style is reminiscent of the repeated lessons of oral classroom proceedings. Rarely is the reader given fewer than three or four chances to master an idea before the author moves on to the next. In practice, the style feels welcoming rather than long-winded. Otherwise, the structure of Forme et objet is surprisingly simple. There is a useful Introduction of less than twenty pages. Then comes Book I: Formally , running to approximately 135 pages. Here Garcia outlines the most basic features of a thing “no matter what it is,” or n’importe quoi , an everyday phrase that Garcia shapes into a technical term. This part of the book feels at times like a more amiable version of Hegel’s Science of Logic , a parallel emphasized further by the threefold articulation of its theme: 1. Thing; 2. Thing and World; 3. Being and Understanding. This is followed by the much longer Book II: Objectively , totaling more than 300 pages. It contains sixteen essay-like meditations on specific kinds of objects—including time, animals, humans, history, gender, and death. Here each chapter rolls smoothly into the next, making this second part of the book feel more like a different work of Hegel: The Phenomenology of Spirit . But these are merely analogies. Garcia is no Hegelian, even if the book contains a few dialectical flourishes that seem to reflect his early enthusiasm for the Frankfurt School. Forme et objet ends with a six-page Coda, followed by the usual page of acknowledgments. In what follows, I will briefly summarize each of these four parts of the book before ending with some more general remarks. Before doing so, it will be useful to situate Garcia biographically (as much as I am able) and philosophically. Though Toulouse is his native city, his formative years were spent largely in Algeria, where his family has deep roots. During our sole private conversation, Garcia mentioned that his parents are professors of literature. 8 As a student of philosopher Garcia flourished so early that many of his current ideas date to his teenaged years: “There are sentences in Forme et objet that I wrote when I was seventeen,” he said in response to a question on that cold night on the Canal St.-Martin. I recalled that remark when reading his brilliant account, late in the book, of the central role of adolescence in contemporary culture. While many prodigies blow through their formal academic training without serious obstruction, Garcia’s student memories are rich in tales of isolation and struggle, though equally rich in gratitude for a half-dozen or so exceptional teachers who provided the intellectual space he needed: Meillassoux and Alain Badiou are simply two of the most prominent figures on that list. Though there are many points of agreement between Garcia’s philosophical position and my own, he not only reached his position years before reading my work, 9 he arrived along a rather different path: not through phenomenology, but via the Frankfurt School, which may be one of the reasons for his profound fascination with aesthetics. Garcia’s cultural background is as broad as one could wish: he is no less informed about punk rock and European football leagues than about the spiritualist roots of Bergson’s philosophy. Curious about everything and contemptuous towards nothing, Garcia can be expected to write insightfully on dozens of topics in the years to come. Given that his philosophy is so personally tantalizing in its agreements and disagreements with my own, and given the great internal richness of Forme et objet itself, the present review is no better than a first effort at coming to terms with the challenges posed by this minstrel from the rising generation. This is especially intriguing for older Generation X’ers like me, since confrontation with the younger generation is one of the many themes treated insightfully in Garcia’s book. 1. Introduction Garcia begins in defense of a so-called “flat ontology,” in which all things are equally things. While Roy Bhaskar 10 used this term pejoratively to refer to anti-realist philosophies that flatten everything onto an epistemic plane of human access, Manuel DeLanda 11 (an admirer of Bhaskar) reversed it into the positive principle that all realities are equally realities. Similar notions can be found in the “absistence” of Alexius Meinong, 12 the “irreduction” of Bruno Latour, 13 and my own critique 14 of the undermining/overmining pair. Also noteworthy is Levi Bryant’s use of the term “flat ontology” throughout The Democracy of Objects 15 and his earlier essay “The Ontic Principle.” 16 But for Garcia, flatness is only one face of the cosmos, and one that he ultimately declares to be rather impoverished. Even so, he always remains an advocate of a flat ontology. Insofar as everything is equally something, no matter what it is ( n’importe qui ), everything is equally a thing, equally solitary in its relation with world. This is why his book abounds in those long lists of random, ontologically equivalent entities that Ian Bogost has playfully termed “Latour Litanies.” 17 The first litany in Garcia’s book runs as follows: “We live in this world of things, where a cutting of acacia, a gene, a computer-generated image, a transplantable hand, a musical sample, a trademarked name, or a sexual service are comparable things.” (7) Yet Garcia is frankly dualistic; his flat ontology only lasts until page 159 and the end of Book I (entitled “Formally”), which deals entirely with things that are equally things. Thereafter Garcia turns his attention from things to objects, which are not flat in the least, but engage in hierarchical relations with one another. In agreement with both DeLanda and the speculative realists, Garcia proclaims that his book “proposes to put to the test a thought about things rather than a thought about our thought about things .” (8) Just as ducklings are “imprinted” (9) after hatching and treat the first creature they see as their mother, philosophers are imprinted by the idea with which they begin. Hence, philosophies that begin with human access will never truly find their way back to things. This makes Garcia rather suspicious of twentieth century philosophy, since “the twentieth century—to which in some way this work proposes to bid adieu—has been a period of theorizing modes of access to things rather than things...” (9) Among other possible benefits of the philosophy of things that Garcia proposes, it is fully able to account for thought as a special variant of things, while the reverse is not possible.(10) In Book I of Forme et objet , Garcia’s “things” are so flat, so de-determined, that he is forced to renounce some of the most basic features ascribed to things by most realists. As he tells us in his foreboding third footnote: “We will maintain that the solitude [of things] is less than unity, less than identity, and that it does not imply acceptance (any more than refusal) of the principle of non-contradiction.” (11) In a contemporary world cluttered with too many things, Garcia’s flat and formal plane provides us with some breathing room: “The formal plan of thought enables or re-enables us to cut short all accumulation—whether of knowing, experience, or action—by a simplicity, an impoverished surface...” (13) As Garcia says elsewhere in responding to a Deleuzian critic of the book, his starting point in flat ontology is designed to obstruct the claims of both analytic philosophy and Hegelianism: “Hence, this work seeks to protect each thing—real, imaginary, inconsistent, contradictory—both against Ockham’s Razor and against the Aufhebung or dialectical process.” 18 Yet contrary to the equalizing spirit of many flat ontologies, “we will add to our formal ontology of the equal, an objective ontology of the unequal.” (13) But initially, Garcia joins all flat ontologists in holding that everything is irreducible: “this irreducibility, which we will term the ‘chance’ of each thing... also marks the refusal of a positive thought that reduces things exclusively to natural things, or social things, or historical things, etc.” (15) This irreducible “chance” of a thing emerges as an important technical term in the book, always paired with its inverted brother, the “price to pay” ( prix à payer ). On pages 17-19, we find the only diagrams in the book. What they illustrate is that Garcia wishes to avoid two equally dangerous extremes. The first is the philosophy of substance, featuring the thing-in-itself as a mighty river fed by attributes as if by subordinate tributary streams. This model can be found in many of the classic thinkers of West and East alike. In it, “there is obviously a hierarchization between that which is dragged towards something other than itself, and this other which serves it as an ontological support while supporting its proper being.” (16) For Garcia, the second extreme worth avoiding is the philosophy of events: “One thus conceives trajectories of being, identified as events, facts, powers, intensities, or intentionality. These vectors of being come first, bearing and supporting being, displacing it, but without ever finding a stopping point, a buffer, an objective consistency.” (17) The first model gives us a thing too wrapped up in itself, too compact . This word “compact” (the French and the English are the same) is another technical term for Garcia. But if the “compact” model of things leads us to something more than things, the philosophy of events gives us less than things, by dissolving them into a play of vectors. Garcia’s alternative lies midway between these two extremes: Being enters the thing, being comes out of it. And a thing is nothing other than the difference between the enters and the being that comes out. Thus, the circuit of being is never halted. In the thing, there is never the thing-in-itself. And the thing is never in-itself, but outside of itself. Nonetheless, being is not eventally “pollinated” by vectors: it possesses an objecting halting-point... (19) This single idea is the key to Garcia’s book: the thing is neither a self-contained durable lump nor some sort of evental flux. Instead, the thing is the difference between its various components and its relations with its environment. Or stated differently: “the price to pay for this disposition is a circulation of being that systematically distinguishes two senses of things: that which is in the thing , and that in which the thing is , or that which encompasses it and that which it encompasses,” (19) translating comprendre here as “encompass.” 19 In a beautiful description of a piece of black slate, Garcia sums up the various minerals, qualities, and shapes that compose [ comprend ] it, and calls them “that which is in the thing,” (20) noting that this tells us nothing about “that in which [the slate] is”—namely, all the various situations in which the black slate can be found. Instead, the slate is the difference between these two: the most characteristic principle of Garcia’s philosophy. 2. Formally Book One of Forme et objet , “Formally,” is concerned with the formal equality of all things in a flat world. “Two questions mark the boundaries of reflection: of what is everything composed [ composé ], and: what do all things compose?” (27) Looking downward, we wish to know what everything is made of; looking upward, we want to know the ultimate result of the combination of all things. Here we must turn our attention to the thing n’importe quoi— no matter what it is. (30) Anything with finite qualities is obviously too specific to be relevant to global ontological questions. To an equal degree, something possessing all qualities (think of Whitehead’s God) 20 would not be n’importe quoi either, since it would still be too definite, even if incredibly vast. The same holds for contradictions, since these all differ from each other. The square circle, the non-white black white, and the non-city city are all too distinct to count as the thing no matter what it is. The n’importe quoi must be devoid of all specific qualities, including contradictory ones. In one of the more intriguing points in his book, so reminiscent of Meinong, Garcia proclaims that “the ‘no matter what it is’ is neither a reality nor an abstract construction, nor both of these at once; the ‘no matter what it is’ is simply the plane of equality of that which is real, that which is possible, that which is inexistent, that which is past, that which is impossible, that which is true, that which is false, that which is bad.”(39-40) Since everything has two faces, it would be a grievous mistake to focus on just one of them at the expense of the other, as physicalism or materialism do when reducing the world to minuscule physical underpinnings. For scientistic materialism, “it is either atoms, particles, or fields of force... which are the things.” (47-48) Moreover, “these more-than-things are accompanied by less-than-things: for example, ideas or facts of consciousness are determined by the state of matter and are not autonomous things, but manifestations reduced to secondary effects of material processes...” (48) On this point, Garcia’s position is in complete accord with my own critique of undermining and overmining. 21 Where we disagree is that Garcia is more deeply suspicious of the notion of substance, which I view as salvageable with a few needed changes, while Garcia sees this operation as hopeless: “A substance, in the history of philosophy, is the more-than-thing par excellence.” (51) Another agreement between our positions is visible when Garcia claims (correctly, in my opinion) “that it is vain to distinguish between things which are material and those which are not.” (52) Yet we also find an even more important disagreement, since for Garcia withdrawal cannot be the quality of a thing. Instead, the absence of a thing is simultaneous with it, embodied in all that is not it– the absence of the sculpture of a woman is to be found in the mold that appears at the same time as it, and thus withdrawal must be viewed as an “event” rather than as something pertaining to an object. For Garcia, nothing withdraws beyond access. Since we must distinguish between “that which is something” and “that which something is,” and since the former is identified with “no matter what it is is” and the latter with “ not no matter what it is,” we can say that “everything is thus a milieu, a fragile link between ‘no matter what it is’ and ‘ not no matter what it is.’” (62) And here we find Garcia’s critique of the thing-in-itself: “A thing is never defined en bloc . We can affirm that a thing is this or that, but that does not suffice. It is still necessary to state precisely that which is this thing .” (62) Stated differently, “something is not in itself : for that which is in the thing is not the thing, and that in which the thing is is not the thing.” (62) And here Garcia and I, facing the same evidence, draw opposite conclusions. For me, the fact that nothing can be identified with either its components or its concrete location means that the thing must be something in-itself distinct from both of these. Yet for Garcia, to be in-itself would mean to be identified with just one of these two extreme terms, and hence the thing can only be the difference between them. Garcia is equally suspicious of the classical tendency to view “unity” as a property of the thing, since in his eyes unity is too relational a property to belong to things. (65) While specific things are situated determinately with respect to other things, we are still speaking here about the thing no matter what it is, and this can be viewed only in terms of solitude, which all things share: a human being, a hand, or a chair or all equally things insofar as they are on their own , not insofar as they are one . (64) A thing is alone, and relates only to the one thing that is not another thing: world. In a striking parallel to my own argument for a partial revival of occasionalism, Garcia tells us that “the things communicate only by their solitude: it is because everything is equally on its own in the world that things can be together, enmeshed in one another.” (67) Alone in their solitude, things all relate to world, which serves as a mediator allowing them to become mixed up in one another. As we have seen, one reason that nothing can be in itself is because everything is in something else. For Garcia, “to be in something and to be something are equivalent.” (69) Stated more broadly, “being is thus the difference between the two aspects of each thing: that which is it, and that which it is.” (70) And even more vividly: “a thing is almost like a sack: there is that which one puts in the sack and that which remains outside the sack.” (70) But not quite like a sack, “since a thing is not a thin skin or film. Instead, a thing is comparable to a sack that is immaterial and without thickness: it is nothing other than the difference between that which is this thing and that which thing is, between content and container.” (71) Nothing can be in-itself because everything is two selves at once. For example, we cannot say that our self is defined by our consciousness: “Everything has a self because nothing is in itself. The self is not the quality of that which is related to itself (which is conscious, for example) or which thinks itself related to itself. Nonetheless, for an entity called ‘conscious’ to be related to itself, it is necessary that this very relation should be another thing than the self to which it is related.” (71) Consciousness cannot be the self, precisely because it is other than that of which it is conscious. Nothing is able to grasp itself. The self is “the function by which being and composition [ compréhension ] are mutually excluded...” (72) The self is “the point of shadow of everything that projects some light...” (72) The in-itself faces two opposite dangers: “For something to be in-itself is to be a self. Something which is a self flies out through one of its two sides... Stated differently, being in-itself is simply the possibility of a double failure.” (73) The in-itself can be termed compact : “There remains to us a means of thinking that which does not fully enter into the world, though without exiting from it. This means is what we call the compact.” (76) In a sense, the compact is the opposite of the world. For in the case of the world, everything enters it and it enters nothing; as for the compact, it enters the world (since it is something, after all) while nothing enters it. (77) The compact marks the presence of the impossible in the world. (78) It is not impossible, but possible only on the condition that it fails. (78) The time has come to speak of where a thing is located. “The sole condition of a thing is that of being in another thing than itself, and thus in another thing than something.” (78) A condition is “that which determines something, that which forms something, that in which something is.” (78) As for humans, “the condition of someone is his situation; my social condition is that which socially determines me, my place and my function...” (79) More generally, “to be conditioned is to find oneself reduced to that in which one is.” (79) Everything is conditioned, but nothing is reducible to this condition. To determine the condition of something is to determine in what it is. A thing is located in that which contradicts it, just as a statue exists in its mold, which is precisely that which it is not. Since the thing is finite and definite, its condition or form must be infinite and indefinite. That in which all things are is the world, which Garcia also terms “the whole.” (81) “To try to be in-itself is to attempt to remain outside the world. And indeed, to try to be in-itself is only a path of entry into the world.” (83) For Garcia, “the world is not the pre-existent container of the things it contains, a priori , nor the construction by the mind of a fictional ensemble of all things, a posteriori .” (85) Instead, the world is simultaneous with all things; the two always go together. The world cannot be a determinate world, such as the physical universe or mathematical space, since these are already too specific and limited. “Every determinate world, which is in fact a universe , is a ‘big thing’ [ grosse chose ]: it is a set, however vast, of composite things which itself embodies a thing.” (85) Every determinate world is really just a “big thing.” Stated differently, “it is nothing other than a balanced milieu between the things that compose it and the thing that it composes.” (85) We generally picture the world as a physical univer. (shrink)

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that the family \({\mathcal {F}}\) is linearly orderable (...) (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

The present article is an attempt to set forth and examine the conclusions of what is perhaps Husserl’s finest piece of philosophical investigation, and one of the finest pieces in the whole history of philosophy: the investigation of the consciousness of time, with its extraordinary combination of an unchanging form with an absolute flux of which it is none other than the very form itself. This investigation puts Husserl on a level with the wisest heads on the matter, with Aristotle (...) in Books IV and VI of the Physics, with Augustine in Book X of the Confessions, and with Kant, whose whole Critique of Pure Reason may be said to be an examination of what is necessary to temporal experience. In Husserl’s work we have, we may say, the greatest of recent philosophers tackling the greatest of philosophical problems, one in which contradiction is always appearing in novel forms, to be evaded only by the naïve superficiality of a Minkowski or a Grünbaum, or by such infinitely useful subtlety as Husserl himself practises. As Husserl himself put it near the beginning of his 1905 Lectures. (shrink)

continent. 2.1 (2012): 29–35. Translated by Vincent W.J. van Gerven Oei from Jeroen Mettes. "Politieke Poëzie: Enige aantekeningen, Poëtica bij N30 (versie 2006)." In Weerstandbeleid: Nieuwe kritiek . Amsterdam: De wereldbibliotheek, 2011. Published with permission of Uitgeverij Wereldbibliotheek, Amsterdam. L’égalité veut d’autres lois . —Eugène Pottier The modern poem does not have form but consistency (that is sensed), no content but a problem (that is developed). Consistency + problem = composition. The problem of modern poetry is capitalism. Capitalism—which has no (...) image: the unrepresentable Idea of “everything.” The problem is that a poem cannot be justified. There is no excuse for it. Political poetry— pure poetry—has to be problematic, though not in a mannerist way. Yes, its problem is first its own problem—poetry’s existence in the same world as the newspaper—but therefore also always everybody’s problem (the problem of any world at all). The cult of the sublime points at a suspect desire for transcendence, nostalgia for paradise lost (the womb?). Melancholia of the post-. But a problem neither sorrows nor mourns, it is alive, and the fact that it is alive is the problem—the problem for death (rigidity, the status quo). Our symbols and ideologies do not hide any god: symbolic = state; imaginary = human; real = money. Problem: the possibility of communal speech (poetry) in the absence of a “we.” Or: what is a “we” that is not a collective subject (or in any case is not a volonté générale )? What is a universal history that is not a History? This work was started in the shade of the anti-globalization protests at the end of November 1999. I considered N30 to be the closure of the nineties, of my adolescence, and of the a seemingly total extinction of social desire. From the beginning I was skeptical about the alterglobalization movement as the avant-garde of a new politics, but something was happening . Maybe this event did not show that, as the slogan would have it, “another world” is possible, but for me it indicated that such possibility was at least still possible. That naked possibility is carrying forward. And if the fundamental tone of this work sounds more desperate than utopian, this is not caused by the catastrophic sequence that since 1999 has plunged us ever deeper into the right-wing nightmare—a nightmare that this work also gives an account for—but because my hope as yet remains empty. Composition . Composition is no design, but the production of an autonomous block of affects (i.e. a POEM), rhythmically subtracted from the language of a community. A poem does something. Is something. New Sentence . Choosing the non sequitur as compositional unit has the advantage that an abstract composition is subjected to the stress of concrete, social references. Where there is a sentence, there is always a world. (This does not hold necessarily for words on their own.) And where sentences collide, something akin to a textual civil war takes place. It is not about “undermining” whatever, or de-scribing the raging global civil war, but about writing social (or even: ontological) antagonism -- including all its catastrophic and utopian possibilities. Minor resistance. Why would poetry be the no protest zone par excellence? It is nothing but protest, not simply qua “content,” but in its most fundamental essence: rhythm. Rhythm is resistance against language, time, and space, and the basis of (what we will continue to call) autonomy. Rhythm starts with the anti-rhythmic caesura as Hölderlin remarked about Sophocles, a disruption of the quotidian drone. The destruction of everything that is dead inside of us. The noise of the avant-garde has never been the representation of the noise of (post)modernity (from the television or shopping mall), but the sober noise of the systematic exchange of an unbearable worldview. The poet does not describe, but looks for a way out: There is a Grain of Sand in Lambeth that Satan cannot find Nor can his Watch Fiends find it, tis translucent & has many Angles But he who finds it will find Oothoons palace, for within Opening into Beulah every angle is a lovely heaven William Blake was not mad. And there has always been only one poetry: the poetry of paradise. The principle is that there is something in art (the essentially creative element) that is disgusted by that which, unlike art, does not aim for the supreme. Wonder is not supreme, tranquility is not supreme, beauty is not supreme. Even amusement is not supreme! The supreme is supremely open, “das Einfache,/ Das Schwer zu machen ist” 1 : paradise. That is abstract. Literally. For me it is not about a concrete imagination, an idyll or utopia. There is no doubt a need for that, but it is not so much the supposed lack of imagination or ideals (human rights are ideals), but a fundamental lack of desire (human rights are no desires) that we suffer from, and from which we do not need to remove Nietzsche’s label of “nihilism.” “We.” George Oppen: “ Of Being Numerous asks the question whether or not we can deal with humanity as something which actually exists.” What is less actual than humanity? Nowadays it appears as a lifeless ideology of cynical power politics. Or as what makes one think. It is a shame to be human. The event is the caesura that defines rhythm. Writing toward the event is not the description of the event, but marking an abstract and intense space in which the event may unfold and keep itself. It is a task. “Remember that thou blesseth the day on which I seized thee, because such is thy obligation.” The event is a contraction (or a series of contractions) with its own rhythm and unique qualities. It is more than an explosion or demonstration. But at the same time less. The endless repetition of images and stories in the media points to a fear for the indeterminate and indeterminable void of the event. In the end there is nothing to see. We do not live in disaster’s shade or miracle’s light, but rather in the rhythm, which is contracted time, having little to do with omnipresent representations. For this book I did not intend a rhythm of evental representations (a narrative rhythm), but a rhythm which would be an event itself , because it draws the border between artwork and history. My desire for a direct engagement with the “extra-textual reality” has nothing to do with the representation of “rumor in the streets.” (What has less street cred than representation?) Naturally, a poem is no historical event and does not change anything. But a poem is a part of history that wants to be repeated forever, constructed in such a way that it is worthy of repetition. It is a part of desire (composition) made consistent (durable). The “historical event” flares up and burns down, and has to burn down to be effective. The leftovers are images and stories (representations), History—no event. The artwork—that is the ambition— remains event (though monumental and inefficient/inoperable). (No wonder that a historical singularity, a revolution, reminds us of a work of art; the resurrection yearns for a judgment, an affirmation; everything depends on it.) Hence the title does not summarize the book, let alone contract its “content” into a quasi-transcendental signifier. The title is juxtaposed to the book, like everything else inside the book, and in that relation it precisely forms a part of it. The ideal work is an open whole, lacking nothing but to which everything may be added. I have been interested in this “everything,” the world, or as I said above: capitalism. “Everything” is not the space for “wonder”—a code word, a shibboleth for petty bourgeois imagination (I recognize myself in the strangest things, a speaking dog, a canal, a pond standing straight—oh my god). No. The world is a social world, not YOUR world, poet. Power is number one. I will call “Dutch,” or “shitty,” whatever denies this power. That hurts, but this pain is an expression of the desire in the world to write another world, or as Blanchot says, “the other of all worlds” 2 : the world. Not as what “is there,” but rather as that which urges for an escape from what “is.” This is a testament of how radical reality has become, for me—or rather, a writing body—in a having-been-written. I am not interested in the problem of “meaning” as misunderstood by literary scholarsi: “order” in “chaos,” “symbolization.” Bullshit. What is there, hop, hope, now: the meaning of the taste in my mouth. Bullshit. I am not interested in the frustration of interpretation; I am writing for readers who do not want to interpret. I do not know how many “professional readers” will hear the music of a paragraph like: Sun. Sushi. Volvo. I hope more than I would think. There is a suggestion (or rather, an actual production) of speed and infinitive owing to the absence of plosives, i.e. articulations such as /k/, /t/, or /p/. Can you hear the slick suaveness? Driving car dark, vocal chiaroscuro of the word “sushi.” The unstressed /i/ stands in the middle of dark vowels and thus acquires its own special out of focus , like a momentary flash or brilliance—an obscure light. It is not about recognizing a story, but about avoiding any story whatsoever: the car disappears in the glow, cars and raw fish have nothing in common except their articulation in a language that brings them together, blurring them. A world appears in its disappearance. For a moment, light is a metaphor for language, though it cannot be reduced to tenor. It is not necessary to be a linguist or philosopher to hear this—a “difficult” poem all too often becomes an allegory of its own impenetrable being-language. The only demand: leave your hermeneutical fetish at home. This was no interpretation. Most shit has been stolen etcetera. That is no longer interesting. You cannot shoot the body with information and let your lawyers reclaim the bullets. So every sentence has been stolen. Also the ones “out” “of” “my” “head.” Why would I be allowed to steal from myself and not from others? Man takes what he needs to move forward. Whatever he encounters, finds in front of him, “occurs” to him. The writer as text editor, or singing pirate. Nothing new here. Important difference with for example Sybren Polet’s 4 montage technique: anti-thematicism. Most of the time ferocious citation from whatever I was reading, listening to, ended up in, and so on. I wrote chapter 12 on my laptop while watching CNN. On the air instead of en plein air . I often employed search engines to generate material. Chapter 20 offers the purest example of this. Often I stop recognizing a particular citation after some time. It is not uncommon for a stolen sentence to conform itself to the paragraph in which it finds itself. Sometimes I nearly arbitrarily replace words. Arbitrariness as a guarantee for absolute democracy. It is a poetics of the non sequitur : a conclusion that does not follow from the premises, the strange element in the discourse. A discourse of strangers. No logical, narrative, thematic unity. There is unity in speed/flight. It has to be read linearly, but not necessarily (not preferably) from beginning to end. The shortest distance between two points is a straight line, but this line precedes every point. The middle, the acceleration, comes first. A point occurs where two lines cross. It has been written from up close, at the level of the tension between sentences. Nothing to be seen from a distance: no form except the exchange of form, no geometrical or mythical meaning. You have to get in, “groping toward a continuous present, a using everything a beginning again and again” (Stein). 5 In Dutch, experimental poetry has been mainly dense: a small rectangular form filled with a maximum amount of poetic possibility. But at the moment the poem starts to relax, the anecdotical content seems to increase. This is what is called “epic”: long, narrative. I believe that an epic is more than that, in fact something completely different. An epic is “a poem including history,” 6 a long poem tied up with the life of community, that as a whole does not need to be narrative. The American poets of the twentieth century (Pound, Williams, Zukofsky, Oppen, Olson, Silliman) have put the epic back on the map by interpreting the poem itself as a map, and writing it as navigation. They have invented the experimental epic, a genre that has generated little original following in “our” poetry. N30 is the middle part—“always start in the middle”—of a trilogy, the contours of which remain as of yet unclear, although each episode investigates one of the three “ecstasies of time”—past, present, future—concerning society X. N30 concerns itself with the PRESENT: not with the description of actual facts but of the rhythm and the intense depth in which facts appear to us. Where are we? We are camping in the desert. Sometimes we are looking at the stars. As opposed to maximum density and minimal tension (a characteristic of most (post-)experimental lyricism), I have sought a minimal density and maximum tension in this book, considered as a long non-narrative prose poem. On the one hand, the minimal density is obtained by the inherent formlessness of prose, on the other hand by the conscious refusal of any active (formal, non-rhythmic) synthesis: the poem tells nothing, shows nothing, has no theme. I did not seek maximum tension either by loading the quotidian with epiphanic radioactivity (“wonder,” confirmation from above), or by means of the intensity of the linguistic structure. I want an abstract tension, but social in its abstraction, in other words, not neutralized by and subjected to Form. Instead of form (transcendent): composition (immanent). The concept is series. Ideal: every unit is necessary for the efficacy of the others and the whole, their relation is purely linear, i.e. non-hierarchic, non-syllogistic, non-discursive, non-narrative. Sentence related to sentence like paragraph to paragraph and chapter to chapter; the whole means nothing and represents nothing. Inside the sentence: syntax (Chomsky’s tree, a type of parallel circuit), outside: parataxis (coordination, an asyntactic line through language and world). I consider duration—the energy of duration (rhythm)—to be the fundament of a poem, the temporal inclination to delimit a “space.” Being as consistency, its consistency. A spatial part of time is not merely a metaphor for an inevitable trajectory, an inescapable time, something like “our time.” Not merely—because rhythm comes from language and is not projected onto it; the poem derives from the world like a scent and a color and a life from a flower. A series, a sequence: nothing potential, but truly infinite—the movement of an infinitude. The infinite series = everything minus totality. That means that there is no container—no Form, no Self, no Image, no Structure, not even a Fragment—just “the prose of the world.” No representation, but also no staging of the impossibility of representation (the postmodern sublime). These are no fragments, no image of a fragmented world or personality, no cautious incantations around the Void. It does not exist. It is a movement. Buying bread, a flock of birds, a bomb falling—they do not depict or represent anything, not literally, not metaphorically. There is an Idea, which is however nothing more than a rhythm, in the same way that capitalism is nothing more than a pure function. Parataxis: the white space between two sentences stresses, which is nevertheless always there, also between words, even between letters: the out of focus of idle talk, the gutter, the irreducible Mallarméan mist which renders even the seemingly most transparent text legible. The white space suggests a neutral medium for free signification, a substance of language. A non sequitur is an element from a foreign discourse, which stresses the white space as space, and problematizes freedom for supra-sentential signification. I start by withdrawing material, leaving the initiative to the sentences. In general a word presupposes less often a discourse than a sentence. What discourse is presupposed by “dog”? We could think of several, but why would we? It is more probable that, when faced with the naked word, we think of its naked (dictionary) meaning, of its denotative signified. By means of two simple interventions we may also write the word as sentence: Dog. In no way this suggests the discourse from which this sentence originates, but in any case we’re presupposing one. This is shown by questions like: “Whose dog? Who’s a dog? What kind of dog?” Etc. (Sentences are question marks.) A sentence implies/is a microcosm—a subject, a verb, an object, and so on. Even an incomplete or ungrammatical sentence does so. My main fascination while writing this book is the worldly and social aspect of language, an aspect that often becomes invisible, or rather, transparent in narrativity—the stretching of sentences into stories. Narrativity organizes a new discourse and a new world, and places a sometimes all too dispersing relation of transparence in between. The conventional novel is the brothel of being. I do not intend to prohibit brothels, and I have certainly not intended to write an anti-novel (THIS IS A POEM), but I do consider narrativity (in general, in poetry, in the news, in daily life) to be ontologically secondary with regard to an immediate being in the world through sentences, also if the latter have been withdrawn from a narrative or otherwise externally structured discourse (which in that case would therefore be chronologically primary ). Naturally, two or more sentences are always in danger of telling stories or arguing, just like the world is always in danger of becoming an objective representation, facing us, strangers. That is why need to wage war—against representation and against the interface, against interaction. AGAINST THE “READER.” To the extent that a sentence is worldly, writing is a condensed global war, and in so far as there is ultimately only one world and one open continuum of languages, it is a global civil war. Nice subject for an epic. The elaboration of a singular problem—prose as the outside of poetry, the form of the novel as purely prosodic composition scheme—“expresses” the universal problem: capitalism as Idea of the world vs. poetry as language of an (im)possible community. The paragraphs are blocks of rhythmically contracted social material. By choosing the sentence as the basic compositional component, an abstract whole may contain social sounds, without telling a story or showing an image. Composition is subrepresentative —a rhythmic, passive synthesis, or rather: a synthesis of syntheses. I never write large blocks of prose in one sitting, because there is no obvious organizational vector —plot, theme, conscience—outside the inherent qualities of the material itself. Usually I write down one sentence, sometimes two, but rarely more than three. Those sentences are usually placed in the text which I am editing at the time. In fact, there is no original composition, new chapters split off from chapters which became too long during the editing process. (Revision mainly consists of adding and inserting, displacing and dividing; only during the last phase, when the text has gained enough consistency, there may be subtraction to tighten the composition; each chapter requires a season of daily revision). This constant revision, accompanied by a continuous influx of collective background noise (to speak with Van Bastelaere), 7 makes every chapter a block condensed (“historical” and “personal”) time. The block itself is a-personal and a-historic; it is ontologically autonomous. If there is such a thing as a spirit of the times, I do not try to offer an image of it, but rather to cancel something of it by erecting a monument of its own excrement within its own boundaries. Tuning and dis-tuning , “in de taal der neerslachtigen een eigen geluid doen klinken,” 8 in other words, desiring in an Elysian way. In this sense I have intended to be able to write a political poetry. The ultimate political poem is the epic, “the tale of the tribe.” I consider N30 to be a prolegomenon to a future epic (of which it in the end will form a part a structural moment, as introduction-in-the-middle), an extended pile on top of an epic as narrative, a question of the tribe and question of its history. I was burdened by too much satire, too much bullshit. But: satire willy-nilly = the only justifiable satire. Against the abstract universalism of the market (“globalism”): concrete disgust, a positive way of saying “No.” Moreover, disgust is a specifically total attitude, which ultimately concerns the world as a whole. I hate this or that, but I am disgusted by EVERYTHING (when I am disgusted), and so it appears that satire is in fact related to the epic, in so far as it concerns society, the cosmos, history. Maybe it is no coincidence that the Dutch literary canon knows no great poet of disgust; what could be more fearful to us than society, the cosmos, and history? The T-tendency (T from Tollens 9 ) clearly points into the direction of the small, friendly, ironic, melancholic, acquiescent, wondrous, and so on. The anti-political, anti-cosmic, anti-historical. (Why am I so philosophical? To scare away the Dutchies.) And most of all: the “poetical” (the pseudo-mysticism from the backyard). Yes, the N in N30 also stands for the Netherlands (just like 30 indicates the number of chapters). I was not in Seattle, I do not live in Iraq. But is not the whole world bleeding to death on Dutch paving stones? Let’s hope that we mowed away something with this total satire, also “in myself.” The arrogant stupidity that definitely thinks to know the essence of freedom (the free development of esthetic needs inside the void), that cannot take anything serious, only believes in the disciplined bestiality of the individual (“norms and values”) and the mere functioning of a social factory which finds no justification whatsoever outside its functioning (“get to work”)… Who knows. A certain aimed destruction leaves grooves and craters, mapping out a next adventure. Pound’s periplum : sailing while mapping the coasts. Immanent orientation. The terrain changes with the map, history changes with the poem. Maps never merely organize the chaos, transcendent schemes imposed on a formless Ding-an-sich . They organize from within, surfing. But they are most of all routes back into the chaos or forward to paradise (final identity of chaos and paradise; Schlegel: “ Nur diejenige Verworrenheit ist ein Chaos aus der eine Welt entspringen kann ”10). A poem is not only a piece of history, it is also a flight from history. Maps give chaos to the form of reality , open escape routes, break through representations, make us shivery and dazed. Paradise is immanent to a fleeting desire. History is the history of labor—this is Adam’s curse—and the poet works too: For to articulate sweet sounds together Is to work harder than all these, and yet Be thought an idler by the noisy set Of bankers, school masters, and clergymen The martyrs call the world 11 But: the poet works in paradise. The paradox of the artwork, the work that is no work, the piece of history that cannot be reduced to History—this is explained by The Space of Literature , a virtual space, an autonomous rhythm, not outside, but in the midst of the noise, a piece of paradise in hell, a postcard from the vale of tears addressed to paradise, to X. Political poetry means: a poetry that dares to think about itself, about its language and about its world and about the problematic relation between both, which is this relation as problem. A poetry that thinks at all, articulates its problem. It has nothing to do with journalism or morality or debate, let alone the law or the state. It has nothing to do with “criticism” if this means the replacement of incorrect representations by other, more correct representations. It has something to do with ethics in the sense of learning to live. It has something to do with the community and the language of the community (whichever that may be) and the role of the poet regarding the community. It concerns justice without judgement or measure. In the end the just word is just a word , to paraphrase Godard: it is from a future that is unimaginable. It Is no rational engagement, but an aversion against everything that obstructs life, and love for everything what is worthy of having been loved. The world is engaged with me, not the other way round. First Exodus, then Sinai. A desire does not start with an agenda. To answer the question whether I am really so naive as to want to change the world: “We only want the world.” Justice is the world appealing to us to liberate it from all possible chains, from each organization and inequality, to be it, smooth, equal, under a clear sky—a desert and a people in a desert. That moment between Egypt and the Law. It is not a revolution, but the sky above the revolution. Poetry = the science of escape. There is no art that we already know. The weakness of modernistic epic poetry seems to me to be the unwillingness to completely abandon narrative as a structural principle, in favor of a composition “around” or from an event. The China Cantos and Adams Cantos are the low point, and the Pisan Cantos the high point of Pound’s poetry. Two types of research: archival representation of the past vs. ontology of the present (which virtually presupposes the entire history). Presupposing an event means that it is impossible for the poet to stage his own absence, but in no way makes the work personal. An event is the unknown, the new invading into the business as usual, so also the personal. The question heading this research is not: “Who am I?” but “What is happening?” The book is as little illegible as Mondrian’s work is invisible. Form is of interest only to the extent that it empowers liberation. Ron Silliman So no formalism, but what it means to live in this world and to have a future in it. I want something that holds together that’s not smooth. Bruce Andrews The past above, the future below and the present pouring down: the roar, the roar of the present, a speech— William Carlos Williams If my confreres wanted to write a work with all history in its maw, I wished, from the beginning to start all over again, attempting to know nothing but a will to create, and matter at hand. Ronald Johnson NOTES 1) “The easy thing/ that is difficult to make.” Bertold Brecht, Lob des Kommunismus . (All footnotes are the translator’s) 2) Maurice Blanchot, The Space of Literature , trans. Ann Smock. Lincoln/London: University of Nebraska Press (1989), 75. 3) Mettes uses the word “Neerlandicus,” which refers to scholars of Dutch language and literature. 4) Dutch poet. 5) Gertrude Stein. “Composition as Explanation.” A Stein Reader . Ed. Ulla E. Dydo. Evanston, IL: Northwestern University Press (1993), 495-503. 6) Ezra Pound. 7) Flemish poet. 8) “Resounding an original sound in the language of the despondent.” A. Roland Holst, De afspraak . 9) Dutch poet. 10) “Only such a confusion is a chaos which can give rise to a world.” 11) W.B. Yeats, “Adam’s Curse.&rdquo. (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is (...) class='Hi'>known. In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

We write and for the cardinalities of the set of permutations with n non‐fixed points and the set of subsets with n elements, respectively, of a set which is of cardinality, where n is a natural number greater than 1. With the Axiom of Choice, and are equal for all infinite cardinals. We show, in ZF, that if is assumed, then for any infinite cardinal. Moreover, the assumption cannot be removed for and the superscript cannot be replaced by n. (...) We also show under that for any infinite cardinal, implies is Dedekind‐infinite. (shrink)

Let a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a sufficient condition on a, so that for every \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Sigma ^{-1}_a$\end{document}‐computable family of two embedded sets, i.e., two sets A, B, with A properly contained in B, the Rogers semilattice of the family is infinite. This condition is satisfied by every notation of ω; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satisfies this condition. On the (...) other hand, we also give a sufficient condition on a, that yields that there is a \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Sigma ^{-1}_a$\end{document}‐computable family of two embedded sets, whose Rogers semilattice consists of exactly one element; this condition is satisfied by all notations of every successor ordinal bigger than 1, and by all notations of the ordinal ω + ω; moreover every computable ordinal that is sum of two smaller ordinals has a notation that satisfies this condition. We also show that for every nonzero n ∈ ω, or n = ω, and every notation a of a nonzero ordinal there exists a \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\Sigma ^{-1}_a$\end{document}‐computable family of cardinality n, whose Rogers semilattice consists of exactly one element. (shrink)

continent. 1.3 (2011): 149-155. The world is teeming. Anything can happen. John Cage, “Silence” 1 Autonomy means that although something is part of something else, or related to it in some way, it has its own “law” or “tendency” (Greek, nomos ). In their book on life sciences, Medawar and Medawar state, “Organs and tissues…are composed of cells which…have a high measure of autonomy.”2 Autonomy also has ethical and political valences. De Grazia writes, “In Kant's enormously influential moral philosophy, autonomy (...) , or freedom from the causal determinism of nature, became prominent in justifying the human use of animals.”3 One of the oldest uses of autonomy in English is a description of the French civil war from the late sixteenth century: “Others of the…rebellion entred in counsell, whether they ought to admit the King vpon reasonable conditions, specially hauing their autonomy.”4 Life, and in particular human life, and in particular human politics, is well served by the usages of autonomy . What about the rest of reality, however? Should it be thought of, if it's even considered real and mind-independent, as pure stuff for the manipulation or decorative tastes of truly autonomous beings? We tend to think of things such as paperweights and iPhones as mere tools of human design and human use. To use them is to cause them to exist as fully and properly as they can. But according to Martin Heidegger, when a tool such as a paperweight is used, it disappears, or withdraws ( Entzug ). We are preoccupied with copying the page that the paperweight is holding down. We are concerned with an essay deadline, and the paperweight simply disappears into this general project. If the paperweight slips, or if the iPhone freezes, we might notice it. All of a sudden it becomes vorhanden (present-at-hand) rather than zuhanden (ready-to-hand).5 Yet Heidegger is unable to draw a meaningful distinction between what happens to a paperweight when it slips from the book I'm copying from and what happens to the paperweight when it presses on the still resilient pages of the thick paperback itself. Further still and related to this point, even when I am using the paperweight as part of some general task, I am not using the entirety of the paperweight as such. My project itself selects a thin slice of paperweight-being for the purposes of holding down a book. Even when it is zuhanden the paperweight is withdrawn. Graham Harman is the architect of this way of thinking.6 Harman discovered a gigantic coral reef of withdrawn entities beneath the Heideggerian submarine of Da-sein, which itself is operating at an ontological depth way below the choppy surface of philosophy, beset by the winds of epistemology, and infested with the sharks of materialism, idealism, empiricism and most of the other isms that have defined what is and what isn't for the last several hundred years. At a moment when the term ontology was left alone like a piece of well chewed old chewing gum that no one wants to have anything to do with, object-oriented ontology (OOO) has put it back on the table. The coral reef isn't going anywhere and once you have discovered it, you can't un-discover it. And it seems to be teeming with strange facts. The first fact is that the entities in the reef—we call them “objects” somewhat provocatively—constitute all there is: from doughnuts to dogfish to the Dog Star to Dobermans to Snoop Dogg. People, plastic clothes pegs, piranhas and particles are all objects. And they are all pretty much the same, at this depth. There is not much of a distinction between life and non-life (as there isn't in contemporary life science). And there is not much of a distinction between intelligence and non-intelligence (as there is in contemporary artificial intelligence theory). A lot of these distinctions are made by humans, for humans (anthropocentrism). And the concept autonomy has come into play in policing such distinctions. In this essay I shall to try to liberate autonomy for the sake of nonhumans. I shall do so by parsing carefully the title, which is taken from Hakim Bey's work The Temporary Autonomous Zone .8 First we shall explore the term autonomous . Then we shall explore what the full meaning of zone is. Finally, we shall investigate what temporary means. Each of these terms is of great value. An object withdraws from access. This means that its very own parts can't access it. Since an object's parts can't fully express the object, the object is not reducible to its parts. OOO is anti-reductionist. But OOO is also anti-holist. An object can't be reduced to its “whole” either, “reduced upwards” as it were. The whole is not greater than the sum of its parts. So we have a strange irreductionist situation in which an object is reducible neither to its parts nor to its whole. A coral reef is made of coral, fish, seaweed, plankton and so on. But one of these things on its own doesn't embody part of a reef. Yet the reef just is an assemblage of these particular parts. You can't find a coral reef in a parking lot. In this way, the vibrant realness of a reef is kept safe both from its parts and from its whole. Moreover, the reef is safe from being mistaken for a parking lot. Objects can't be reduced to tiny Lego bricks such as atoms that can be reused in other things. Nor can be reduced upwards into instantiations of a global process. A coral reef is an expression of the biosphere or of evolution, yes; but so is this sentence, and we ought to be able to distinguish between coral reefs and sentences in English. The preceding facts go under the heading of undermining . Any attempt to undermine an object—in thought, or with a gun, or with heat, or with the ravages of time or global warming—will not get at the withdrawn essence of the object. By essence is meant something very different from essentialism . This is because essentialism depends upon some aspect of an object that OOO holds to be a mere appearance of that object, an appearance-for some object. This reduction to appearance holds even if that object for which the appearance occurs is the object itself! Even a coral reef can't grasp its essential coral reefness. In essentialism, a superficial appearance is taken for the essence of a thing, or of things in general. In thinking essentialism we may be able to discern another way of avoiding OOO. This is what Harman has christened overmining .? The overminer decides that some things are more real than others: say for example human perception. Then the overminer decides that other things are only granted realness status by somehow coming into the purview of the more real entity. When I measure a photon, when I see a coral reef, it becomes what it is. But when I measure a photon, I never measure the actual photon. Indeed, since at the quantum scale to measure means “to hit with a photon or an electron beam” (or whatever), measurement, perception ( aisthesis ), and doing become the same. What I “see” are deflections, tracks in a diffusion cloud chamber or interference patterns. Far from underwriting a world of pure illusion where the mind is king, quantum theory is one of the very first truly rigorous realisms, thinking its objects as irreducibly resistant to full comprehension, by anything.9 So far we have made objects safe from being swallowed up by larger objects and broken down into smaller objects—undermining. And so far we have made objects safe from being mere projections or reflections of some supervenient entity—overmining. That's quite a degree of autonomy. Everything in the coral reef, from the fish to a single coral lifeform to a tiny plankton, is autonomous. But so is the coral reef itself. So are the heads of the coral, a community of tiny polyps. So is each individual head. Each object is like one of Leibniz's monads, in that each one contains a potentially infinite regress of other objects; and around each object, there is a potentially infinite progress of objects, as numerous multiverse theories are now also arguing. But the infinity, the uncountability, is more radical than Leibniz, since there is nothing stopping a group of objects from being an object, just as a coral reef is something like a society of corals. Each object is “a little world made cunningly” (John Donne).10 We are indeed approaching something like the political valance of autonomy . The existence of an object is irreducibly a matter of coexistence. Objects contain other objects, and are contained “in” other objects. Let us, however, explore further the ramifications of the autonomy of objects. We will see that this mereological approach (based on the study of parts) only gets at part of the astonishing autonomy of things. Yet there are some more things to be said about mereology before we move on. Consider the fact that since objects can't be undermined or overmined, it means that there is strictly no bottom object . There is no object to which all other objects can be reduced, so that we can say everything we want to say about them, hypothetically at least, based on the behavior of the bottom object. The idea that we could is roughly E.O Wilson's theory of consilience .11 Likewise, there is no object from which all things can be produced, no top object . Objects are not emanations from some primordial One or from a prime mover. There might be a god, or gods. Suppose there were. In an OOO universe even a god would not know the essential ins and outs of a piece of coral. Unlike even some forms of atheism, the existence of god (or nonexistence) doesn't matter very much for OOO. If you really want to be an atheist, you might consider giving OOO a spin. If there is no top object and no bottom object, neither is there a middle object . That is, there is no such thing as a space, or time, “in” which objects float. There is no environment distinct from objects. There is no Nature (I capitalize the word to reinforce a sense of its deceptive artificiality). There is no world, if by world we mean a kind of “rope” that connects things together.12 All such connections must be emergent properties of objects themselves. And this of course is well in line with post-Einsteinian physics, in which spacetime just is the product of objects, and which may even be an emergent property of a certain scale of object larger than 10?¹?cm).13 Objects don't sit in a box of space or time. It's the other way around: space and time emanate from objects. How does this happen? OOO tries to produce an explanation from objects themselves. Indeed, the ideal situation would be to rely on just one single object. Otherwise we are stuck with a reality in which objects require other entities to function, which would result in some kind of undermining or overmining. We shall see that we have all the fuel we need “inside” one object to have time and space, and even causality. We shall discover that rather than being some kind of machinery or operating system that underlies objects, causality itself is a phenomenon that floats ontologically “in front of” them. In so doing, we will move from the notion of autonomy and begin approaching a full exploration of the notion of zone , which was promised at the outset of this essay. Since an object is withdrawn, even “from itself,” it is a self-contradictory being. It is itself and not-itself, or in a slightly more expanded version, there is a rift between essence and appearance within an object (as well as “between” them). This rift can't be the same as the clichéd split between substance and accidents , which is the default ontology. On this view, things are like somewhat boring cupcakes with somewhat less boring sugar sprinkles on them of different colors and shapes. But on the OOO view, what is called substance is just another limited slice of an object, a way of apprehending something that is ontologically fathoms deeper. What is called substance and what is called accidence are just on the side of what this essay calls appearance. The rift (Greek, chorismos ) between essence and appearance means that an object presents us with something like what in logic is known as the Liar: some version of the sentence “This sentence is false.” The sentence is true, which means that it is a lie, which means that it is false. Or the sentence is false, which means that it is telling the truth, which means that it is true. Now logic since Aristotle has tried desperately to quarantine such beasts in small backwaters and side streets so that they don't act too provocatively.14 But if OOO holds, then at least one very significant thing in the universe is both itself and not-itself: the object. An object is p ? ¬p. To cope with this fact, we shall need some kind of paraconsistent or even fully dialetheic logic, one that is not allergic to dialetheias (double-truthed things). Yet if we accept that objects are dialetheic, p ? ¬p, we can derive all kinds of things easily from objects. Consider the fact of motion. If objects only occupy one location “in” space at any “one” time, then Zeno's paradoxes will apply to trying to think how an object moves. Yet motion seems like a basic, simple fact of our world. Either everything is just an illusion and nothing really moves at all (Parmenides). Or objects are here and not-here “at the same time.”15 This latter possibility provides the basic setup for all the motion we could wish for. Objects are not “in” time and space. Rather, they “time” (a verb) and “space.” They produce time and space. It would be better to think these verbs as intransitive rather than transitive, in the manner of dance or revolt . They emanate from objects, yet they are not the object. “How can we know the dancer from the dance?” (Yeats).16 The point being, that for there to be a question, there must be a distinction—or there must not be (p ? ¬p).17 It becomes impossible to tell: “What constitutes pretense is that, in the end, you don't know whether it's pretense or not.”18 In this notion of the emergence of time and space from an object we can begin to understand the term zone . Zone can mean belt , something that winds around something else. We talk of temperate zones and war zones. A zone is a place where a certain action is taking place: the zone winds around, it radiates heat, bullets fly, armies are defeated. To speak of an autonomous zone is to speak of a place that a certain political act has carved out of some other entity. Cynically, Tibet is called TAR, the Tibetan Autonomous Region, for this very reason. In this phrase, Region tries to emulate zone : it sounds as if the place has its own rules, but of course, it is very much under the control of China. What action is taking place? “[N]ot something that just is what it is, here and now, without mystery, but something like a quest…a tone on its way calling forth echoes and responses…water seeking its liquidity in the sunlight rippling across the cypresses in the back of the garden.”19 If as suggested earlier there is no functional difference between substance and accidence; if there is no difference between perceiving and doing; if there is no real difference between sentience and non-sentience—then causality itself is a strange, ultimately nonlocal aesthetic phenomenon. A phenomenon, moreover, that emanates from objects themselves, wavering in front of them like the astonishingly beautiful real illusion conjured in this quotation of Alphonso Lingis. Lingis's sentence does what it says, casting a compelling, mysterious spell, the spell of causality, like a demonic force field. A real illusion: if we knew it was an illusion, if it were just an illusion, it would cease to waver. It would not be an illusion at all. We would be in the real of noncontradiction. Since it is like an illusion, we can never be sure: “What constitutes pretense…” A zone is what Lingis calls a level . A zone is not entirely a matter of “free will”: this concept has already beaten down most objects into abject submission. Objects are far more threateningly autonomous, and sensually autonomous, than the Kantian version of autonomy cited in the first paragraph of this essay. A zone is not studiously decided upon by an earnest committee before it goes into action. One of its predominant features is that it is already happening . We find ourselves in it, all of a sudden, in the late afternoon as the shadows lengthen around a city square, giving rise to an uncanny sensation of having been here before. Objects emit zones. Wherever I find myself a zone is already happening, an autonomous zone. It is the nonautonomous zones that are impositions on what is already the case. Or rather, these zones are autonomous zones that exclude and police. They are brittle. Every object is autonomous, but some objects try to maintain themselves through rigidity and brittleness, like (and such as) a police state. Paradoxically, the more rigidly one tries to exclude contradiction, the more virulent become the dialetheias that are possible. I can get around “This sentence is false” by imagining that there are metalanguages that explain what counts as a sentence. Then I can decide that this isn't a real sentence. This is basically Alfred Tarski's strategy, since he invented the notion of metalanguage specifically to cope with dialetheias.20 For example we might claim that sentences such as “This sentence is false” are neither true nor false. But then you can imagine a strengthened version of the Liar such as: “This sentence is not true”; or “This sentence is neither true nor false.” And we can go on adding to the strengthened Liar if the counter-attack tries to build immunity by specifying some fourth thing that a sentence can be besides true, false, and neither true nor false: “This sentence is false, or neither true nor false, or the fourth thing.” And so on.21 It seems as if language becomes more brittle the more it tries to police the Liars of this world. Why? I believe that this increasing brittleness is a symptom of a deep fact about reality. What is this deep fact? Simply that there are objects, that these objects are withdrawn, and that they are walking contradictions. This means indeed that (as Lacan put it) “there is no metalanguage,” since a metalanguage would function as a “middle object” that gave coherency and evenness to the others.22 Since there is no metalanguage, there is no rising above the disturbing illusory play of causality. This may even have political implications: no global critique is therefore possible, and attempts to smooth out or totalize are doomed to fail. To think the zone is to think the notion of temporary , which we shall now begin to discuss in greater detail. The zone is not in time: rather it “times.” But because a zone is an emanation of an object, it is based on a wavering fragility, since objects are p ? ¬p. When an object is born, that means that it has broken free of some other object. An object can be born because it and other objects are fragile. If not, no movement would be possible. Objects contain the seeds of their own destruction, a dialetheic sentence that says something like “This sentence cannot be proved.” Kurt Gödel argues that every true system of propositions contains at least one sentence that the system cannot prove. In order to be true, the system must have a minimum incoherence. To be real, it has to be fragile. Imagine a record player. Now imagine a record called I Cannot Be Played on This Record Player . When you play it on this record player, it produces sympathetic vibrations that cause the record player to shudder apart. No matter how many defense mechanisms you build in, there will always be the possibility of at least one record that destroys the record player.23 That is what being physical is. An object is inherently fragile because it is both itself and not-itself. When the rift between appearance and essence collapses, that is called destruction, ending, death. When an object breaks, several new objects are born. An opera singer sings a loud note in tune with the resonant frequency of a wine glass. (See the movie included below.) The singing is a zone, an autonomous level of intensity, opening a rift between appearance and essence. The glass ripples—for a moment it is nakedly a glass and a not-glass—almost as if it were having an orgasm, a little death. It is caught in the rift of the singing. Then its structure can't handle the coherence of the sound waves, and it breaks. It is incoherence and inconsistency that is the mark of existence, not consistency and noncontradiction. When things break or die, they become coherent. Essence disappears into appearance. I become the memories of friends. A glass becomes a dancing wave. Instantly, there are glass fragments, new temporary autonomous zones. The fragments have broken free from the glass. They are no longer its parts, but emanate their own time and space, becoming perhaps accidental weapons as they bury themselves in my flesh. Thus Hakim Bey's instructions on creating temporary autonomous zones oscillate disturbingly between performance art and politics, circus clowning and revolution. To play with the aesthetic is to play with causality, to rip from the sensual ether emanating from things new regions, new zones. Anarchist politics is the creation of fresh objects in a reality without a top or a bottom object, or for that matter a middle object: Everything in nature is perfectly real including consciousness, there's absolutely nothing to worry about. Not only have the chains of the Law been broken, they never existed; demons never guarded the stars, the Empire never got started, Eros never grew a beard. … There is no becoming, no revolution, no struggle, no path; already you're the monarch of your own skin—your inviolable freedom waits to be completed only by the love of other monarchs: a politics of dream, urgent as the blueness of sky.24 Bey imagines that this is because chaos is a primordial “undifferentiated oneness-of-being.” A Parmenides or a Spinoza or a Laruelle would read this a certain way. Individual objects, or decisions to talk about this rather than that, are just maggot-like things crawling around on the surface of the giant cheese of oneness.25 Yet he also describes chaos as “Primordial uncarved block, sole worshipful monster, inert & spontaneous, more ultraviolet than any mythology.” This image is of an inconsistent object, not of an undifferentiated field. An object, indeed, that can be distinguished from other things. If not, then the first part of The Temporary Autonomous Zone , subtitled “The Broadsheets of Ontological Anarchism,” is a kind of onto-theology. Onto-theology proclaims that some things are more real than others. Bey, however, is writing poetically, and thus ambiguously. We are at liberty to read “undifferentiated oneness-of-being” as something like the irreducibility of a thing to its parts and so forth (undermining and overmining). This certainly seems closer to the language in the following paragraph: “There is no becoming … already you're the monarch of your own skin.”26 On this view, there is no difference between art and politics: “When ugliness, poor design & stupid waste are forced upon you, turn Luddite, throw your shoe in the works, retaliate.” Since Romanticism this has been the war cry of the vanguard artist.27 To say to is to fall prey to the tired axioms of the avant-garde, and we think we know how the game goes. But OOO is not simply a way to advocate “new and improved” versions of this shock-the-bourgeoisie boredom. Bey's text is certainly full enough of that. Rather, since causality as such is aesthetic, and since nonhumans are not that different from humans, the new approach would be to form aesthetic–causal alliances with nonhumans. These alliances would have to resist becoming brittle, whether that brittleness is right wing (authoritarianism) or left wing (the endless maze of critique). No “ism,” especially not the ultimate forms, nihilism and cynicism, is in any sense effective at this point. All forms of brittleness are based on the mistaken assumption that there is a metalanguage and that therefore “Anything you can do, I can do meta.” I will not be listing any approaches here, as Bey does. Such lists and manifestos belong to the vanguardism that no longer works. Why? Not because of some marvelous revolution in human consciousness, but because nonhumans have so successfully impinged upon human social, psychic and aesthetic space. It is the time after the end of the world. That happened in 1945, when a thin layer of radioactive materials was deposited in Earth's crust. Geology now calls it this era the Anthropocene . Ironically, this period, named after humans, is the moment at which even the most thick headed of us make decisive contact with nonhumans, from mercury in our blood to manta rays to magnesium. Richard Dawkins, Pat Robertson and Lady Gaga all have to deal with global warming and mass extinction, somehow. We now live in an Age of Asymmetry marked by a skewed, spiraling relationship between vast knowledge and vast nonhuman things—both become vaster and vaster because of one another and for the same reasons.28 This means that coming up with the perfect attitude or the perfect aesthetic prescription just won't work any more. Even the most hardened anthropocentrist now has to pay through the nose for basic food supplies, and has to use more sunscreen. Whether he knows it or acknowledges it, he is already acting with regard towards nonhumans. There is nothing special to think, no special critique that will get rid of the stains of coexistence. The problem won't fit into the well-established modern boxes, which is why the “mystical,” “spiritual” quality of Bey's prose is welcome. Of course, when I put it this way, you may immediately close off and decide that I am talking about perfect attitudes after all, or something outside of politics, or other ways that the radical left marshals to police its thinking of the nonhuman. Because that is what is really at stake in all this: the nonhuman in its coexistence with the human—bosons, gods, clouds, spirits, lifeforms, experiences, the sunlight rippling across the cypresses. Bey begins to get at this in a Latour litany in the second part of The Temporary Autonomous Zone , “The Assassins”: Pomegranate, mulberry, persimmon, the erotic melancholy of cypresses, membrane-pink shirazi roses, braziers of meccan aloes & benzoin, stiff shafts of ottoman tulips, carpets spread like make-believe gardens on actual lawns—a pavilion set with a mosaic of calligrammes—a willow, a stream with watercress—a fountain crystalled underneath with geometry— the metaphysical scandal of bathing odalisques, of wet brown cupbearers hide-&-seeking in the foliage—“water, greenery, beautiful faces.”29 This will be conveniently dismissed as orientalism. If we're never allowed to escape the crumbling prison of modernity for fear of imperialism there is truly no hope. In a similar way, the fear of anthropocentrism and anthropomorphism is very often staged from a place that just is anthropocentrism .30 Critique turns into ressentiment . An object radiates a zone that is aesthetic and therefore causal. Because objects “time” they are temporary. Not because they exist “in” time that eventually gets the better of them. Their very existence implies the possibility of their non-existence. Since objects are not consistent, they can cease to exist. But nothing, no one, will ever be able to insert a blade between appearance and existence, even thought there is a rift there. Now that's what I call autonomy. NOTES 1. John Cage, Silence: Lectures and Writings (Middletown, CT: Wesleyan University Press, 1973), 96. 2. P. B. Medawar and J. S. Medawar, The Life Science: Current Ideas in Biology (London: Wildwood House, 1977), 8. 3. David DeGrazia, Animal Rights: A Very Short Introduction (Oxford: Oxford University Press, 2002), 5. 4. Antony Colynet, A True History of the Civil Warres in France (London, 1591), 480. 5. Martin Heidegger, Being and Time , tr. Joan Stambaugh (Albany, N.Y: State University of New York Press, 1996) 62–71. 6. Graham Harman, Tool-Being: Heidegger and the Metaphysics of Objects (Peru, IL: Open Court, 2002). 7. Hakim Bey, The Temporary Autonomous Zone (Brooklyn: Autonomedia, 1991). 8. Graham Harman, The Quadruple Object (Ripley: Zero Books, 2011), 7–18. 9. This is not the place to get into an argument about quantum theory, but I have argued that quanta also do not endorse a world that I can't speak about because it is only real when measured. This world is that of the reigning Standard Model proposed by Niels Bohr and challenged by De Broglie and Bohm (and now the cosmologist Valentini, among others). See Timothy Morton, “Here Comes Everything: The Promise of Object-Oriented Ontology,” Qui Parle 19.2 (Spring–Summer, 2011), 163–190. 10. John Donne, Holy Sonnets 15, in The Major Works: Including Songs and Sonnets and Sermons , ed. John Carey (Oxford: Oxford University Press, 2009). 11. Edward O. Wilson, Consilience: The Unity of Knowledge (New York: Knopf, 1998). 12. Martin Heidegger, What Is a Thing? (Washington: Regnery, 1968), 243. 13. Albert Einstein, Relativity: The Special and the General Theory (London: Penguin, 2006); Petr Horava, “Quantum Gravity at a Lifshitz Point,” arXiv:0901.3775v2 [hep-th]. 14. Graham Priest, In Contradiction (Oxford University Press, 2006), passim: the most notable recent quarantine officers have been Tarski, Russell, and Frege. 15. Priest, In Contradiction , 172–181. 16. William Butler Yeats, “Among School Children,” Collected Poems , ed. Richard J. Finneran (New York: Scribner, 1996). 17. Paul de Man, “Semiology and Rhetoric,” Diacritics 3.3 (Autumn, 1973), 27–33 (30). 18. Jacques Lacan, Le seminaire, Livre III: Les psychoses (Paris: Editions de Seuil, 1981), 48. See Slavoj Zizek, The Parallax View (Cambridge, Mass.: MIT Press, 2006), 206. 19. Alphonso Lingis, The Imperative (Bloomington: Indiana University Press, 1998), 29. 20. Priest, In Contradiction , 9–27. 21. See Graham Priest and Francesco Berto, “ Dialetheism ,” The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), ed. Edward N. Zalta. 22. Jacques Lacan, Écrits: A Selection , tr. Alan Sheridan (London: Tavistock, 1977), 311. 23. The analogy can be found at length in Douglas Hofstadter, “Contracrostipunctus,” Gödel, Escher, Bach: An Eternal Golden Braid (New York: Basic Books, 1999), 75–81. 24. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 25. This is closest to the language of François Laruelle in Philosophies of Difference: A Critical Introduction to Non-Philosophy (New York: Continuum, 2011) 179. 26. Bey, “ Chaos: The Broadsheets of Ontological Anarchism ,” Temporary Autonomous Zone . 27. Peter Bürger, Theory of the Avant Garde (Minneapolis: University of Minnesota Press, 1984). 28. For further discussion see Timothy Morton, “From Modernity to the Anthropocene: Ecology and Art in the Age of Asymmetry,” The International Social Science Journal 209 (forthcoming). 29. Bey, “ The Assassins ,” Temporary Autonomous Zone . 30. Timothy Morton, The Ecological Thought (Cambridge, Mass.: Harvard University Press, 2010), 75–76. (shrink)

It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 (...) sets. 4. In the minimal fixed point the totally defined sets (sets weakly defined by formulae all of whose instances are true or false) are precisely the ▵1 1 sets. 5. The closure ordinal for Kripke's construction of the minimal fixed point is ωCK 1. In contrast, we show that under the weak Kleene scheme, depending on the way the Gödel numbering is chosen: 1. There may or may not exist nonparadoxical, ungrounded sentences. 2. The number of fixed points may be any positive finite number, ℵ0, or 2ℵ0 . 3. In the minimal fixed point, the sets that are weakly definable may range from a subclass of the sets 1-1 reducible to the truth set of AR to the Π1 1 sets, including intermediate cases. 4. Similarly, the totally definable sets in the minimal fixed point range from precisely the arithmetical sets up to precisely the ▵1 1 sets. 5. The closure ordinal for the construction of the minimal fixed point may be ω, ωCK 1, or any successor limit ordinal in between. In addition we suggest how one may supplement AR + T with a function symbol interpreted by a certain primitive recursive function so that, irrespective of the choice of the Godel numbering, the resulting language based on the weak Kleene scheme has the five features noted above for the strong Kleene language. (shrink)

Regarding the relation of Plato’s early and middle period dialogues, scholars have been divided to two opposing groups: unitarists and developmentalists. While developmentalists try to prove that there are some noticeable and even fundamental differences between Plato’s early and middle period dialogues, the unitarists assert that there is no essential difference in there. The main goal of this article is to suggest that some of Plato’s ontological as well as epistemological principles change, both radically and fundamentally, between the early and (...) middle period dialogues. Though this is a kind of strengthening the developmentalistic approach corresponding the relation of the early and middle period dialogues, based on the fact that what is to be proved here is a essential development in Plato’ ontology and his epistemology, by expanding the grounds of development to the ontological and epistemological principles, it hints to a more profound development. The fact that the bipolar and split knowledge and being of the early period dialogues give way to the tripartite and bound knowledge and benig of the middle period dialogues indicates the development of the notions of being and knowledge in Plato’s philosophy before the dialogues of the middle period. -/- Keywords Plato; early dialogues; middle dialogues; being; knowledge; development -/- Introduction The differences between two groups of the early and middle period dialogues have always been a matter of dispute. Whereas the developmentalists like Vlastos, Silverman (2002), Teloh (1981), Dancy (2004) and Rickless (2007) think that from the early to the middle dialogues Plato’s philosophy changes, at least in some essential points, the unitarists like Kahn, Cherniss and Shorey believe that there happens no development and the differences must be taken as natural, ignorable and even pedagogic. In his well-known article, Socrates contra Socrates in PLATO, Vlastos lists ten theses of difference between two groups of dialogues. The first group which includes Plato’s early dialogues he divides to 'elenctic' (Apology, Charmides, Crito, Euthyphro, Gorgias, Hippias Minor, Ion, Laches, Protagoras and Republic I) and 'transitional' (Euthydemus, Hippias Major, Lysis, Menexenus and Meno) dialogues. These transitional come after all the elenctic dialogues and before all the dialogues of the second group which compose Plato’s middle period dialogues, including (with Vlastos' chronological order) Cratylus, Phaedo, Symposium, Republic II-X, Phaedrus, Parmenides and Theaetetus (1991, 46-49). Vlastos asserts strictly that his list of differences are 'so diverse in content and method that they contrast as sharply with one another as with any third philosophy you care to mention, beginning with Aristotole’s' (ibid, 46). Vlastos’ list of differences between two Socrateses is considered a view breaking sharply between the early and the middle dialogues. Besides all ten differences between the two Socrateses in Vlastos’ list that can be supportive for our doctrine here, we intend to focus on some ontological as well as epistemological distinctions that have not completely been discussed hitherto. Contrary to the developmentalist theory of Vlastos, unitarian theory of Charles Kahn wishes to eliminate any substantial difference between the early and the middle dialogues. He distinguishes seven 'pre-middle' or 'threshold' dialogues including Laches, Charmides, Euthyphro, Protagoras, Meno, Lysis and Euthydemus from the other Socratic dialogues which he calls 'earliest group' (1996, 41). The threshold dialogues, Kahn thinks, 'embarke upon a sustained project' that is to reach to its climax in the middle period dialogues, namely Phaedo, Symposium and Republic. Believing in that there is no 'fundamental shift'between the early and middle dialogues (ibid, 40), Kahn thinks the Socratic dialogues are just the 'first stage' with a 'deliberate silence' towards the theories of later periods (ibid, 339). One of the reasons of the surprising fact that Plato gives no hint of the metaphysics and epistemology of the Forms in the early dialogues, he thinks, is the pedagogical advantages of aporia. He thinks that Plato 'obscurely', and mostly because of education, hinted to some doctrines and conceptions in his early dialogues and with the aim of clarifying them only in the later ones (ibid, 66). The seven threshold dialogues, Kahn asserts, 'had been designed from the first' to prepare the pupils and readers for the views expounded in the middle period dialogues (ibid, 59-60). To show that the differences of the two Socrateses of the early and middle period dialogue are in their onto-epistemological grounds and thence cannot be explained by a unitaristic view, we try to draw the ontological and epistemological principles of the early dialogues in the first part below in order to show, in the second part, that those principles have been developed in the middle period dialogues. -/- A. The Onto-Epistemologic Principles of the Early Dialogues Socratic dialogues are paradoxical about knowledge because while being knowledge-oriented always searching for knowledge, they deny it and even never discuss it directly. Three elements of Socrates’ way of searching Knowledge throughout the early dialogues, i.e. Socratic 'what is X?' question, his disavowal of knowledge and his elenctic method combined together produce something like a circle which works, more or less, in the same way in these dialogues. Though this circle is an embaressing inquiry always resulting in ignorance instead of knowledge, its motivation is surprisingly Socrates’ passionate enthusiasm for knowledge, an intensive love of wisdom. The starting point of this circle is Socrates’ confession of having no knowledge which might be explicitly asserted or presupposed, maybe because it was one of the famous characteristics of Socrates; a confession always paradoxically accompanied with his intense longing for knowledge (e.g., Gorgias 505e4-5). Every time Socrates encounters with someone who thinks he knows something (οἴεταί τι εἰδέναι) (Apology 21d5) and tries to examine him. This examination seems to be the simplest one asking just what it is that he knows. Socrates’ elenchus, therefore, is always connected with 'what is X?' (τίς ποτέ ἐστιν) question, a question that most of the early dialogues of Plato are concerned with; 'what is courage?' in the Laches, 'what is piety?' in Euthydemus, 'what is temperance?' in Charmides and 'what is beauty?' in Hippias Major. This question we call here 'Socratic question' and probably is the very question the historical Socrates used to employ, is tightly interrelated with both his disavowal and his elenchus. He disclaims knowledge because he cannot find the answer to the question himself and he rejects others’ since they cannot offer the correct answer too. Every interlocutor can claim he knows X, if and only if he can answer the Socratic question. Otherwise, he is more of an ignorant than of a knower of τί ποτέ ἐστι X. Knowing the answer to this question is, thus, knowledge’s criterion for Socrates. Having found out that he cannot answer what it is which he would claim to know, the interlocutor comes to the point Socrates was there at the beginning. The least advantage of this circle is that he becomes as wise as Socrates does about the subject, becoming aware that he does not know it. At the end of the circle they are both still at the beginning, not knowing what X is. So let us first take a glance at these three elements. Socratic disavowal of knowledge is strictly asserted in some passages. At Apology 21b4-5, Socrates says: -/- I do not know of myself being wise at all (οὔτε μέγα οὔτε σμικρὸν σύνοιδα ἐμαυτῷ σοφὸς ὤν) -/- Moreover, at 21d4-6: -/- None of us knows anything worthwhile (καλὸν κἀγαθὸν εἰδέναι) …. I do not know (οἶδα) neither do I think I know. -/- In Charmides Socrates speaks about a fear about his probable mistake of thinking that he knows (εἰδέναι) something when he does not (166d1-2). The somehow generalization of this disavowal can be seen in Gorgias. After calling his disavowal 'an account that is always the same' (509a4-5), Socrates continues (a5-7): -/- I say that I do not know (οἶδα) how these things are, but no one I have ever met, like now, who can say anything else without being absurd. -/- At the end of Hippias Major (304d7-8), Socrates affirms his disavowal of knowledge of 'what is X?' this time about the fine: -/- I do not know (οἶδα) what that is itself (αὐτὸ τοῦτο ὅτι ποτέ ἐστιν). Some other passages, however, made a number of scholars dubious about Socrates’ disavowal. Vlastos mentions Apology 29b6-7 as an evidence : 'that to do wrong and to disobey one’s master, both god and men, I know (οἶδα) to be evil and shameful'. He thinks that if we give this single text 'its full weight' it can suffice to show that Socrates does claim knowledge of a moral truth (1985, 7). Vlastos’ claim is not admittable since it would be too strange, I think, for a man like Socrates to violate his disavowal claim just after emphasizing it. We can see his claim just before the already mentioned passage: -/- And surely it is the most blameworthy ignorance to believe that one knows what one does not know. It is perhaps on this point and in this respect, gentlemen, that I differ from the majority of men and if I were to claim that I am wiser than anyone in anything it world be in this, that, as I have no adequate knowledge (οὐκ εἰδὼς ἱκανῶς) of things in the underworld, so I do not think I have (οὐκ εἰδέναι) (Apology 29b1-6) Vlastos tries to solve what he calls the 'paradox' of Socrates’ disavowal of knowledge distinguishing the 'certain' knowledge from 'elenctic' knowledge (1985, 11) and thinking that when Socrates avows knowledge, we must perceive it as an elenctic knowledge, a knowledge its content 'must be propositions he thinks elenctically justifiable' (ibid, 18). Irwin’s solution is the distinction of knowledge and belief. He approves that Socrates does not 'explicitly' make such a distinction, but still thinks that Socrates’ 'test for knowledge would make it reasonable for him to recognize true belief without knowledge, and his own claims are easily understood if they are claims to true belief alone' (1977, 40). While I agree with Vlastos up to a point, I strongly disagree with Irwin about the early dialogues. As I will try to show below, we are not permitted to consider any kind of distinction within knowledge in Socratic dialogues because only one category of knowledge is alluded to there and the distinction of knowledge and belief thoroughly belongs to the second Sorcates. Although no kind of distinction can be admittable here, I think Vlastos’ distinction can be accepted only if we regard it as a distinction between knowledge, which is unique and without any, even incomparable, rival, and a semi-idiomatic and ordinary one that is a necessary requirement for any argument, and thus, unavoidable even for someone who does not claim any kind of knowledge. An apparent evidence of this is Gorgias 505e6-506a4: -/- I go through the discussion as I think it is (ὡς ἄν μοι δοκῇ ἔχειν), if any of you do not agree with admissions I am making to myself, you must object and refute me. For I do not say what I say as I know (οὐδὲ γάρ τοι ἔγωγε εἰδὼς λέγω ἃ λέγω) but as searching jointly with you (ζητῶ κοινῇ μεθ᾽ ὑμῶν). -/- The minimal degree of knowledge everyone must have to take part in an argument, conduct it and use the phrase "I know" when it is necessary is what Socrates cannot deny. We can call it elenctic knowledge only if we agree that it is not the kind of knowledge that Socrates has always been searching, the one that can be accepted as the answer of Socratic 'what is X?' question. His disavowal of knowledge is applied only to the knowledge which can truly be the answer of Socratic question and pass the elenctic exam; a knowledge that, I believe, is never claimed by first Socrates. Socrates conducts his method of examining his interlocutors’ knowledge, our second element here, by almost the same method repeated in Socratic dialogues. That whether we are allowed to regard all the examinations of Socrates in the early dialogues as based on the same or not has been a matter of dispute. Vlastos himself (1994, 31) distinguished Euthydemas, Lysis, Menexenns and Hippias Major from the other Socratic dialogues because he thinks Socrates has lost his faith to elenchus in there. Irwin (1977, 38) distinguishes Apology and Crito where Socrates’ own convictions is present. Contrary to some scholars like Benson (2002, 107) who take elenchus in all the Socratic dialogues as a unique method, Michelle Carpenter and Ronald M. Polansky (2002, 89-100) argue pro the variety of methods of elenchus. Thomas C. Brickhouse and Nicholas D. Smith (2002, 145-160) even reject such a thing as Socratic elenchus which can gather all of the Socrates’ various arguments under such a heading. There can be no solution for the problem of elenchus, they think, is due to 'the simple reason that there is no such thing as 'the Socratic elenchos"'(p.147). Though we consider elenchus a somehow determined process and a part of Socratic circle in the early dialogues, all we assume is that whatever differences it might have in different dialogues, it has the same onto-epistemological principles and, thus, we are not going to take it necessarily as a unique method. This method sets out to prove that the interlocutors are as ignorant as Socrates himself is. That whether elenchus is constructive, capable of establishing doctrines as Vlastos (1994) or Brickhouse and Smith (1994, 20-21) believe or not is another issue to which this paper is not to claim anything. What is crucial for our discussion here is that elenchus does not reach to the very knowledge Socrates is looking for. This is strictly against Irwin who thinks that not only elenchus leads to positive results, 'it should even yield knowledge to match Socrates’ conditions'(1977, 68, cf. 48). He does not explain where and how they really yield to that kind of knowledge. He explains his elenctic method in his apology in the court (Apology 21-22), that how he used to examine wise men, politicians, poets and all those who had the highest reputation for their knowledge and every time found that they have no knowledge. If we accept, as I strongly do, that Socrates’ disavowal of his knowledge is not irony, it might seem more reasonable to agree that the process that has that disavowal as its first step cannot be irony as well. The key of the circle which can explain why Socrates disclaims knowledge and how he can reject others’ claim of having any kind of knowledge lies in the third element, Socratic question. In Hippias Major (287c1-2), Socrates asks: 'Is it not by Justice that just people are Just? (ἆρ᾽ οὐ δικαιοσύνῃ δίκαιοί εἰσιν οἱ δίκαιοι). He insists at 294b1 that they were searching for that by which (ᾧ) all beautiful things are beautiful (cf. b4-5, 8). At Euthyphro 6d10-11 it is said that the Socratic question is waiting for 'the form itself (αὐτὸ τὸ εἶδος) by which (ᾧ) all the pious actions are pious; and at 6d11-e1: -/- Through one form (που μιᾷ ἰδέᾳ) impious actions are impious and pious actions pious. -/- Since the X itself is that by which X is X, knowing 'X itself' is the only way of knowing X. It is probably because of this that Socrates makes the distinction between the ousia as a right answer to the question and effect as a wrong one: -/- I am afraid, Euthyphro, that when you were asked what piety is (τὸ ὅσιον ὅτι ποτ᾽ ἐστίν) you did not wish to make clear its nature itself (οὐσίαν … αὐτοῦ) to me, but you said some effect (πάθος) about it. (Euthp. 11a6-9) -/- 1. Knowledge of what X is Now it is time to look for the onto-epistemological principles of Socratic circle and its three elements. It cannot reasonably be expected from the first Socrates to present us explicitly and clearly formulated principles of his onto-epistemology when such explications cannot be found even in the second Socrates who has some obviously positive theoris. Since there must be some principles underlying this first systematic inqury of knowledge, we must seek to them and be satisfied with elicitation of the first Socratas’ principle. What will be drawn out as his principles cannot and must not, thus, be taken as very fix and dogmatic principles. Some very slightest principles and grounds suffice for our purposes here. The first principle that is the prima facie significance of the Socratic question and his implementation of all those elenctic arguments I call the principle of 'Knowledge of What X is' (KWX): -/- KWX To know X, it is required to know what X is. -/- Aristotle (Metaphysics 1078b23-25, 27-29, 987b4-8) takes Plato’s τί ἐστι question as seeking the definition of a thing that is the same as historical Socrates’ search but applying to a different field. That Plato’s 'what is X?' question was a search for definition became the prevailed understanding of this question up to now. I am going neither to discuss the answer of Socratic question nor to challenge taking it as definition. What I am to insist is that knowledge is attached firmly to the answer of the question: Knowledge of X is not anything but the knowledge of what X is. It entails, certainly, the priority of this knowledge to any other kind of knowledge about X but it also has something more fundamental about the relation of knowledge and Socratic question. Socrates’ exclusive focus on the answer of his question can authorize the consideration of such an essential role for KWX in his epistemolgoy. The total rejection of his interlocutors’ knowledge when they are unable to answer the question can be regarded as a strong evidence for it. Socrates’ elenctic method and his rejection of others’ knowledge in the early dialogues, which all end aporetically with no one accepted as knower and nothing as knowledge, prevent us from finding any positive evidence for this. We have to be content, therefore, of negative evidences which, I think, can be found wherever Socrates rejects his interlocutors’ knowledge when they are not able to give an acceptable answer to his 'what is X?' question. 2. Bipolar Epistemology Socrates’ rejection of his interlocutors’ knowledge has another epistemological principle as its basis. Let me call this principle Bipolar Epistemology' (BE): BE There is no third way besides knowledge and Ignorance. -/- BE says that about every object of knowledge there are only two subjective statuses: knowledge and Ignorance. Socrates’ disavowal, however, says nothing but that he is ignorant of knowledge of X because he does not know what X is. This means that BE is presupposed here. Socrates’ elenchus and his rejection of interlocutors’ having any kind of knowledge are the necessary results of the fact that he does not let any third way besides knowledge and ignorance. The first Socrates never let anyone partly know X or have a true opinion about it, as he would not let anyone know anything about X when he did not know what X is. -/- 3. Bipolar Ontology The principle of BE in first Socrates’ epistemology is parallel to another principle in his ontology. Plato’s bipolar distinction between being and not being is as strict and perfect as his distinction between knowledge and ignorance. This principle I shall call the principle of 'Bipolar Ontology' (BO): BO Being is and not being is not. BO is apparently the same with the well-known Parmenidean Principle of being and not being (cf. Diels-Kranz (DK) Fr. 2.2-5). Euthydemus’ statement against the possibility of false knowledge can be good evidence for this principle: -/- The things which are not surely do not exist (τὰ δὲ μὴ ὄντα … ἄλλο τι ἢ οὐκ ἔστιν). (Euthydemus 284b3-4) -/- He continues (b4-5): -/- There is nowhere for not being to be there (οὖν οὐδαμοῦ τά γε μὴ ὄντα ὄντα ἐστίν). -/- That BE does not let true opinion as a third option besides knowledge and ignorance seems to be related to BO’s rejecting a third option besides being and not being, which is itself the basis of the impossibility of false belief. Socrates’ elaborate discussion of the problem of false belief in Theatetus that leads to a more decisive discussion and finally to some solutions in Sophist can make our consideration of BO for the first group of dialogues authentive. -/- 4. &5. Split Knowledge and Split Being The fourth principle I shall call the principle of 'Split Knowledge' (SK): -/- SK Knowledge of X is separated from any other knowledge (of anything else) as if the whole knowledge is split to various parts. -/- This Principle is hinted and criticized as Socrates’ way of treating with knowledge in Hippias Major: -/- But Socrates, you do not contemplate the entireties of things, nor do people you have used to talk with (τὰ μὲν ὅλα τῶν πραγμάτων οὐ σκοπεῖς, οὐδ᾽ ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). (301b2-4) -/- Contrary to Rankin who regards the passage as 'antilogical, almost eristic in tone rather than presenting a serious philosophy of being' (1983, 54), I think it can be taken as serious. Hippias criticizes Sorcates that he does not contemplate (σκοπεῖς) the entireties of things (ὅλα τῶν πραγμάτων), a critique which Socrates is not its only subject but all those whom Socrates accustomed to talk with (ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι). This last phrase, I think, extends this critic beyond this dialogue to other Socratic dialogues. Hippias’ use of the perfect tense of the verb ἔθω (to be accustomed) is a good evidence of this extension. We can get, thus, these ἐκεῖνοι as Socrates’ interlocutors in his other dialogues that hints that this criticism has the epistemological groundings of the previous dialogues as its subject. What ἐκεῖνοι οἷς σὺ εἴωθας διαλέγεσθαι points to is that Hippias does not have in mind Socrates’ way of treating things only in this dialogue, but he is also criticizing Socrates’ way throughout his dialogues. At 301b4-5, Socrates and his interlocutors’ way of beholding things is described as such: -/- You people knock (κρούετε) at the fine and each of the beings (ἕκαστον τῶν ὄντων) by taking each being cut up in pieces (κατατέμνοντες) in words (ἐν τοῖς λόγοις). This leads us to our next principle that is parallel to, and the ontological side of, SK, the principle of 'Split Being'(SB): -/- SB Everything (being) is separated from any other thing as if the whole being is split to many beings. -/- Socrates and his interlocutors and thus, as we saw, the Socratic dialogues are accused to regard everything as it is separated from all other things. This separation is en tois logois that, I think, can reasonably be taken as saying that Socratic dialogues (it refers of course to the dialogues before Hippias Major) cut up all things which have the same name/definition from all other things and try to understand them separately, without considering other things that are not in their logos. They, for example in Hippias Major, are cutting up to kalon and try to understand what it and all others inside this logos are by separating it from all other things. This is directed straightly against Socratic question and the way Socratic dialogues follow to find its answer, every time separating one logos. As Meyer (1995, 85) points out, every question 'presupposes that the X in question in a logos is something' and 'every answer to every question aims at unity' (84). The critique of Hippias Major is, therefore, at the same time a critique of SK and SB. It is also a critique of KWX because it is only based on KWX that Socratic dialogues could search for the answer of 'what is X' question supposing that knowing what X is is enough for the knowledge of X. SK and KWX are absolutely interdependent. What Socrates and all his previous interlocutors have neglected in Socratic dialogues, Hippias says, was 'continuous bodies of being' (διανεκῆ σώματα τῆς οὐσίας) (301b6). Either this theory actually belongs to the historical Hippias as it is being said or not, it is strictly criticizing SB. We have the same phrase with changing sūma to logos some lines later at 301e3-4: διανεκεῖ λόγῳ τῆς οὐσίας. Although this theory that can be observed as both an ontological and an epistemological theory is rejected by Socrates (301cff.), it is still against first Socrates’ onto-epistemological principles and might let us look at what is rejected as Socratic prineple. -/- 6. Knowledge is of Being The sixth principle that I think is presupposed by the first Socrates, is the 'Knowledge of Being' Principle (KB): -/- KB Knowledge is of Being. -/- This principle is obviously the source of the problem of false knowledge, a very important problem throughout Plato’s philosophy. We face this problem maybe for the first time in Euthydemus. In less than 20 Stephanus’ pages, 276-295, we are encountered with different interwoven problems about knowledge , all grounded in the problem of false opinion. Having challenged the obvious possibility of telling lies at 283e, at 284 Euthydemus discusses it saying that the man who speaks is speaking about 'one of those things that are (ἓν μὴν κἀκεῖνό γ᾽ ἐστὶν τῶν ὄντων)' (284a3) and thus speaks what is (λέγων τὸ ὄν) (a5). He must necessarily be saying truth when he is speaking what is because he who speaks what is (τὸ ὄν) and the things that are (τὰ ὄντα) speaks truth (τἀληθῆ λέγει) (a5-6). This is based on Parmenidean principle of the impossibility of being of not being which Euthydemus restates (284b3-4) and we mentioned discussing BO principle above. The things that are not are nowhere (οὐδαμοῦ) and there is no possibility for anyone to do (πράξειεν) anything with them because they must be made as being before anything else can be done, which is impossible (b5-7). The words, then, are of things that exist (εἰσὶν ἑκάστῳ τῶν ὄντων λόγοι) (285e9) and as they are (ὡς ἔστιν) (e10). The result is that no one can speak of things as they are not. It is this impossibility of false speach that is extended to thinking (δοξάζειν) at 286d1 and leads to the impossibility of false opinion (ψευδής … δόξα) (286d4). The general conclusion is asserted at 287a extending this impossibility to actions and making any kind of mistake. Not only knowledge is of being but speech, thought and action are of being simply because of the fact that nothing can be of not being. -/- B. First Socrates’ Principles in the Middle Period Dialogues Out of what were presupposed or criticized mostly in five dialogues, Euthyphro, Euthydemus, Hippias Major, Laches and Charmides, we tried to draw the first Socrates’ principles. Our inquiry here is directed to find out the fate of these principles in the three dialogues of the middle period, Meno, Phaedo and Republic. To do this, first we ought to check the situation of Socratic circle in these dialogues. The Socratic circle that was predominant in the early dialogues, does not look like a circle here anymore though they certainly have some features in common. Meno, Phaedo and Republic II-X are not committed to the principles of the circle and the whole circle in disrupted in them. The difference of the two Socrateses towards acquiring knowledge is obvious. The Socrates of Meno, Phaedo and Republic is evidently more self-confident that he can get to some truths during his arguments as he does. They are in their first appearance, as almost all other dialogues, committed to Socrates’ disavowal. All of them try to keep the shape of the Socratikoi Logoi genre, which is committed to the historical Socrates’ way of discussion; a dramatic personage who is to challenge his interlocutors, ask them and refuse the answers. Nevertheless, the fact is that what we have in common between two groups of dialogues is mostly a dramatic structure. Whereas the first group’s arguments are based on Socrates’ disavowal and lead to no positive results, the second group is decisively going to achieve some positive results. The aim of the first Socrates was to show others that they are ignorant of what they thought they knew. The new Socrates of Meno, on the opposite, makes so much efforts to show that the slave boy has within himself true opinions (ἀληθεῖς δόξαι) about the things that he does not know (οἶδε) (85c6-7). Despite his lack of knowledge, he has true opinions nevertheless. The way from these true opinions to knowledge, as Socrates states, is not so long. These true opinions are now like a dream but 'can become knowledge of the same things not less accurate than anyone’s' (οὐδενὸς ἧττον ἀκριβῶς ἐπιστήσεται περὶ τούτων) (c11-d1), if they be repeated by asking the same questions. The most outstanding text regarding Socrates’ disavowal is Meno 98b where he explicitly claims knowledge: -/- And indeed I also speak as (ὡς) one who does not know (εἰδὼς) but is guessing (εἰκάζων). However, [about the fact] that true opinion and knowledge are different, I do not altogether expect (δοκῶ) myself to be guessing (εἰκάζειν), but if I say about anything that I know (εἰδέναι) -which about few things I say- this is one of the things that I know (οἶδα). (98b1-5) This passage is very significant about Plato’s disavowal of knowledge. There can hardly be found, I think, anywhere else in Plato’s corpus where Socrates speaks about his knowledge of something as such. He says first that he speaks as someone who does not know. This ὡς οὐκ εἰδὼς λέγω comparing with what he used to say in the first group, οὐκ οἶδα, has this added ὡς. Socrates does not claim strongly anymore that he does not know anything but speaks only as someone who does not know. He needs this ὡς not only because he is going to accept that he does know some, though few, things immediately after this sentence, but also because he needs his previous disavowal to be loosened from Meno on. He does not merely say here that he knows something. It is then different from the examples mentioned before which could be taken as idiomatic or at least not emphatic. Socrates’ remarkable emphasis on distinguishing εἰδέναι from εἰκάζειν departs it from all other passages where he says only he knows something. Moreover, he claims definitely that he has knowledge about few (ὀλίγα) things. From the early to the middle dialogues, Socrates’ attitude to knowledge has totally renewed its face. He brings forth a new concept, true opinion, and he does not speak of knowledge as he used to before; the rough, perfect and unachievable knowledge of the first group has turned to something more smooth, realistic and achievable. Comparing with the early dialogues that did not set out from the first to reach positive results, the middle ones are extraordinarily and surprisingly positive and hence destroy the basis of the Socratic circle. The questions and answers are purposely directed to some specific new theories; most of them are not directly related to the topics or the main questions of the dialogues. They are suggested when Socrates draws the attention of the interlocutor away from the main question because of the necessity of another discussion. Even if the main question remains unanswered, we have still many positive theories, prominently of metaphysical type. These theories are so abundant and dominant in these dialogues, especially Phaedo and Republic, that one might think that they may appear to be arbitrarily sandwiched in there. This helps dialogues to keep their original Socratic structure while they are suggesting new theories. Hence, the Socratic question of 'what is X?', though is still used to launch the discussion, is loosened and is forgotten for most part of the dialogues. Meno that has first a differently formulated question, 'can virtue be taught?', leads finally to the Socratic question of 'What is virtue?'. Phaedo is dedicated to the demonstration of the immortality of soul and the life after death without having a central Socratic question. The case of Republic is more complicated. The first book, on the one hand, has all the criteria of a Socratic circle: its 'what is justice?' question, Socrates’ strong disavowal (e.g. 337d-e), his rejection of all answers and coming back to the first point without finding out any answer. This Book, considered alone, is a perfect Socratic dialogue, as many scholars regard it as early and separated from other books. The books II-X are, on the other hand, far from implementing a Socratic circle. They have still the 'what is justice?' question as their incentive leading question, but they are, in most of the positive doctrines and methods that encompass the main parts, ignoring the question. Even these books that, I believe, are the farthest discussions from the Socratic circle are so cautious not to break the Socratic structure of the dialogue as long as it is possible. What is changed is not the structure of the dialogue but the ontological and epistemological grounds based on which new theories are suggested. -/- 1. Knowledge of the Good We can clearly see in the second group of dialogues that the KWX principle loses the place it had before in our first group. It is not, of course, rejected, but still we cannot say that it has the same situation. KWX that was based on Socratic question, as we discussed before, was the leading principle of the first Socrates’ epistemology and of the highest position. Other epistemological principles, SK directly and BE indirectly, were relying on Socratic question and therefore on KWX. Such a position does not belong to KWX from Meno on. What makes it different in the second Socrates is another principle that is needed it not only as its complementary principle but also as what is more fundamental. Plato, then, does not reject KWX in this period, but, it seems, he transcends to another more basic principle; a principle we shall call the principle of 'Knowledge of the Good' (KG): -/- KG Knowledge of X requires knowledge of the Good. -/- Whereas all the dialogues of our first group are free from any discuscon about KG, it bears a very important role in the second group so as becomes the superior principle of knowledge in Republic. Trying to solve the problem of teachability of virtue, Socrates says that it can be teachable only if it is a kind of knowledge because nothing can be taught to human beings but knowledge (ἐπιστήμην) (Meno 87c2). The dilemma will be, then, whether virtue is knowledge or not (c11-12) and since virtue is good, we can change the question to: whether is there anything good separate from knowledge (εἰ μέν τί ἐστιν ἀγαθὸν καὶ ἄλλο χωριζόμενον ἐπιστήμης) (d4-5). Therefore, the conclusion will be that if there is nothing good which knowledge does not encompass, virtue can be nothing but knowledge (d6-8). What let us discuss KG as an epistemological principle for the second Secrates is the relation he tries to establish between knowledge and the Good which, though is alongside with the mentioned thesis and the idea of virtue as knowledge, goes much deeper inside epistemology asking to regard the Good as the basis of knowledge. The effort of Phaedo cannot succeed in establishing the Good as the criterion of explanation and knowledge since, I think, it needs a far more complicated ontology of Republic where Socrates can finally announce KG. What is said in Republic is totally compatible with Phaedo 99d–e and the metaphor of watching an eclipse of the sun. In spite of the fact that we do not have adequate knowledge of the Idea of the Good, it is necessary for every kind of knowledge: 'If we do not know it, even if we know all other things, it is of no benefit to us without it' (505a6-7). The problem of our not having sufficient knowledge of the Idea of Good is tried to be solved by the same method of Phaedo 99d-e, that is to say, by looking at what is like instead of looking at thing itself (506d8-e4). It is this solution that leads to the comparison of the Good with sun in the allegory of Sun (508b12-13). What the Good is in the intelligible realm corresponds to what the sun is in the visible realm; as sun is not sight, but is its cause and is seen by it (b9-10), the Good is so regarding knowledge. It has, then, the same role for knowledge that the sun has for sight. Socrates draws our attention to the function of sun in our seeing. The eyes can see everything only in the light of the day being unable to see the same things in the gloom of night (508c4-6). Without the sun, our eyes are dimmed and blind as if they do not have clear vision any longer (c6-7). That the Good must have the same role about knowledge based on the analogy means that it must be considered as a required condition of any kind of knowledge: -/- The soul, then, thinks (νόει) in the same way: whenever it focuses on what is shined upon by truth and being, understands (ἐνόησέν), knows (ἔγνω) and apparently possesses understanding (νοῦν ἔχειν). (508d4-6) -/- Socrates does not use agathon in this paragraph and substitutes it with both aletheia and to on. He links them with the Idea of the Good when he is to assert the conclusion of the analogy: -/- That which gives truth to the objects of knowledge and the power of knowing to the knower, you must say, is the Idea of the Good: being the cause of knowledge and truth (αἰτίαν δ᾽ ἐπιστήμης οὖσαν καὶ ἀληθείας) so far as it is known (ὡς γιγνωσκομένης μὲν διανοοῦ). (508e1-4) Knowledge and truth are called goodlike (ἀγαθοειδῆ) since they are not the same as the Good but more honoured (508e6-509a5). KG, which had been implicitly contemplated and searched in Phaedo, is now explicitly being asserted in Republic. As what was quoted clearly proves, this principle is the very one which we can observe as the most fundamental principle of the second Socrates in Republic, corresponding to the role KWX had in the first Socrates. The Form of the Good in Republic, of which Santas speaks as 'the centerpiece of the canonical Platonism of the middle dialogues, the centerpiece of Plato’s metaphysics, epistemology, ethics and …' (1983, 256) much more can be said. Plato’s Cave allegory in Book VIII dedicates a similar role to the Idea of the Good. The Idea of the Good is there as the last thing to be seen in the knowable realm, something so important that its seeing equals to understanding the fact that it is the cause of all that is correct and beautiful (517b). Producing both light and its source in visible realm, it controls and provides truth and understanding in the intelligible realm (517c). -/- 2. Tripartite Epistemology BE is thoroughy rejected in the second Socrates and substituted by its opposite, the principle of 'Tripartite Epistemolgy' (TE): -/- TE Opinion is an epistemological status between knowledge and ignorance. BE of the first Socrates was denying any third way besides knowledge and ignorance which was the foundation of Socratic circle without which Socrates could not reject his interlocutors’ possessing any kind of knowledge. We cannot say, however, that the first Socrates had a third epistemological status in mind but rejected it. Such a status was unacceptable for him so that one can say that he would reject any kind of such status if suggested. There were only two possibilities about knowledge: either one knows something or he does not know it. TE, thus, was not the first Socrates’ discovery and, I think it is not the second Socrates’discovery. All we can see in our second group of dialouges is that he uses this principle as an already demonstrated one. Having examined the slave boy in Meno for the prupose of showing the working of recollection, it truns out that he has some opinions in him while he still does not know. Without trying to prove it, Socrates takes this as the distinction between knowledge and opinion: -/- So, he who does not know (οὐκ εἰδότι) about what he does not know (περὶ ὧν ἂν μὴ εἰδῇ) has within himself true opinions (ἀληθεῖς δόξαι) about the same things he did not know (περὶ τούτων ὧν οὐκ οἶδε) (85c6-7). -/- The same distinction is set between ὀρθὴν δόξαν and ἐπιστήμην at 97b5-6 ff. (also cf. 97b1-2: ὀρθῶς μὲν δοξάζων … ἐπιστάμενος). He connects then their difference to the myth of Daedalus, the statue that would run away and escape. So are true opinions, not willing to remain long in mind and thus not worthy until one ties them down by αἰτίας λογισμῷ (98a3-4). Socrates says that this tying down is anamnesis. We face, in Phaedo, the same relation is settled between knowledge as the process of being tied down and getting the capability to give an account, on the one hand, and anamnesis, on the other hand. When a man knows, he must be able to give an account of what he knows (Phaedo 76b5-6) and since not all people are able to give such an account, those who recollect, recollect what once they learned (76c4). Although the distinction between knowledge and opinion is not explicitly used in Phaedo, referring to the parallel link between knowledge plus account and anamnesis in Phaedo and Meno, one can say that those who cannot recollect are not able to give account and, thus, are in a state of opinion. What is said at Phaedo 84a, though not yet a definite distinction between knowledge and opinion, makes a distinction between their objects so as we can agree that it is presupposed. The soul of the philosopher, Socrates says, follows reason, stays with it forever and contemplates the divine, which is not the object of opinoin (ἀδόξαστον) (84a8, cf. Meno 98b2-5). The distinction of knowledge and belief in Republic has a significant difference with what we discussed in Meno and Phaedo since the distinction of Meno was based on anamnesis and thus more an epistemological distinction. Even in Phaedo that we do not have any elaborate discussion about the distinction, the only hint to the matter at 76 is bound to the theory of anamnesis. In addition to the relation of the distinction with this theory, there is another evidence that does not permit us to consider the distinction as an ontological distinction. Let’s see Meno 85c6-7: -/- So, he who does not know about what he does not know has within himself true opinions about the same things he did not know (τῷ οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ ἔνεισιν ἀληθεῖς δόξαι περὶ τούτων ὧν οὐκ οἶδε). (85c6-7) -/- This last sentence persists that the objects of knowledge and true opinion are the same. What Socrates is to say here is that whereas he does not know X he has true opinion about the same X. I think Socrates’ sentence that the slave boy οὐκ εἰδότι ἄρα περὶ ὧν ἂν μὴ εἰδῇ and his restatement of it by saying περὶ τούτων ὧν οὐκ οἶδε is because he wants to emphasize that the slave boy who does not know, has true opinion about the same thing. Socrates could say this just with using τούτων and there would be no necessity to bring περὶ ὧν ἂν μὴ εἰδῇ for οὐκ εἰδότι if he did not want to emphasize. -/- 3. Tripartite Ontology The distinction between knowledge and true opinion in Republic, on other side, has nothing to do with recollection, but is based on an ontological principle, 'Tripartite Ontology' (TO): -/- TO There are things that both are and are not. -/- This principle I confine, among our three dialogues of the second group, to Republic not extended to Meno and Phaedo, is obviously the opposite of BO. Speaking about the lovers of sights and sounds in the fifth book, Socrates distinguishes them from philosophers because their thought is unable to understand the nature of beautiful itself besides beautiful things (476a6-8) and hence they can only have opinions. The philosopher who, on the contrary, believes in beautiful itself and can distinguish it from beautiful things (476c9-d3), has knowledge because he knows, contrasting others who have opinion because they only opine (d5-6). Since those whose knowledge were degraded as opinion will complain about Socrates’ such calling their thought, he provides them the following argument (476e7-477b1): -/- - Does the person who knows, knows (γιγνώσκει) something (τὶ) or nothing (οὐδέν)? - He knows something (τί). - Something that is (ὂν) or is not (οὐκ ὄν)? - Something that is (ὂν) for how could something that is not be known (πῶς γὰρ ἂν μὴ ὄν γέ τι γνωσθείη)? - Then we have an adequate grasp of this: No matter how many ways we examine it, what completely is (παντελῶς ὂν) is completely knowable (παντελῶς γνωστόν) and what is in no way (μὴ ὂν δὲ μηδαμῇ) is in every way unknowable (πάντῃ ἄγνωστον). - A most adequate one. - Good. Now, if anything is such as to be and also not to be (ὡς εἶναί τε καὶ μὴ εἶναι), won’t it be intermediate (μεταξὺ) between what purely is (εἰλικρινῶς ὄντος) and what in no way is (μηδαμῇ ὄντος)? - Yes, it’s intermediate. - Then as knowledge (γνῶσις) is set over what is (τῷ ὄντι), while ignorance (ἀγνωσία) is of necessity set over what is not (μὴ ὄντι) mustn’t we find an intermediate between ignorance (ἀγνοίας) and knowledge (ἐπιστήμης) to be set over the intermediate, if there is such a thing? -/- From the third status of being we must reach to the third status of knowledge. The simple reading of this text can be an existential reading, taking the "is" of the mentioned sentences as existence. The problem is that when it is said that there is something that both is and is not reading "is" existentially, it sounds too bizarre to be acceptable. It cannot easily be understandable to have something as both existent and non-existent at the same time. This problem arose so many debates and led many scholars to reject the existential reading of "is" and suggest some other readings like predicative or veridical readings. I think though Plato’s complicated ontology of Republic cannot be correctly understood by a simple existential reading, this "is" cannot be free from existential sense of being and, thus, cannot be reduced to just a predicative or veridical sense of being. -/- 4. Bound Knowledges In addition to KG, the Good is also the basis of another principle in the second Socrates, namely the principle of 'Bound Knowledge' (BK): -/- BK Knowledge of everything is bound to the knowledge of the Good. -/- We distinguished BK from KG because we want to insist, in BK, on what had not been insisted upon in KG, that is, the binding role that the Good plays in the second Socrates, contrasting the absence of such a role in the first Socrates. Socrates remembers, in Phaedo, his wonderful keen on natural philosophers' wisdom when he was young. The origin of this enthusiasm was Socrates’ hope to know the cause of everything as they used to claim. When he was searching the matters of his interest on their basis, Socrates says, he became convinced he can get no acceptable answer from them and found himself blind even to the things he thought he knew before. One day he hears Anaxagoras’ theory that 'it is Mind that arranges and is the cause of everything (ὡς ἄρα νοῦς ἐστιν ὁ διακοσμῶν τε καὶ πάντων αἴτιος)' (Phd. 97c1-2 cf. DK, Fr.15.8-9, 11-12, 12-14) and thinks that he can finally find what he has always expected, i.e. something which can explain all things. What I intend to show here is that what makes Socrates hopeful is that Anaxagoras’ theory tries 1) to explain all things by one thing and 2) this explanation is understood by Socrates as if it is based on the concept of the Good. That Socrates was searching for one explanation for all things can be proved even from what he has been expecting from natural philosophers. The case is, nonetheless, more clearly asserted when he speaks about Anaxagoras’ theory. In addition to διακοσμῶν τε καὶ πάντων αἴτιος of 97c2 mentioned above, we have τὸ τὸν νοῦν εἶναι πάντων αἴτιον (c3-4) and τόν γε νοῦν κοσμοῦντα πάντα κοσμεῖν (c4-5) all emphasizing on the cause of all things (πάντα) which can clearly prove that one of the reasons which caused Socrates to embrace it delightfully was its claim to provide the cause of all things by one thing. Another reason was that Anaxagoras’ Mind, at least in Socrates’ view, was attempting to explain everything by the concept of the Good. This connection between Mind and Good belongs more to the essential relation they have in Socrates’ thinking than Anaxagoras’ theory because there are almost nothing about such a relation in Anaxagoras. The reason for Socrates’ reading can be that Mind is substantially compatible with Socrates’ idea of the relation between good and knowledge. Both the thesis 'no one does wrong willingly' and the theory of virtue as knowledge we pointed to above are evidences of this essential relation. Nobody who knows that something is bad can choose or do it as bad. The reason, when it is reason, that means when it is as it should be, when it is wise or when it knows, works only based on good-choosing. In this context, when Socrates hears that Mind is considered as the cause of everything, it sounds to him like this: good should be regarded as the basis of the explanation of all things. We see him, thus, passing from the former to the latter without any proof. This is done in the second sentence after introducing Mind: -/- I thought that if this were so, the arranging Mind would arrange all things and put each thing in the way that was Best (ὅπῃ ἂν βέλτιστα ἔχῃ). If one then wished to find the cause of each thing by which it either perishes or exists, one needs to find what is the best way (βέλτιστον αὐτῷ ἐστιν) for it to be, or to be acted upon, or to act. On these premises then it befitted a man to investigate only, about this and other things, what is the most excellent (ἄριστον) and best (βέλτιστον). The same man must inevitably also know what is worse (χεῖρον), for that is part of the same knowledge. (97c4-d5) This passage is a good evidence of Socrates’ leap from Anaxagoras’ Mind to his own concept of the Good that can explain why Socrates found Anaxagoras theory after his own heart (97d7). Mind is welcomed because of its capability for explanation on the basis of good to 'explain why it is so of necessity, saying which is better (ἄμεινον), and that it was better (ἄμεινον) to be so' (97e1-3). What Socrates thought he had found in Anaxagoras can indicate what he had been expecting from natural scientists before. Socrates could not be satisfied with their explanations because they were unable to explain how it is the best for everything to be as it is. It can probably be said, then, that it was the lack of the unifying Good in their explanation that had disappointed him. We must insist that we are discussing what Socrates thought that Anaxagoras’ theory of Mind should have been, not about Anaxagoras’ actual way of using Mind. Phaedo 97c-98b, is not about what Socrates found in Anaxagoras but what he thought he could find in it. On the contrary, it should also be noted that it was not this that was dashed at 98b, but Anaxagoras’ actual way of using Mind. It was Anaxagoras’ fault not to find out how to use such an excellent thesis (98b8-c2, cf. 98e-99b). Socrates gives an example to show how not believing in 'good' as the basis of explanation makes people be wanderers between different unreal explanations of a thing. His words δέον συνδεῖν (binding that binds together) as a description for the Good we chose as the name of BK principle: They do not believe that the truly good and binding binds and holds them together (ὡς ἀληθῶς τὸ ἀγαθὸν καὶ δέον συνδεῖν καὶ συνέχειν οὐδὲν οἴονται). (99c5-6) -/- Having in mind Plato’s well-known analogy of the sun and the Good at Republic 508-509, we can dare to say that his warning of the danger of seeing the truth directly like one watching an eclipse of the sun in Phaedo (99d-e) is more about the difficulty of so-called good-based explanation than its insufficiency, a difficulty which is precisely confirmed in Republic (504e-505a, 506d-e). Moreover, BK is asserted in a more explicit way in the Republic, where the Good is considered not only as a condition for the knowledge of X, as was noted above discussing KG, but also as what binds all the objects of knowledge and also the soul in its knowing them. At Republic VI, 508e1-3, when Socrates says that the Form of the Good 'gives truth to the things known and the power to know to the knower (τοῦτο τοίνυν τὸ τὴν ἀλήθειαν παρέχον τοῖς γιγνωσκομένοις καὶ τῷ γιγνώσκοντι τὴν δύναμιν ἀποδιδὸν)', he wants to set the Good at the highest point of his epistemological structure by which all the elements of this structure are bound. This binding aspect of the Good is by no means a simple binding of all knowledges or all the objects of knowledge, but the most complicated kind of binding as it is expected from the author of the Republic. The kind of unity the Good gives to the different knowledges of different things is comparable with the unity which each Form gives to its participants in Republic: as all the participants of a Form are united by referring to the ideas, all different kinds of knowledge are united by referring to the Good. If we observe Aristotle's assertion that for Plato and the believers of Forms, the causative relation of the One with the Forms is the same as that of the Forms with particulars (e.g. Metaphysics 988a10-11, 988b4), that is to say the One is the essence (e.g., ibid, 988a10-11: τοῦ τί ἐστὶν, 988b4-6: τὸ τί ἢν εἶναί) of the Forms besides his statement that for them One is the Good (e.g., ibid, 988b11-13) the relation between the Good and unity may become more understandable. Since the quiddity of the Good (τί ποτ᾽ ἐστὶ τἀγαθὸν) is more than discussion (506d8-e2), we cannot await Socrates to tell us how this binding role is played. All we can expect is to hear from him an analogy by which this unifying role is envisaged, the sun. The kind of unity that the Good gives to the knowledge and its objects in the intelligible realm is comparable to the unity that the sun gives to the sight and its objects in the visible realm (508b-c). The allegory of Line (Republic VI, 509d-511), like that of the Sun, tries to bind all various kinds of knowledges. The hierarchical model of the Line which encompasses all kinds of knowledge from imagination to understanding can clearly be considered as Plato’s effort to bind all kinds of knowledges by a certain unhypothetical principle. The method of hypothesis starts, in the first subsection of the intelligible realm, with a hypothesis that is not directed firstly to a principle but a conclusion (510b4-6). It proceeds, in the other subsection, to a 'principle which is not a hypothesis' (b7) and is called the 'unhypothetical principle of all things' (ἀνυποθέτου ἐπὶ τὴν τοῦ παντὸς ἀρχὴν) (511b6-7). This παντὸς must refer not only to the objects of the intelligible realm but to the sensible objects as well. Plato does posit, therefore, an epistemological principle for all things, a principle that all things are, epistemologically, bound and, thus, unified by. -/- 5. Bound Beings The ontological aspect of BK we shall call the principle of 'Bound Beings' (BB): -/- BB Being of all things are bound by the Good. -/- We saw in our principle of Split Being (SB) how the first Socrates was criticized because of his approach to split being and separate each thing from other things. The principle of Bound Beings intends to make the things more related, a duty which is done again by the Good. In the allegory of Sun, there are two paragraphs that evidently and deliberately extend the binding role of the Good to the ontological scene: -/- You will say that the sun not only makes the visible things have the ability of being seen but also coming to be, growth and nourishment. (509b2-4) -/- This clearly intends to remind the ontological role the sun plays in bringing to being all the sensible things in order to display how its counterpart has the same role in the intelligible realm (b6-10): -/- Not only the objects of knowledge (γιγνωσκομένοις) owe their being known (γιγνώσκεσθαι) to the Good, but also their existence (τὸ εἶναί) and their being (οὐσίαν) are due to it, though the Good is not being but superior to it in rank and power. That the Good is here represented as responsible for being of things in addition to their being known means, in my opinion, that Plato wants to posit BB in addition to BK. The allegory of Cave at the very beginning of the seventh Book (514aff.) can be taken as another evidence. The role of the Good, one might say, is confined to the intelligible realm because it is asserted that the role the Good plays in this realm is corresponding to that of the sun in the visible realm. The fact that Plato wants to observe the Good also as the ontological cause of the sensible things is obvious from his saying, in the allegory of Cave, that the Form of the Good 'produces light and its source (τὸν τούτου κύριον) [i.e. the sun] in the visible realm' (517c3). We can conclude, then, that the ontological function of the Good is not confined to the intelligible realm in which it is the lord and provides truth and understanding (c3-4) because it is also responsible to produce τὸν κύριον of light. 6. Proportionality of Being and Knowledge Insofaras BE and BO principles of the first Socrates gave way to TE and TO principles of the second Socrates, we cannot expect him to preserve KB in the same way as it was in the first Socrates. The new tripartite ontology and epistemology necessitates some modifications in KB which results in the principle of 'Proportionality of Being and Knowledge' (PBK): -/- PBK To every class of being there is a proportionate category of knowledge. -/- This principle, of course, does not entail the refutation of KB and thus is not kind of rejecting PBK but only a more complicated version of it. Based on PBK, we can still agree that knowledge is of being (KB) but the issue is that since none of the concepts of knowledge and being in the second Socrates are as simple as they were for the first Socrates, we need a more complicated principle for their relation here. Although from Meno 97a where the distinction of knowledge and true opinion is drawn out in the second group of the dialogues, we can expect a new relation, it is articulated in its most complete way in Republic and specifically in the allegory of Line. All the beings are divided there hierarchically to four classes, to each of them belongs a class of knowledge: imagination to images, belief to the sensible things (more correctly: the things of which they[in previous class] were images (ᾧ τοῦτο ἔοικεν)), thought to mathematical objects (?) and understanding to the Forms and the first principle. The degree of clarity that each of the classes of knowledge shares in (σαφηνείας ἡγησάμενος μετέχειν) is proportionate to the degree that its object shares in truth (ἀληθείας μετέχει). (511e2-4) -/- Conclusion From the six onto-epistemilogical principles of the first Socrates, four principles turn to their opposite in the middle period dialogues. While bipolar epistemology and ontology of the early dialogues give place to tripartite epistemology in the middle period dialogues and tripartite ontology in Republic, the split knowledge and being of the first Socrates are inclined to be substituted by bound knowledges and bound beings in the second Socrates and specifically in Republic. Not all our system of principles in this article is necessarily determinative. Either they are rightly formulated or not, our result would not be vulnerable if we accept that 1) making the distinction of knowledge and belief, 2) accepting the being of not being and 3) trying to bind both being and knowledge by the concept of the Good happens only in middle period dialogues, having been absent in the early ones. These are the favourite results all those somehow arbitrary and even oversimplified principles were to illustrate; that there is kind of a development in the epistemological as well as the ontological grounds of Plato’s philosophy. -/- Notes . (shrink)

This paper aims to suggest a new approach to Plato’s theory of being in Republic V and Sophist based on the notion of difference and the being of a copy. To understand Plato’s ontology in these two dialogues we are going to suggest a theory we call Pollachos Esti; a name we took from Aristotle’s pollachos legetai both to remind the similarities of the two structures and to reach a consistent view of Plato’s ontology. Based on this theory, when Plato (...) says that something both is and is not, he is applying difference on being which is interpreted here as saying, borrowing Aristotle’s terminology, 'is is (esti) in different senses'. I hope this paper can show how Pollachos Esti can bring forth not only a new approach to Plato’s ontology in Sophist and Republic but also a different approach to being in general. -/- Keywords Plato; being; difference; image; pollachos esti; pollachos legetai 1. Being, Not-Being and Difference The three dialogues where the notion of "difference" attaches to the notion of being, namely Parmenides II, Sophist and Timaeus,and specifically the first two we try to discuss here. In these dialogues, Plato is going to achieve a new and revolutionary understanding of being which is not anymore based on the notion of "same" as it was before in Greek ontology. It was his discovery, I think, that the notion of being in the Greek ontology is attached to the notion of the "same" and it is because of this attachment that there have always been many problems understanding being especially after Parmenides. That being has always been relying on the "same" can be found out from the way most of the Presocratics understood it. It was based on such a relationship between being and "same" that a later Ionian, Heraclitus of Ephesus, rejected Being by rejecting its sameness: unable to be the same, being cannot be being anymore but becoming. Heraclitus’ criticism of his predecessors’ understanding of being was due to his discovery that what they call being is not the same but different in every moment. The relation of being and sameness reaches to its highest point in Parmenides. What Plato does in using the "difference" is nothing but the establishment of a creative relation between being and "difference". In this new relation, although he is in agreement with Heraclitus that being is not the same but different, he does not do it by use of becoming. He disagrees, on the other hand, with Parmenides that such a relation between being and difference leads to not being. At Parmenides 142b5-6 it is said that if One is, it is not possible for it to be without partaking (μετέχειν) of being (οὐσίας), which leads to the distinction of being and one: -/- So there would be also the being of the one (ἡ οὐσία του̑ ἑνὸς) which is not the same (ταὐτὸν) as the one. Otherwise, it wouldn’t be its being, nor the one would partake of it. (142b7-c1) -/- The fact that what is (ἔστι) signifies (σημαῖνον) is other (ἀλλο) than what One signifies (c4-5), is being taken as a reason for their distinction. The conclusion is that when we say 'one is', we speak of two different things, one partaking of the other (c5-7). Having repeated these arguments of the otherness of being and one at 143a-b, Parmenides says that the cause of this otherness can be neither Being nor One but "difference": -/- So if being is something different (ἕτερον) and one something different (ἕτερον), it is not by being one that the one is different from being nor by its being being that being is other than one, but they are different from each other (ἕτερα ἀλλήλων) by difference (τῷ ἑτερῳ) and otherness (ἄλλῳ). (143b3-6) -/- The fifth hypothesis, 'one is not' (160b5ff.) is also linked with the notion of difference. When we say about two things, largeness and smallness, that they are not, it is clear that we are talking about not being of different (ἕτερον) things (160c2-4). When it is said that something is not, besides the fact that there must be knowledge of that thing, we can say that it entails also its difference: 'difference in kind pertains to it in addition to knowledge' (160d8). Parmenides explains the reason as such: -/- For someone doesn’t speak of the difference in kind of the others when he says that the one is different from the others, but of that thing’s own difference in kind. (160e1-2) -/- Although the theory of being as "difference" is not fulfilled yet, an exact look at what occurs in Sophist can make us sure that this was the launching step for "difference" to get its deserved role in Plato’s ontology. The notion of the "difference" is not yet well-functioned in Parmenides because we can see that being is still attached to the same: -/- For that which is the same is being (ὄν γὰρ ἐστι τὸ ταὐτόν) (162d2-3). -/- The notion of difference in Sophist is the key element based on which a new understanding of being is presented and the problem of not being is somehow resolved. The friends of Forms, the Stranger says, are those who distinguish between being and becoming (248a7-8) and believe that we deal with the latter with our body and through perception while with the former, the real being (ὄντως οὐσίαν) with our soul and through reasoning (a10-11). Being is then bound with the "same" by adding: -/- You say that being always stays the same and in the same state (ἣν ἀεὶ κατὰ ταὐτὰ ὡσαύτως ἔχειν) but becoming varies from one time to another (δὲ ἄλλοτε ἄλλως). (248a12-13) -/- That the theory of the relation of being and capacity (247d8f., 248c4-5) matches more with becoming than with being (248c7-9) must be rejected because being is also the subject of knowledge which is kind of doing something (248d-e). It does, however, confirm that 'both that which changes and also change have to be admitted as existing things (ὄντα) (249b2-3). I believe that this is what Socrates would incline to do at Theaetetus 180e-181a, that is, putting a fight between two parties of Parmenidean being and Heraclitean becoming and then escaping. The solution is that becoming is itself a kind of being and we ought to accept what changes as being. This is what must be done by a philosopher, namely, to refuse both the claim that 'everything is at rest' and that 'being changes in every way' and beg, like a child, for both and say being (τὸὄν) is both the unchanging and that which changes (249c10-d4). This kind of begging for both is obviously under the attack of contradiction (249e-250b). For both and each of rest and change similarly are (250a11-12) but it cannot be said either that both of them change or both of them rest, being must be considered as a third thing both of the rest and change associate with (250b7-10). The conclusion is that 'being is not both change and rest but different (ἕτερον) from them instead' (c3-4). The notion of difference helps Plato to take being departed from both rest and change because it was their sophisticated relation with being that made the opposition of being and becoming. Plato is now trying to separate being from rest and, thus, from "same" by "difference". Such a crucial change is great enough to need a 'fearless' decision (256d5-6). The possibility of being of not being is resulted (d11-12) comes as the answer to the question 'so it’s clear that change is not being and also is being (ἡ κίνησις ὄντως οὐκ ὄν ἐστι καὶ ὄν) since it partakes in being?' (d8-9). It is then by the notion of difference that becoming is considered as that which both is and is not. This coincidence of being and not being about change is apparently similar to Socrates’ paradoxical statement at Republic 477a about what both is and is not. -/- Introduction The Republic 476-477 has always been a matter of controversy mainly about two interwoven points. The first problem is the meaning of being here; that whether what he has in mind is a veridical, existential or propositional sense of being. The second problem is his distinction between the objects of knowledge and opinion which seems to lead, some believe, to the Two Worlds (TW) theory. The crucial point in Republic is that what is considered between knowledge (ἐπιστήμης) and ignorance (α͗γνοιας), namely opinion, must have a different object that leads Socrates to draw the distinction of knowledge and opinion between their objects. The problem of understanding being in the fifth book of the Republic is that when it is said that the Form of F is F but a particular participating in F, both is and is not F, it sounds too bizarre and unacceptable. It cannot be imaginable how a thing can be existent and non-existent at the same time. At the first sight, the only solution seems to be the degrees of existence which is called by Annas (1981, 197) a 'childish fallacy' and a 'silly argument'. Kirwan (1974, 118) thinks that Republic V does not attribute 'any doctrine about existence' to Plato and Kahn (1966, 250) claims that the most fundamental value of einai when used alone (without predicate) is not "to exist" but "to be so", "to be the case" or "to be true". The problems of understanding being in Republic and Sophist besides the difficulties of the existential reading led scholars to the other senses of being, mostly related to the well-known Aristotelian distinctions between different senses of being. In the predicative reading, Annas, for example, refers this difference to the qualified and unqualified application. Whereas the Form of F is unqualifiedly F, a particular instance of F can be F only qualifiedly (1981, 221). Vlastos’ well-known substitution of 'degrees of reality' for 'degrees of being/existence' must be categorized as a predicative reading. Kahn thinks that the basic sense of being for Plato is 'something like propositional structure, involving both predication and truth claims, together with existence for the subject of predication' (2013, 96). Believing that the complete-incomplete distinction terminology is misleading about Plato, he thinks that semantic functions are only second-order uses of the verb and it is the predicative or incomplete function which is fundamental. Suggesting a veridical reading, Fine (2003, 70 ff) thinks that while both existential and predicative readings separate the objects of knowledge and belief, it is only her reading which does not force such separation of the objects and thus does not imply TW. Stokes (1998, 266) thinks that though Fine is right saying that Plato does not endorse TW in book V, she is wrong in rejecting existential in favor of the veridical reading. The reception of existential reading can be seen more obviously in Calvert who thinks, in agreement with Runciman, that 'it would be safer to say that Plato’s gradational ontology is probably not entirely free from degrees of existence' (1970, 46). At Sophist 254d-e Plato singles out five most important kinds (or Forms!?) in which the same (ταὐτὸν) and difference (θάτερον) are regarded besides being, rest and change. They are, therefore, neither the same nor the difference but share in both (b3). Being (τὸ ὄν) cannot be the same also because if they 'do not signify distinct things' both change and rest will have the same label when we say they are (255b11-c1). We have then four distinct kinds, being, change, rest and same, none of them is the other. The case of difference is more complicated. When the stranger wants to assess the relation of being and difference, he can say simply neither that they are distinct nor that they are not. He has to make an important distinction inside being to get able to draw the relation of being and difference: -/- But I think you'll admit that some of the things that are (τῶν ὄντων) are said (λέγεσθαι) by themselves (αὐτὰ καθ’ αὑτά) but some [are said] always referring to (πρὸς) other things (ἄλλα) (255b12-13) -/- The difference is always said referring to other things (τὸδέγ’ ἕτερον ἀεὶ πρὸς ἕτερον) (255d1). It pervades all kinds because each of them should be different from the others and is so due to the difference and not its own nature (253e3f.) After asserting that change is different from being and therefore both is and is not (256d), the difference is described as what makes all the other kinds not be, by making each different from being. Given that all of them are by being, this association of being and difference is the cause of their being and not-being at the same time, the issue that its version at RepublicV made all those controversies we discussed above: -/- So in the case of change and all the kinds, not being necessarily is (Ἔστιν ἄρα ἐξ ἀναγκης τὸ μὴ ὄν). Τhat’s because as applied to all of them, the nature of the difference (ἡ θατέρον φύσις) makes each of them not be by making it different from being. And we’re going to be right if we say that all of them are not in the same way. And conversely [we’re also going to be right if we say] that they are because they partake in being. (Sophist 256d11-e3) -/- Plato’s new construction of five distinct kinds and the role he gives to thedifference among them is aimed to resolve the old problem of understanding being which has always been annoying from the time of Heraclitus and Parmenides. Both the ontological status of becoming and that of not being were, in Plato’s mind, based on the absolute domination of the notion of the Same over being. Now, not only becoming is understandable as being but also not being which is not the contrary of being anymore but only different (ἕτερον) (257b3-4). Though I agree partly with Frede that the account of not being which is needed for false statements is more complicated than just saying, as Cropsey (1995, 101) says, that Plato is substituting 'X is not Y' with 'X is different from Y', I totally disagree with him that when we say X is not beautiful, Plato could not have thought that it is not a matter of its being different from beautiful because 'it would be different from beauty even if it were beautiful by participation in beauty' (1992, 411). Conversely, as we will discuss, it is exactly the relation of the beautiful thing, X, and the beautiful itself, in which X shares that is to be solved by the notion of not being as difference. Though it is beautiful because of sharing in beauty, X is not beautiful because it is different from beautiful itself. What the difference is to do is to show how something can both be and not be the same thing. The difference is what makes one thing both be and not be a certain other thing. This equips the difference with the ability to explain a certain thing’s not-being when it is. Thanks to the notion of difference, it is now possible to explain not only not being but also the simultaneous being and not being of a thing: 'What we call "not-beautiful" is the thing that ἕτερόν ἐστιν from nothing other than του̑ καλου̑ φύσεως' (257d10-11). The result is that not beautiful happens to be (συμβέβηκεν εἶναι) one single thing among kinds of beings (τι τῶν ὄντων τινὸς ἑνὸς γένους) and at the same time set over against one of the beings (πρός τι τῶν ὄντων αὖ πάλιν ἀντιτεθὲν) (257e2-4) and thus be something that happens to be not beautiful (εἶναί τις συμβαίνει τὸ μὴ καλόν); a being set over against being (ὄντος δὴ πρὸς ὄν ἀντίθεσις) (e6-7). Neither the beautiful is more a being (μα̑λλον ... ἐστι τῶν ὄντων) nor not beautiful less (e9-10) and thus both the contraries similarly are (ὁμοίως εἶναι) (258a1). This conclusion, it is emphasized again (a7-9), owes to θατέρου φύσις now turned out as being. Therefore, each of the many things that are of the nature of the difference and set over each other in being (τῆς τοῦ ὄντος πρὸς ἄλληλα ἀντικειμένων ἀντίθεσις) is being as being itself is being (αὐτοῦ τοῦὄν τοςοὐσία ἐστιν) and not less. They are different from, and not the contrary of, each other (a11-b3). This is exactly τὸμὴὄν, the subject of the inquiry (b6-7). Hence, not being has its own nature (b10) and is one εἶδοςamong the many things that are (b9-c3). Such far departing from Parmenides’ ontological principle is done on the basis of the nature of the difference. It was the discovery of such a notion that made the stranger brave enough to say that not being is each part of the nature of the difference that is set over against being (258d7-e3, cf. 260b7-8). That the relation of being and difference is difference is the key element of the new ontology. The difference is, only because of its sharing in being, but it is not that which it shares in but different from it (259a6-8). Not being is exactly based on this difference: ἕτερον δὲ τοῦ ὄντος ὄν ἔστι σαφέστατα ἐξ ἀνάγκης εἶναι μὴ ὄν (a8-b1). 2. Difference and the Being of a Copy We discussed above that the sense of being of particulars in Republic V made so many debates that whether being is there used in an existential sense or not. Particulars in Republic are regarded as images in the allegories of Line and Cave. The being of an image/copy makes, thus, the same problem. Plato’s analogy of original -copy for the relation of Forms and their particulars in Republic has obviously a different attitude to being. The main question is that what is the ontological status of a copy in respect of its original? Are there two kinds of being, 'real being' versus 'being' as Ketchum says (1980, 140) or only one kind? What is the difference of being in an original and its copy? Is it a matter of degrees of being or reality as some commentators have suggested? Is it a matter of being relational? By reducing the ontological issue to an epistemological one, Vlastos’ suggestion of degrees of reality in an article with the same name does neither, I think, pay attention to the problem nor resolve it. He agrees that Plato never speaks of "degrees" or "grades" of reality (1998, 219). What allows him to entitle it as such are some of Plato’s words in Republic as well as Plato’s words in some other dialogues (1998, 219). When Plato states that the Forms only can completely, purely or perfectly be real he means, Vlastos says, they are cognitively reliable (1998, 229); an obvious reduction of the issue to an epistemological one. He thinks that when in Republic we are being said that a particular’s being F is less pure than its Form, it is because it is not exclusively F, but it is and is not F and this being adulterated by contrary characters is the reason of our confused and uncertain understanding of it (1998, 222). Ketchum rightly criticizes Vlastos’ doctrine in its disparting from ontology thinking that 'to understand Plato’s talk of being as talk of reality is to obscure the close relation that exists between "being" and the verb "to be"' (1980, 213). He thinks, therefore, that οὐσία must be understοοd as being rather than reality, τὸὄν as "that which is" and not "that which is real" and … (ibid). His conclusion is that degrees of reality cannot interpret Plato correctly and we must accept degrees of being. Allen believes that a 'purely epistemic' reading of the passage in Republic is patently at odds with Plato’s text (1961, 325). He thinks that not only degrees of reality but also degrees of reality must be maintained (1998, 67). What Cooper suggests gets close to this paper’s solution: -/- Plato does not I think wish to suggest that existence is a matter of degree in the way in which being pleasant or painful is a matter of degree. Rather there are different grades of ontological status. (1986, 241) -/- A more ontological solution for the problem of understanding the being of a copy and its relation with the being of its original is suggested by the theory of copy as a relational entity. Based on this interpretation, 'the very being of a reflection is relational, wholly dependent upon what is other than itself: the original…' (Allen, 1998, 62). As relational entities, particulars have no independent ontological status; they are purely relational entities which derive their whole character and existence from Forms (ibid, 67). Although these relational entities are and have a kind of existence, we must also say that 'they do not have existence in the way that Forms, things which are fully real, do' (ibid). Allen (1961, 331) extends his theory to Phaedo where it is said that particulars are deficient (74d5-7, 75a2-3, 75b4-8), 'wish' to be like (74d10) or desire to be of its nature (75a2); an extension that, like F.C. white (1977, 200), I cannot admit. He correctly states that Plato did not start out with a doctrine of particulars as images and semblances but come to such a view after Phaedo, or perhaps after Republic V (1977, 202). Though we may not agree with him about Republic V, if we have to consider its last pages also, we must agree with him that not only the ontology of Phaedo but also that of Republic II-V (except the last pages of the latter book) are somehow different from (but at the same time appealing to) the ontology of original-copy which should exclusively assign to Sophist, Timaeus and RepublicVI-VII besides the last pages of book V. The answer to the problem of Plato’s sense of being in RepublicV can be reached only if we read Republic V based on and as following Sophist. We can find out his meaning of that which both is and is not only by the ontological status he assigns to a copy in Sophist. The kind of being of a copy in Sophist reveals as Plato’s key for the lock of the problem of not being. Let’s see how the ontological status of a copy is the critical point of Plato’s ontology. In the earlier pages of Sophist, we are still in the same situation about not being. To think that that which is not is is called a rash assumption (237a3-4) and Parmenides’ principle of the impossibility of being of not being is still at work (a8-9). At 237c1-4, the problem of "not being" is noticed in a new way which shows some kinds of a more realistic position to the problem of not being. Nevertheless, not being is still unthinkable, unsayable, unutterable and unformulable in speech (238c10). Soon after mentioning that it is difficult even to refuse not being (238d), the solution to the problem appears: the being of a copy (εἴδωλον) (239d). A copy is, says Theaetetus, something that is made referring to a true thing (πρὸς τἀληθινὸν) but still is 'another such thing (ἕτεροντοιου̑τον)' (240a8). Nevertheless, this 'another such thing' cannot be another such real or true thing. In answer to the question of the Stranger that if this 'another such thing' is the true thing (240a9), Theaetetus answers: οὐδαμῶς ἀληθινόν γε, ἀλλ’ ἐοικὸςμὲν (240b2). A copy’s being 'another such thing' does not mean another true thing but only a resemblance of it. Not only is not a copy another true thing besides the original, but it is the opposite of the true thing (b5) because only its original is the thing genuinely and being a copy is being the thing only untruly. The word ἐοικὸς is opposed to ὄντως ὄν in the next line (240b7): 'So you are saying that that which is like (ἐοικὸς) is not really that which is (οὐκ ὄντως [οὐκ] ὄν)'. But still a copy 'is in a way (ἔστι γε μήν πως)' (b9). While it is not really what it is its resemblance, it has its own being and reality because it really is a likeness (εἰκων ὄντως) (b11). The Stranger asks: -/- So it is not really what is (οὐκ ὄν ἄρα [οὐκ] ὄντως ἐστὶν) but it really is what we call a likeness (ὄντως ἣν λέγομεν εἰκόνα)? (b12-13) -/- This is Plato’s innovative ontological solution to the problem of not being. Theaetetus’ answer confirms this: 'Maybe that which is not is woven together with that which is' (c1-2). Therefore, a copy neither is what really is nor is not-being but only is what in a way is. Thanks to the ontological status of a copy, the third status intermediate between being and not being is brought forth. The essence of an image, in Kohnke’s words, does not consist 'solely in the negation of what is genuine and has real being' because otherwise 'it would be an ὄντως οὐκ ὄν,essentially and really a not being' (1957, 37). The characteristics of a copy can be summed up as folows: i) A copy is a copy by referring to a true thing (πρὸς τἀληθινὸν). ii) A copy is different from that of which it is a copy (ἕτερον). iii) A copy is not itself a true thing (ἀληθινόν) as that of which it is a copy but only that which is like it (ἐοικὸς). iv) It is not really that which really is (ὄντως ὄν) but only really a likeness (εἰκων ὄντως). The conclusion is that: v) A copy in a way (πως) is that means it both is and in not, the product of interweaving being with not being. This leads to the refutation of father Parmenides’ principle, accepting that 'that which is not somehow is (τό τε μὴ ὄν ὡς ἔστι)' and 'that which is, somehow is not (τό ὄν ὡς οὐκ ἔστι) (241d5-7). Besides copies and likenesses (εἰκόνων), we have also imitations (μιμημάτων) and appearances (φαντασμάτων) as the subjects of this new kind of being and thus false belief (241e3). In Timaeus, the world of becoming which cannot correctly be called and thus we have to call it "what is such" (τὸ τοιου̑τον) (49e5) or "what is altogether such" (τὸ διἀ παντὸς τοιου̑τον) (e6-7), consists solely of imitations (μιμημάτα) (50c5) which are identifiable only by the things that they are their imitations. The word τοιου̑τον which had been used to determine the situation of a copy in respect of its original, now becomes the definition of the world of becoming in which everything is an image of another thing, a Being, that stays always the same and is different and separated from its image. Cherniss, in my view rightly, draws attention to the very important point about the ontological status of an image that can at the same time be considered a criticism of the relational theory. What we are being said in Timaeus, he thinks,cannot be explained by saying that an image is not self-related and making its being relational. What is crucial about an image is that it 'stands for something, refers to something, means something and this meaning the image has not independently as its own but only in reference to something else apart from it' (1998, 296). This function finds its best explanation in the theory we are to suggest in the following. 3. πολλαχῶς ἔστι The best way to understand the ontological status of an image in Plato is to see first how his most clever pupil, Aristotle, resolved the same problem that Plato brought his theory of image for its sake. Aristotle’s theory of pollachos legetai is a brilliant and, at the same time, deviated version of Plato’s theory that is able, however, to help us read Plato in a better way. We discuss Aristotle’s theory to reach to a full understanding of Plato’s theory because it is, firstly, constructed in Aristotle in a more clear way and, secondly, it can also be taken as an evidence that our reading of Plato is legitimate. The phrase τὸ ὄν πολλαχῶς λέγεται, a so much repeated phrase in Aristotle’s works, is his resolution for some of the ontological problems of his predecessors all treating being as if it has only one sense. Aristotle is right in his criticism of the philosophical tradition specially Heraclitus, Parmenides and Plato since all did presuppose only one sense for being and his theory is, thus, a creative and revolutionary solution for many problems that all the past philosophers were stuck in. But it is at the same time somehow a borrowed theory. As we will discuss, both the structure of the doctrine and the problems it tries to resolve are the same as Plato’s doctrine (and even is comparable in its phraseology) though it is in Aristotle, as can be expected, a more clear and better structured doctrine. 1) Associated with the theory of pros hen and the theory of substance, the theory of several senses of being provides a structure which, I insist, is the best guide to understand Plato’s theory of Being in Sophist, Timeaus and Republic. a) Although the theory of pollachos legetai is not necessarily based on the theory of pros hen, they become tightly interdependent about being: -/- Being is said in many ways/senses (τὸ δὲ ὄν λέγεται μὲν πολλαχῶς) but by reference to one (πρὸς ἕν) [way/sense] and one kind of nature (μίαν τινὰ φύσιν). (Metaphysics 1003a33-34) -/- The doctrine of pros hen which is Aristotle’s initiative third alternative besides the homonymous and synonymous application of words, is primarily a linguistic theory that tries to provide a new theory to explain the different implementations of the same word. The pros hen implementation of being is to provide an alternative for the theory of the synonymous (in Plato: homonymous) implementation of being which says being is said in one sense (kath hen) (1060b 32-33). That both the pros hen and the kath hen implementation of a word has one thing (hen) as what is common, makes them in opposition to the homonymous implementation which does not consider anything in common. Whereas both pros hen and kath hen assume a common nature, with which all the implementations of the word have some kind of relation, their difference is that while kath hen takes all the implementations of the word as the same with the common nature, pros hen makes them different. Substance is called πρῶτον ὄν because it is said to be primarily: -/- For as is (τὸ ἔστιν) is predicated of all things, not however in the same way (οὐχ ὁμοίως) but of one sort of thing primarily and of others in a secondary way. So too τὸτί ἐστιν belongs simply (ἁπλῶς) to substance but in a limited sense (πῶς) to the others [other categories] (1030a21-23). -/- The word ἁπλῶς standing against κατὰ συμβεβηκός tries to make substance different from the accidents. When we are being said that τὸ ὄν πολλαχῶς λέγεται, it means that only the substance that is simply (ἁπλῶς) the ἕν, the common nature, τὸὄν. When we use the word 'being' about a substance, the being is said differently from when we use 'being' about an accident. The distinction between the substance and the other categories is a distinction between what simply is said to be and what only with reference to (pros) the substance is said to be. The doctrine of pros hen, changing kath hen to pros hen in respect of to on, makes a distinction that wants to show that while there is a kind of implementing the word being that is simply being, there is another kind which is called being only by reference to that which is simply being. In the doctrine of pros hen it is not so that all the things that are said to be are only by reference to a common one thing, but that while one thing is called being because it is that thing itself, the other things are called so without being that thing itself but only by referring to it. At the very beginning of book Γ, it is said that: -/- Being is said in many senses but all refer to one arche. Some things are said to be because they are substances, others because they are affections of substances, others because they are a process towards substances or destructions or privations or qualities of substances … (1003b5-9, cf. 1028a18-20) -/- Substance is what really is said to be and all other things that are said to be are said only in favor of it. This difference of substance from all other senses of being is what is, I believe, primarily aimed in Aristotle’s interrelated theories of pollachos legetai,pros hen and the theory of substance. b) The difference of the implementation of being in the case of substance and the accidents goes so deep that while substance is considered as the real being, the accidents are almost not being. An accident is a mere name (Metaphysics 1026b13-14) and is obviously akin to not being (b21). Aristotle adds that Plato was 'in a sense not wrong' saying that sophists deal with not being (τὸ μὴ ὄν) because the arguments of sophists are, above all, about the accidental (1026b13-16). At the beginning of book , he says about quality and quantity (which look to be more of a being than other accidents) that they are not existent (οὐδ̕ ὄντα ὡς εἰπεῖν) in an unqualified sense (ἁπλῶς) (1069a21-22). The two above-mentioned points, Aristotle’s (a) interwoven theories of pollachos legetai, pros hen and the theory of substance and (b) taking accidents almost as not being, comparedwith substance, brings forth a structure that I shall call Pollachos Legetai (with capital first letters). What is of the highest importance in this structure for me is the difference of substance from accidents and the kind of relation which is settled between them. There is a substance that without any qualification is said to be and the accidents that are said to be only by reference (pros) to it. Adding Aristotle’s point about accidents that they are nearly not being to this relation and difference, we can obviously see how much this structure is close to Plato’s original-copy ontology. We spoke of the relation of being and difference in Plato’s model and the way Plato construes the being of a copy. A copy is a copy only by referring to (pros) a model; it is different from (ἕτερον) that of which it is a copy; it is not itself a true thing as its model and not really that which is (ὄντως ὄν) but only is in a way (πῶς). If we behold the difference of substance and accident in the context of the theory of pollachos legetai and pros hen, we can observe its fundamental similarity with Plato’s original-copy theory in its structure. Allen draws attention to the fact that the relation between Forms and particulars in Plato’s original-copy model is 'something intermediate between univocity and full equivocity' (1998, 70, n. 24) and the same as what Aristotle calls it pros hen (ibid). What made us compare the two structures was not, of course, the complete similarity of two structures (we have to agree with many possible differences of the two theories) but exactly the specific relation between an original and its copy on the one hand, and a substance and its accident on the other hand. As substance and accident do not share a common character and the substance -accident model hints that they stand in a certain relation, there is no common character between the original and copy in Plato’s model as well. Furthermore, their similarity is not confined to their structure only; they are also aimed to solve the same problem. The central point of the theory is that all the predecessors took being in one sense and this was their weakness point. Besides the mentioned above passages about the relation of pollachos legetai and presocratics’, as well as Plato’s, ontology, the relation of the theory with the problem of not being is clear in several passages. In Metaphysics, it is said: 'Being is then said in many senses… It is for this reason that we say even of not being that it is not being' (1003b5-10). Discussing the accidental sense of being, Aristotle points that it is in the accidental way that we say, for example, that not-white is because that of which it is an accident is (1017a18-19, cf. 1069a22-24). We mentioned that he thought Plato was right saying that sophistic deals with not being because sophistic deals with accidental, which is somehow not being (1026b14-16). Plato turned sophistic not-being to what both is and is not and Aristotle to what accidentally is said to be. What helps Aristotle to resolve the problem of not being is his distinction between ἁπλῶς and κατὰ σθμβεβηκός. Aristotle’s "qua" (ᾕ) which is directly linked with his distinction between καθ’ αὑτο λέγεται and κατὰ συμβεβηκός λέγεται, is used to resolve the old problem of coming to be out of not being (Physics 191b4-10). He strictly asserts that his predecessors could not solve the problem because they failed to observe the distinction of "qua itself" from "qua another thing" (b10-13). He then continues: -/- We ourselves are in agreement with them in holding that nothing can be said simply (ἁπλως) to come from not being (μὴὄντος). But nevertheless we maintain that a thing may come to be from not being in an accidental way (κατὰ συμβεβηκός). For from privation which ὅ ἐστι καθ’ αὑτο μὴ ὄν, nothing can become. (Phy. 191b13-16, cf. b19-25) . (shrink)

Given a Δ1 ultrapower ℱ/[MATHEMATICAL SCRIPT CAPITAL U], let ℒU denote the set of all Π2-correct substructures of ℱ/[MATHEMATICAL SCRIPT CAPITAL U]; i.e., ℒU is the collection of all those subsets of |ℱ/[MATHEMATICAL SCRIPT CAPITAL U]| that are closed under computable functions. Defining in the obvious way the lattice ℒ) with domain ℒU, we obtain some preliminary results about lattice embeddings into – or realization as – an ℒ. The basis for these results, as far as we take the matter, (...) consists of the well-known class of minimal ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, which function as atoms, and the class of minimalfree ℱ/[MATHEMATICAL SCRIPT CAPITAL U]'s, to whose nonemptiness a substantial section of the paper is devoted. It is shown that an infinite, convergent monotone sequence together with its limit point is embeddable in an ℒ, and that the initial segment lattices {0, 1,…, n } are not just embeddable in , but in fact realizable as, lattices ℒ. Finally, the diamond is embeddable; and if it is not realizable, then either the 1 - 3 - 1 lattice or the pentagon is at least embeddable. (shrink)

Elekes proved that any infinite-fold cover of a σ-finite measure space by a sequence of measurable sets has a subsequence with the same property such that the set of indices of this subsequence has density zero. Applying this theorem he gave a new proof for the random-indestructibility of the density zero ideal. He asked about other variants of this theorem concerning I-almost everywhere infinite-fold covers of Polish spaces where I is a σ-ideal on the space and the set of indices (...) of the required subsequence should be in a fixed ideal ${{\mathcal{J}}}$ on ω. We introduce the notion of the ${{\mathcal{J}}}$ -covering property of a pair ${({\mathcal{A}}, I)}$ where ${{\mathcal{A}}}$ is a σ-algebra on a set X and ${{I \subseteq \mathcal{P}(X)}}$ is an ideal. We present some counterexamples, discuss the category case and the Fubini product of the null ideal ${\mathcal{N}}$ and the meager ideal ${\mathcal{M}}$ . We investigate connections between this property and forcing-indestructibility of ideals. We show that the family of all Borel ideals ${{\mathcal{J}}}$ on ω such that ${\mathcal{M}}$ has the ${{\mathcal{J}}}$ -covering property consists exactly of non weak Q-ideals. We also study the existence of smallest elements, with respect to Katětov–Blass order, in the family of those ideals ${\mathcal{J}}$ on ω such that ${\mathcal{N}}$ or ${\mathcal{M}}$ has the ${\mathcal{J}}$ -covering property. Furthermore, we prove a general result about the cases when the covering property “strongly” fails. (shrink)

Reproduced with the kind permission of the author. Currently available in the collection I Looked Alive . © 2010 The Brooklyn Rail/Black Square Editions | ISBN 978-1934029-07-7 Originally published 2003 Four Walls Eight Windows. continent. 1.1 (2011): 43-51. Introduction Ben Segal What interests me is instigated language, language dishabituated from its ordinary doings, language startled by itself. I don't know where that sort of interest locates me, or leaves me, but a lot of the books I see in the stores (...) seem to lack language entirely. Gary Lutz (2006). This issue of continent.'s fiction section features a reprint of “This Is Nice of You” from the first edition of Gary Lutz's collection I Looked Alive . That book was originally released by Four Walls Eight Windows in 2003 and has since been reissued in 2010 by The Brooklyn Rail/Black Square Editions. Calamari Press has also reissued Lutz's Stories in the Worst Way (originally published by Knopf, largely forgotten and dismissed, and then re-issued by the too-short-lived 3rd Bed). “This Is Nice of You” was edited for the re-issue of I Looked Alive and, as the original book is out of print, the earlier version of the story has been hard to come by for some time. This initial version is a bit longer than the new version—Lutz is a master of tightening down his texts to their most linguistically intensified cores—but it is in no way sloppy. It is a great privilege for continent. to be able to make available rare texts of (first) aesthetic and (second) scholarly value. For those readers unfamiliar with Gary Lutz, I believe this story will serve as a worthy introduction. Like Raymond Carver, Diane Williams, Christine Schutt, and so many other important twentieth century and contemporary short story writers, Lutz studied with and was edited by Gordon Lish. This connection is apparent in his attention to sound and the sentence as compositional unit, but Lutz's is a unique voice. “This Is Nice of You” bears Lutz's trademark torqued and turning syntax, his sexed-but-nameless characters, his rendering of the human body and its emissions as utterly discomfiting. Lutz's preoccupations with the mundane raise ordinariness, via startling language and observation, to grandiosity and grotesquery. In the fall of 2008, Lutz delivered a lecture entitled “The Sentence is a Lonely Place” to writing students at Columbia University. The lecture was later printed in The Believer (and is linked below). In it, he spoke about the importance of the sentence as a compositional unit, as even the distinguishing formal characteristic of prose. Specifically, Lutz explained that, from Lish, he had developed a "poetics of the sentence." Accordingly, Lutz constructs his stories at the level of the sentence, paying extreme attention to the material of words- their letters and their sounds- and the way they abut one another and interact on this material level even before they are employed in the service of traditional aims of fiction like meaning or story. Lutz often uses a(n almost constraint-related) technique called consecution. Letters or sounds from one word are carried forward into the following, producing drama and movement in the language itself at a level entirely apart from that of plot. For example, you can see how the 't's in the first sentence of “This Is Nice of You” repeat fast and hard through met and then soften into the 'th's of brothers and they. This close attention to the specific material and characteristic conditions of prose means that Gary Lutz's work always involves both a happening in language and of language. “This Is Nice of You” has a richness and depth that is hidden not in symbolism or obscure reference but on the surface of the page, in the language of every sentence. FURTHER READING Lutz, Gary. “ The Sentence Is a Lonely Place. ” The Believer January, 2009. Web. Short stories and excerpts at Web del Sol . Web. Taylor, Justin. “ An Interview with Gary Lutz .” Bookslut. July, 2006. Web. THIS IS NICE OF YOU [156] [1] I was a man dropping already well through my forties, filthy with myself, when, taking a turn at the toilets one afternoon, I met two brothers-they said they were brothers-who swore they had a sister, a schoolteacher, an officer of instruction at the county college, a whirlwind midlife turmoil of everything already put to ruin, who had gone off from a new marriage in an old car, an upkept and ennobling sedan, but had returned now to the apartment and [157] was living there alone with the little runoff there was from the marriage-some outcurved appliances, apparently, and low-posted furniture promoting its own mystery but becoming figurable in certain concentrations of TV light-and, above all, a telephone (on a pedestal, they insisted), the handpiece of which she gripped in lieu of exercise, or in fury, and I thus let out my little, reliable cry that I was in fact a student of the telephone, that it was a debasing apparatus in the main, with its meager economy of bells and tones, and the intimacy of the mouthpiece that sent your breath, tiny aftervapors of it, back toward your lips, so that regardless of the party accepting the outgoing products of your voice, you were, at most, in a further, rivaling exchange with yourself alone, and this is what must have brought the two of them around, the men who proclaimed brotherhood with the woman, because they offered me her phone number, put it at my disposal on a piece of paper one of them had already committed it to, a tearing from a menu, and the looks the men were now giving me had deletions in them, already, of my exact, beanpole shape and size. So off I went to a pay phone, the nearest canopied one I could find. The woman answered after the second ring and said she needed a lift right that very moment into the little, unlevel city close by. She was idling in the doorway of the building when I pulled up in front, and I helped her into the car, then got back in myself. I had always had a way of not having to look at people that nonetheless brought them to me in full, and so I still am certain of the susceptive and impressible comp-[158]lexion, the shimmer on the mouth, a lipstick of low brilliance, a difficulty around the eyes, the hair short and rayed out exclamation ally, skin bagged up over the elbow bone, conflict even in how her arms stayed at her sides—in sum, a spinal loveliness for me, an off-blonde quantity with shadowed, thumbworn hollows that put me out of as much as I might have ever known of women before. I set the two of us into the narrow traffic, and I remember telling her, by way of explaining the little burden which I had shifted, by now, from the shelf of the dashboard and onto my lap, that when you lived in filth, as I then did, a daily newspaper came to count for a lot, although instead of the thick-supplemented local paper I bought a trimmer one from a backlying town—not, of course, for any affluences of native data it carried, but as an article of house ware: a rough immaculacy in four lank sections, a set of fresh, hygienic surfaces to come between the table, say, and whatever I had going for me at the table, if the table was where I was going forward—because what else so cheap comes so clean and far-spreading? The woman told me that her own trouble with paper was that through a modest hole, no larger than a quarter, that had been drilled a foot or so above the floor (the standard height, she had reasoned, of legitimate electrical outlets), and by means of which her faculty office had at last gained communication with the roomier but unoccupied office next door, more and more often shot a single sheet of paper, plain copier paper she had rolled just barely into a tube, [159] so that after landing on the floor of the neighboring office the paper would preserve little if any of the curl, and there would be nothing written or typed on it, of course, and it was always a blank sheet that had been ageing on her desk for some time and had already been moved around, or advanced, from station to station on the desktop, coming into further creaselets and crimps and other infirmities—paper, in short, still too bare and unfraught to be thrown responsibly and forgettably away, and yet too seasoned and beset with irritations of the surface (a molelike blemish, say, or what looked like a tiny hair, an eyelash, sunk into it, or frecklings, or notational pressings of a fingernail), too wrought, in sum, for the paper to be appointed to any secure curricular purpose. Her office, she claimed, was in fact full of such paper, much-handled and singularized sheets of it by the loose, functionless hundred. I had to get it across to the woman that I myself no longer had an office, or any other place to divide me reliably from everybody else, and that for much of the daylight I thus appeared to be among people because I kept putting myself where people came together into even closer-fitting assortments, the viewing areas and showrooms and rotundas and such: I took in the lean-to look of the women, the tongues coming and going in what the men kept thinking of to say—whole families of low knees for me to bark my shins against during the crowded and involving way out. At home afterward, in the one room where my life was packed down, I would keep my nose stuck in the safehold of the phone [160] book, where the names of people suffered reduction to mere episodes of the alphabet and underwent humbling declensions down every column (Lail, Lain, Laine, Lainerd), and he names of streets, of the towns and townships, got docked in crude, heedless abbreviations (the vowels almost always the first to get poked out), and I would run my eyes over the telephone numbers themselves, each sequence of digits another fallible run of the infinite. I thus corrected my feelings for people and assembled myself emotionally into whatever else I had at hand—the obligating arms of the clothes hangers, usually, or the keen-angled understructure, the guardian legginess, of the ironing board. The woman said that in her case, though, it was more a matter of making slow circuits of the classroom where she had to put across the Emporial Sciences, retail theory and methods, to heat-giving and suggestive young women, some of them world cruelties already. There was the cooing of empty stomachs in the hour just before lunch, and the braying and fizzle of loaded stomachs in the low hours of the afternoon. She would recite her notes in a voice barely loyal to anyone octave, a tiny alluvium of slaver hardening at the corners of her mouth on the days she gave the glassy lozenges a slow, warming suck, and she would take lowering notice of how whatever she said succumbed at once to freak spellings and razzing paraphrase in the big, dividered notebooks; and because in midafternoon light the world looked as thorough, as filled in, as it was ever going to get, a better way to set about ruining her eyes was to review how hair had [161] established itself on the arms of the young women, because almost every arm had brought across itself a welcome and diversifying shadow. On one girl it would be a fine, driftless haze afloat above the white of the arm, never seeming to touch down on the skin itself. (An atmosphere, at most, of chestnut brown.) On another, it was as if copper wire, the narrowmost lengthlets of it, had been stuck into the fleshy batter of the thick, freckled forearms. On a third: a field of it–wheat-colored, thin-spun. On a fourth; a differencing, darkish updrift that shaded off as it approached the inner bend of the elbow, then re-emerged at the base of the upper arm as whiskery fringe. On others it was a brassy or rust-colored frizz, or it was as coarse as cornsilk, or it looked fussed on, as if the arm had been slowly stroked with charcoal. But here the woman broke off, or I may well have made an interruption of my own—I think I must have asked whether she was hungry, and she said if I was, and so on one of the lesser streets I parked the car and led her down into a belowstairs eating house I still remembered. Sandwiches were presently lowered in front of us. I watched her remove the festooned toothpick from hers and then play her fingers over the toasted planes before she took a fond first bite. "This is nice of you," she said. I must have looked at her in the way I then had of getting people to speak so they would not seem to be dwelling any longer on my features, because if on the well-set face the mouth and eyes are said to seem frozen in elegant orbit about the til) of the nose, then mine was a face that behold-[162]ers, regarders, could not help trying to round off with greater success, to goad the particulars of it back into the arcs they had wandered away from—the mouth, for instance, having been pursed and pinched suchwise that it seemed resident more on one side of the face than the other—and there were other signs of original strife to be busied with (slapdash eyebrows unbunched, it appeared, from reserves of hair elsewhere on my person; a showing of adult acne, a shrivelly little relevance of it, confined to the declivity of my nose); and so to be polite, the woman thus sank her gaze into her sandwich, and told me, in a voice lowered accordingly, that, one late-childhood summer, she had devoted herself to collecting postage stamps: it was a tongue-involving sideline to early-arriving puberty, and she liked having to lick the pale, gummed hinges instead of the sticky backs of the stamps themselves before entering everything into the hosting album; and once, during some foul weather between her and a brother (the older, thrown-over one, who had already made a habit of fooling the underside of his arm across the top of hers and calling her "pussified"), she reached for the shoe box in which she had let duplicate stamps accumulate—Spanish ones, mostly, of a fading orange—and sent the box slooshing through the lower air so that the stamps showered onto the brother's bare legs with a full, delicate harm. The woman was now touching up the surface of her iced tea with tiny activities, initiatives, of the longspun spoon. I myself was good at getting my touch onto things, although in a way that seemed to mix up the motive atoms inside [163] them, but I was satisfied that for the moment my sandwich, the unbitten-at half of it, was displayable and fit and local to my plate. The woman went on to say that, as a child, she had been bundled off, many an afternoon, to the slope-ceilinged quarters of a bachelor uncle who, when speaking of anybody not immediately present, could not bring himself to use the person's name but instead would say "an acquaintance of mine in ..." and then mention the name of some lapsed homeland, or little-loved rural orchestra, or backset building about to come down; and it was never a riddle, this device of his (not once could the girl have been expected to identify any of the subjects), and no matter how often and aloud he insisted that particularizing persons any further—bringing even a first name down upon anyone of them—would have been indecent, he claimed, much like doing things to people while they slept, the girl accepted all of the uncle's prim and extravagant evasion for what he surely must have intended it to be: a neat, protective trick to space the world out a little further in her favor, to scatter the population so that wherever her hand might at last come down, it would have to be on herself alone. And here I could sense that the woman wanted from my mouth an account of as much as I myself might have ever managed of attachment, so I told her I had once owned a house (a rising, really, of much-fingered, handwrought architecture that amounted to a little family of rooms above garages: a boxlike building with a rattly thorax of downspouts [164] and drainpipes and an unfolded but full-toned fire escape), and I had had for a time a boarder, a student, a high-colored, loose-packed representative of declining girlhood, hung with necklaces and barrettes, a girl of precise but shifting leanings and inclinations; and the afternoon she had come round to ask after the room, I stood in the entranceway, handshaken and asweat, and from what would later be my memory of the girl, I made off with, first, how every pore of her nose seemed to be sheltering within itself a tiny dark seedlet, a grain of something immediately, enormously valuable. And an almost lipless mouth (just a slit, practically), the teeth inside looking wet, watered-it was my life's chore, at that instant, to keep from sending the back of my thumb blotterlike across the line of them (I was later to learn she drank everything cold and through the narrowest of straws). And her hair: it was tea-colored hair she had, long and reachful, an unstopped downcome of it. Tall for a girl, but she managed to stay out of much of her height and put herself across as somebody backward, or behind. I must have told the girl, as best I could, that I of course had a wife, a full-faced, imperishable partner, though for the moment she was gone otherwhere in the marriage, and here the woman, my present companion, my tablemate, whose feet were now parked, in parallel, on the grade of my upper leg, interrupted to say that her husband, too, had been such a liar, and what could I bring up by way of reply other than that a lie is a truth struck through with other, further truth, or that a lie is the present multiplied by the past or that a lie [165] is an outcry of borrowed hope? The woman gave me an allowed look of disgust, her eyes lowered but still popular with me, and on I went with what had now become the girl of my story. For there had been a great, gainful carpet in the room I put the girl into, a matty expanse of coarse, grabby piles, an engrossing affair that took things into itself and held them tight, misered them, and I of course insisted that the girl not bother herself with its upkeep, that I enjoyed weekly access to a prestigious, upstanding vacuum cleaner; but no sooner was the girl out of the house each morning than I would withdraw from my room, where time was unportionable, and loose myself into the ticktock impertinence of the girl's room and get down on my knees, and, going after the carpet first with my fingers, then with a forceps, and finally by unspooling lengths of clear package-sealing tape and pressing them against the tufts in neat rectangles to catch what I might have missed, I brought vast tracts of the carpet to depletion, recovering not simply the girlinesses, the girleries, one would expect (buttons, straight pins, downed jewelry), but flirtier personalia in the form, say, of a stray confetto brought into the world when a page had been wrung with out caution from a spiral-bound notebook, or some pleated paper shells of the chocolates she required, or one of the bargain antihistamines she took to get her naps going, or a trash-bag tie ragged enough to show the kinked line of the wire within (this I would get wound around my finger), or a cough drop enwrapped like a bonbon (I would undo the [166] wings of the wrapper and have to decide whether to suck the drop all down or begin chewing it midway)—I became the following, the public, that these things, these off-faIlings, had come to have; but mostly there was hair, afloat above the uppermost pushings of the fabric of the carpet an almost continuous haziness of loose hairs of all lengths and sources, and I would have to set them out on a fresh sheet of paper and assort them according to the regions of the body they had taken their departure from, and in no time I had nest-like filiations of broken filaments and smaller involvements of the hairs that made me think of hooks, of barbs, of treble clefs, and each pile required a separate envelope, to be filed in a separate shoe box for every sector of the body until, I hoped, the boxes themselves would no longer be enough and I would have raised something semblable, brought up something equal in volume to the comprehensive girl herself. And her wastebasket! For every bit of rubbish, every dreariment she tossed into the thing, I would, in secret, deposit a reciprocal discard of my own, matching a spotted, confessory tissue of hers with a lurid throwaway after my own heart–the cardboard substructions of a fresh parcel of underwear, maybe, or tearings from pantyhose I now and again pressed against a span of my forearm to work onto it the complications of female shading I otherwise made do, choosily, without. I thus built the two of us up together in her trash! One afternoon-it was another of those lifeful, unsam-[167]pled days on which the world humors us each a little differently to keep us nicely on our last legs—I discovered in the wastebasket an inch-deep textbook of hers, a paperback with a celery-colored cover that had come partly unglued, and this dilapidation I paired off, naturally, with a name-your baby guide to whose pages, during my recurrent turnings of them, in bed or at table, I had contributed dried produces of my person, a chemical splendor entirely mine. This coupling sent a sudden spigoty thrill from me that forced an unbuckling and an unzipping and a cleanup with a handkerchief I then ventured responsively into the wastebasket as well. It was in the bathroom afterward that I found a suds-clouded puddle on the unlevel floor of the tub, a little undrained remainder, rimmed with offscum, of the girl's prolonged early-morning soak, and this was as much as I needed to get on my hands; I pressed them flat against the wet porcelain, then flapped them around in the air, and that was when I noticed it—in the amphitheater of the toilet bowl, an orange-yellow tint, or value, to the waters. When the girl arrived home that evening, I told her, of course, that I had discovered fresh, unforeseen trouble within the tank of thelet (a misalignment of the trip lever, a waywardness of the float ball, a ulation of the lift wires, kinks and defects, really, throughout the entire system) and that in fine it was an apparatus now operable only by means of advanced and strenuous equilibrial manipulations that it would be unseemly, inhospitable, of me to pre-[168]sume to burd to burden her with–so that from here on out, following any leak or evacuation she need merely lower the lid and then, before quitting the room, ring the handbell that had been placed on the would seeeverythinghing else. But the bell never rang, not even once, and from my window the next morning I watched the girl carry from the house a little plastic bag distended balloonishly, much like those bags you will remember having seen in the hands of children bearing homeward their solitary carnival-prize goldfish. In fact, I never ran across the likes of the girl again. The man who came to collect her things-not the father, apparently, but an advocate, an upholder-l found to be dull-eared and lax in his speech, and the better part of his face seemed to have already begun making tiny, rotational departures from whatever it was that the eyes, themselves impressively mobile, were just that moment having to take in. (Was there a lamp in the house that was not that night slopping its wattage over everything?) I guess I was waiting for the man to take a laggard, last-minute interest in me, and by now I was pushing everything out into the paired first person–it was, I said, “Our night shot,” and I began including the two of us in whatever it might be doing out, the expected sprinkles and such—but he was no friendship buff, and he paid no heed to my telling him that the only dress of hers I'd ever twidged myself into even part of the way had been the simplest of them all, a large-buttoned wonder of depthless blue, and then only on the principle that one naturally fits whatever one has into whatever somebody else [169] had first, or how else would the world keep getting any taller with people? The man just went about the removal of the girl's things without having to be reminded too noticeably, I guess, of how every dick hangs by a thread. My listener, though, had by this time brought about some becoming slowings of her arm—it was an arm inclinable to langorous diagonals and magicianly swoops through the air above the tabletop—but it no longer was involving itself with her plate, so I suggested we shove off, I made payment for the food, and on our way to the car, and then in the car as I took to following her pointings, the directional tilts of her head, she said that you naturally kept putting more and more of yourself into another person, at first wondering how much she can take, how much of you is accumulable and how much she can hold, and you're letting things out, disbursing yourself, and you've soon got things set up in her, and room is being made for even more of you, and if you bring this off with enough people, even two or three, what you've got is at first a comfort, because you can pass yourself along and move a little more widely through the world and leave it to these others to man your grievances, your disappointments; and what brought this to mind, the woman said, was a term of financial hardship she had contrived for herself a few years back, an unpaid leave of absence from scrupling letter grades onto quiz papers (propped-up As, and upended Bs made to look, rather, like fannies; all As and Bs, no Cs or anything lower, the difference between an A and a B having less to do with the accuracy of whatever facts might [170] have been impounded in provided for an answer than with anything recallable about the way the enrollee ad conformed her body to the confining perpendiculars of her chair and the navel-level writing surface that projected from it, or the way there might one day have been an unignorable blush on the instep of a once-moseying foot, disburdened of its shoe, that had got itself trapped in the grillwork of that cagelike involvement, intended for books, that was welded to, or otherwise schemed into, the underworks of the chair)—this had been a duration, in short, of controlled difficulty when the misexpenditure of even a twenty-dollar bill had set her thrilling, gloating, over everything she would miss out on, and one afternoon she had made an engagement for a haircut, just a trim, and very early in the session the haircutter, a woman ill-defined in the face but otherwise full of conspicuities of emotion, set down the prevailing scissors and pressed the flat of a lukewarm hand against the woman's cheek, held it there for a good minute or longer, while the other hand eventually found its way into a drawer, a shallow treasury of slender specialty scissors, one pair of which the cutter withdrew and began routing deductively through the woman's hair, the other hand staying put on the cheek, longer and longer, and the woman went home and for afterward the bathtub was now a more likely destination than any of the upright furniture, and it got easier to fill the tub with further clarifying volumes than to clear space on the difficult heights of the sofa, and she was hardly claiming to have become a cleaner [171] person in result—she in fact would often discover, voyaging about her body, a browned, fractionary detail of a larger crepe of toilet tissue that must have got itself stuck in some assy crevice and was impossible to get plucked out of the revolving suds—she was saying only that she spent more and more of her time thus immersed, ill off in water, and the haircutter had surely had a hand in it, the woman was doing some of the cutter's life now, coming into some of its wrong, because you sometimes have to look to somebody else's life to get dimensions set back even part of the way around your own, and it should not have to be any less your own life when it comes from somebody else, and you could surely fudge a society out of anyone available person and get this person doubling for the many, so that in the little run of things perpetuable from one person to the next, every loose moment stood to become a complete, active finality. But by now this was a new day, with only an hour or so off it already, and the place the woman had made me bring us to, the man's place, with a promise that the man was elsewhere—this was on a little offshoot of a street, a stewy efficiency apartment the color had long ago gone out of; and when, once in bed, still clothed, I found among the sheets and blankets a spoiling pair of the man's underpants, one of the leg openings of which was puckered into an avid, sloppy mouth, I held myself accountable for redisposing the fabric until I got a befitting featurelessness back onto it; but all the while, I am sure I had to make myself go over again in my mind that if the body is the porter of as many organs of affec-[172]tion as there might one day turn out to be, then the idea was to let the thing carry you to where you would otherwise never have any reason to arrive, because I listened for the unmelodiof the the thede ofthe woman's zipper, and then the woman made me put myself out of my own clothes, the attritional corduroys and overshirt, and got herself up at last onto the topic not of the man whose apartment it was (because his story was scarcely the story of how the boy who decides he is half a girl no sooner starts to worry about where the other half might than he gets careless with where he rests his eyes, or what he gives even the feeblest of fingerholds to, and anything, even a crumbly triangle of pie offered on a saucer instead of on a pie plate proper, comes in easy, ready, wronging answer), but of her husband, and how, no more than a couple of months into the marriage, he had begun snugging away in his undershorts a little source of chanc, reliable frictions to nudge him onward through the workday—anything company-keeping that could be counted on not to slide out of the elasticky leg holes: a half-dollar packet of chocolate tittles, maybe, that was barely noticeable in the baggy surround of the widecut trousers so popular at the time. For by now the woman had at last brought what is usually called the other mouth to within only inches of my lips, but it is not a mouth, obviously, although I let myself go along with the goodwill behind the comparison, the way I will remain loyal to anything deliberately and faithfully misunderstood, and I fussed my tongue against the vital trifles hung inside of her, as much of the curtailed finery as I could find, [173] and gave the whole insimplicity of it a slow-circling, examinational lick, until I was taking a sudden tepid downwash on the tongue. It was a familiar, latrine in dribble that must have tasted, no doubt, like trouble just starting out.p [1] Editor's Note: Original pagination from first edition print denoted with bracketed page numbers. (shrink)

The book reconstructs the history of Western ethics. The approach chosen focuses the endless dialectic of moral codes, or different kinds of ethos, moral doctrines that are preached in order to bring about a reform of existing ethos, and ethical theories that have taken shape in the context of controversies about the ethos and moral doctrines as means of justifying or reforming moral doctrines. Such dialectic is what is meant here by the phrase ‘moral traditions’, taken as a name for (...) threads of moral discourse, made in turn of other interwoven threads, including transmission of shared codes, appeals to reform of prevailing custom, rational argument about the justification of some precept on the basis of some shared general teaching or principle, and rational argument about the ultimate basis for principles and justification of authoritative teaching. That is, the approach adopted to the reading of ethical texts depends on a firm belief in the fact that philosophers hardly created any ethical doctrine out of nothing. The main point this book tries to highlight is how different philosophical theories emerged and followed each other as a result of attempts at accounting for what was going on in the world of moral traditions. Changes were propelled by controversies between different schools, and highly abstract arguments were the unintended effects of moves made by controversialists forced to transform (and occasionally to turn upside down) their own doctrines in order to face the challenge posed by other arguments. This is the reason why the book examines not only texts that already enjoy pride of place in the history of philosophy (Aristotle, Kant, Hegel), but also other texts usually treated in the histories of religions (the Bible, the Talmud, the Quran), and others considered to be much less philosophical (Plutarchus, Pufendorf). -/- 1. Plato and a response to ethical scepticism. Two different traditions of morality in VI-V century Greece are described. The birth of philosophical questioning of traditional morality and temporal and spatial variation of custom is described within the context of the v century crisis, the demise of traditional aristocratic and tyrannical rule and the birth of democracy. Two conflicting answers to the challenge are reconstructed, namely conventionalist or immoralist theories formulated by the Sophists and the eudemonist and intellectualist Socratic theory. Plato’s own reformulation of Socrates answer to the Sophists is reconstructed. His psychological views, his classification of the four cardinal virtues and his political theory are described as parts of a unitary system, culminating in an extremely realist moral ontology identifying the idea of the good with the essence of the (moral and extra-moral) world itself. -/- 2. Aristotle and the invention of practical philosophy. Aristotle’s invention of practical philosophy as a field separated from first philosophy is shown to be an implication of his break with Plato moral ultra-realism. Aristotle’s agenda in his moral works is arguably dependent on a polemical intention, namely dismantling Socratic intellectualism. The semi-inductive or virtuously circular method of practical philosophy is illustrated, starting with the received opinions of the better and wiser individuals and trying dialectically to sift what is left of mistake and inconsistence in such opinions, finally trying to correct mistakes and make the overall practical science more consistent. The chapter illustrates then the relationship of individual ethics, or ‘monastics’, with the art and the science of the pater familias, or ‘economics’, and the science of the ruler and citizen, or politics. The nature of virtues, or better, excellences of character, is discussed, highlighting the basic role of hexis, or ‘disposition’. Prudence, or better practical wisdom, is the focus of the chapter. Its relationship with bouleusis or deliberation is examined, and its autonomous status vis-à-vis theoretical knowledge is stressed. -/- 3. Diogenes and philosophy as a way of life. The chapter provides an overview of Hellenistic ethics, which almost amounts to Hellenistic schools of philosophy, in so far as ‘philosophy’ became in these centuries primarily the name for a way of life. The typical character of the Cynical movement is highlighted, that of a school of life, not a school aimed at providing any kind of intellectual training was to be provided. -/- 4. Epicurus and ethics as self-care. The peculiar character of the Epicurean school is described, a combination of a science of well-being aiming, more than at pleasure as in the popular view, at reduction of useless suffering, of unnecessary needs, and at a balanced selection of pleasures of the best and most durable kind. -/- 5. Epictetus and ethics as therapy of the passions. The various phases of Stoicism are described, and the shifting place given to ethics in the Stoic system of idea, culminating in the paradoxical view of ethics, its impossibility in principle notwithstanding, as the only truly significant and necessary part of philosophy. Cicero is treated, showing how his own synthesis of various Hellenistic trends is as a truly philosophical enterprise, deserving serious consideration after one or two centuries when he was confined to the role of literate. Epictetus is chosen as the best example of what the Stoic tradition could yield, an art of living based on sophisticated introspection, in turn aimed at making a kind of cognitive therapy possible, dismantling obnoxious passions at their root by systematically correcting false representations. -/- 6. Philo and the reconciliation of Torah and Platonism. A reconstruction of basic ideas from a few books of the Hebrew Bible is provided, starting with the Prophetic tradition and the focus on God’s mercy as the source of motivation and standard for human behaviour. Then a comparative analysis is undertaken of a parallel tradition, namely the three codifications of the Torā (Law or, better, Instruction), highlighting how a core of moral ideas may be recognized as a basis and preamble of codification of civil law, cultural practice, and regulation of ritual purity. The importance of Leviticus is stressed as the turning point when emphasis mercy, typical of the Prophetic tradition, is combined with the legal tradition, yielding the change in sensibility of the Second Temple time. Philo of Alexandria is described as one of the three leading figures – together with Rabbi Hillel and Rabbi Yeshua – at the apex the emergence of the mentioned new sensibility, gradually including mercy as an essential part of justice and establishing the starting point of both the Rabbinic and the Christian tradition. This consists precisely in the precept of one’s neighbour’s love or of the golden rule, two eventually identical precepts whose meaning is arguably more sober and sensible than the long-lasting Christian tradition deriving from John and Augustine has made us believe and no novelty vis-à-vis so-called Ancient-Testament teachings. -/- 7. Augustine and Christianity as Neo-Platonism. The first section examines the moral doctrines of so-called 'ethical Treaties' from the Talmud, a group of treaties, among which the best known is Pirqé Avot, that were left out of the six "orders" of the canon as they did not fit in any of the six groups of issues ritual or legal on which the division was based. According to Maimonides, their peculiar theme is provided by the Deòt, 'opinions', i.e., mental dispositions, that is, the translation of the Greek term hexeis and Arab akhlak (in turn providing in this language the name for ethics as such). The three topics I reconstruct are: i) the notion of Torah: The Torah is understood as the world order itself, or as the ‘Wisdom’ that existed even before creation and was ‘the tool by which the world was built’; however, the Torah is an earthly and human entity, as it was "received" by humans, and from that very moment belongs to them; ii) the relationship between love of God and love of neighbour; the treaties require us to study and practice the Torah ‘for its own sake’, that is, require us to act out of love, not out of fear or hope of reward; iii) the idea of sanctification of daily life: having disappeared with the destruction of the Temple the possibility of any conflict between liturgical service and everyday life, the latter is assumed to be in itself divine service: to give food to the poor has the same value as sacrifices in the Temple, and as an implication, the insistence become recurrent on the goodness of created things in themselves along with a polemic against ascetic currents. The conclusions drawn are: i) the moral teachings of the Talmud and those of Yeshua are, rather than similar, virtually identical; one may safely say that the precept of love and the golden rule are central ones for all Talmudic rabbis, that mercy plays an indispensable role alongside with justice, and the latter is not a different thing from one’s neighbour’s love; ii) a peculiarity of Talmud rabbis facing Yeshua is the idea of study as worship, and knowledge as a source of justice; but this is an idea of Judaism after the Temple's destruction that cannot be attributed to the Pharisees of Yeshua’s time; iii) the relation of study and practice in the Talmud parallels that between faith and deeds in Paul's epistles, that is, respectively faith or learning are a necessary and sufficient condition to be recognized as righteous , but deeds are the inevitable effect of either faith or learning. The sayings ascribed to Yeshua are examined first, yielding the conclusion that a close equivalent may be found for every saying in Talmudic literature and yet the whole is ascribed to one rabbi, with rather consistent stress on God’s mercy and unconditional forgiving as the mark of true imitation of God. Thus, Yeshua’s teaching is pure Judaism. The third section describes briefly the galaxy of Gnostic currents and Manichaeism, trying to sketch the profile of moral teachings resulting from an encounter of Asian spiritual traditions, Hellenistic lore and sparks of teachings from apocalyptic Jewish currents. The last section summarizes the turbulent history of several encounters between Christian currents and Hellenistic philosophical schools. The first one was with late Cynicism. Recent, rather controversial, literature discovered the jargon and a few topics from the Stoic-Cynical popular philosophy in a few books from the New Testament itself. This, far from proving that Rabbi Yeshua had been influenced by cynic preachers, is a proof of the necessity felt by Christian preachers to translate the original ‘Christian’ teaching into a Greek lexicon deeply impregnated with cynic terminology. The second was with Platonism, yielding the mild and temperate moral teaching of Clemens of Alexandria, teaching the sanctity of nature and the human body, the joy of moderate fruition of ‘natural’ kinds of pleasures, and the beauty of the marital life – in short, the opposite of the standard picture of Medieval Christianity. Ambrose of Milan brings about a different kind of synthesis, namely with Middle Platonism, where Stoic themes prevail. The most shocking case is Augustine, where an early Manichean education is overcome in a former phase by a synthesis of Plotinian Neo-Platonism and Christian preaching, yielding a sustained polemic with the Manicheans and rather optimistic views on life and Creation, the body and sexuality, and Hebrew-Judaic tradition not far from Clemens of Alexandria. In a later phase, occasioned by controversy on the opposite front, with such Christian currents as the Pelagians and Donatists, Augustine comes back to heavily anti-Judaic and world-denying ascetic attitudes where is earlier Manichean upbringing seems to emerge again. The tragedy of medieval Christianity will be the later Augustine’s overwhelming influence. A final section is dedicated to the monastic tradition where a curious mixture of world-denying asceticism with an astonishingly penetrating ‘science’ of introspection emerges. -/- 8. Al Farabi and the reconciliation of Islam and Platonism. The Qurān and the qadit, that is, collections of sayings ascribed to the prophet Muhammad contain a wealth of precepts and catalogues of virtues mirroring moral contents from the Jewish and the Christian traditions, among them the basic notion of imitation of the Deity, where mercy is assumed to be its basic trait. An important tradition within Islam, namely Sufism, stressed to the utmost degree the role of mercy, turning Islam into a mystic doctrine centred on retreat from the world, abandonment to God’s will, and a peaceful and fraternal attitude to our fellow-beings. A secular literary tradition originating in the Sassanid Empire, the literature of advice to the Prince had for a time a widespread influence in the newly constituted Arabic-Islamic commonwealth. In a later phase, the legacy of Hellenic philosophy made its way into the intellectual elite of the Islamic world. The first important legacy was Platonic, and the Republic became the main text for Islamic Platonism. Al-Farabi wrote an enjoyable remake of the Platonic Republic, arguing that the citizen’s virtues were the basis on which the political building needs to rest. The secular lawgiver is enlightened by the light of reason in his everyday practice of governance, but room is made for the Prophet as the voice of revealed truth that confirms and completes the rational truth that philosophy may afford. In a second phase also Aristotelian and Stoic influence were assimilated. Miskawayh’s treatise was the masterwork at the time Arabic philosophy reached its Zenith. It is a treatment of the soul’s diseases and their remedies, combining the Aristotelian doctrine of the golden mean with the Stoic doctrine of the passions and elements of Galenic medicine. Towards the eleventh-twelve centuries a war raged among theologians and philosophers, finally won by the former with disappearance of philosophy as such. The newly established mainstream, yet, was no kind of intolerant fanaticism. It drew from the work of mystic theologian Al-Ghazālī, the best heir of Sufism, teaching a tolerant and peaceful attitude to our fellow-beings and a passive attitude to destiny as an expression of the Divine will. -/- 9. Moshe ben Maimon and the reconciliation of Torah and Aristotelian ethics. The encounter between the Talmudic tradition and Hellenic philosophy had taken place a first time in Alexandria at the time of Philo but the two traditions had parted way again. In fact, the kind of Platonic Judaism founded by Philo survived only within Christianity, in the fourth Gospel and then in writings by Clemens of Alexandria. The Talmudic literature had absorbed just less striking traits from the Hellenic Philosophy, namely an idea of ethics as care of the self and a role for the education of character as propaedeutic to theoretical knowledge. In the Arabic-Islamic world, a second round started when Jewish authors writing in Arabic undertook the task to prove the full compatibility of the tradition deriving from Torah and Platonic philosophy. The culmination of this attempt is provided by Moshe ben Maimon who tried to use Aristotelian ethics as a language into which the teaching from the Pirké Avot could be translated. -/- 10. Thomas Aquinas and the reconciliation of Christian morality and Aristotelian ethics. In the first section the fresh start is described of philosophical ethics in Latin Europe at the turn of the Millennium. In a first phase, Anselm and Peter Abelard built on a Platonic and Augustinian legacy. In this phase. remarkable innovations are introduced, including Abelard’s claim of the obliging character of erring consciousness. In a second phase, the rediscovery of Nicomachean Ethics thanks to Latin translation of Arabic versions gives birth to a new wave of ethical studies, recovering the very idea of Aristotelian practical philosophy, with the potential implication of full legitimization of natural morality, i.e. ethics without Revelation. Aquinas’s ethics is a theological ethics out of which it would be vain to try to extract a self-contained philosophical ethics. His treatment of topics in philosophical ethics, yet, does not boil down to repetition of Aristotelian arguments but is rather a creative reshaping of such arguments. For example, he introduces also in the practical philosophy a first principle parallel to the principle of non-contradiction; and he also carries out a synthesis of Aristotelianism, Stoicism, and neo-Platonism. Even though it is essentially moral theology, Aquinas’s doctrine - unlike Augustine – grants full citizenship to "natural" morality, firstly by rejecting the claim that the corruption of human nature due to the original sin is so radical as to leave "pure nature" incapable of moral goodness. The doctrine is presented in a more sophisticated formulation in a few of the Quaestiones, such as De Malo and De Veritate, in the Summa contra Gentes and in the commentaries to Aristotle than in the famous Summa Theologica, but the latter work includes the only or the largest exposition of some decisive part of the theory. Thus, the Summa Theologica should be read for what it is more than criticized for not being what it was not meant to be. It was not meant to be the brilliant synthesis of all that Reason he had been able to produce with what Revelation had added about which the Neo-Thomists used to dream, but rather a manual for the training of preachers and confessors, where theoretical claims are not too demanding and a few serious tensions are left. Besides a jump between the Prima Secundae and the Secunda Secundae, being the former an essay in virtue theory and the latter a handbook for confessors, the most serious tension is perhaps the one between the ethics of right reason presented in most of Ia-IIae and the eudemonistic ethics developed in quaestiones 1-5 of the same part; the alternative ethical theory which also may be found in Augustine, the Stoic view of a cosmic reason eventually coincident with the moral law, was believed by Anselm (followed by John Duns Scotus and William of Ockham) to be incompatible with eudemonism. It is questionable whether Thomas could reduce the tension proving that it is just an apparent tension, in so far as the right reason and bliss derived from knowledge of God tend to coincide, but this is just a conjecture. Thomas’s ethics is a virtue ethic, not a law-based one, and moral judgment focuses on the virtues, particularly charity, not on the commandments and even less on absolute prohibitions; Thomas, however, would not have considered a drastic alternative between law and the virtues such as the one which has been advanced in late twentieth-century philosophy to be justified. Nonetheless, when it discusses ‘special’ virtues, it ceases to be an ethics of virtue and becomes a disappointing and often contradictory discussion of legal and illegal acts. Such a discussion takes most of the time ‘reasonable’ middle positions on controversial issues but not the alternative approach that Aristotelianism would have made possible; even when some occasional Aristotelian claim shows up, such as money’s barrenness as a reason against usury, this seems to be made by an author who apparently ignores the Aristotelian Thomas of the Prima Secundae. It is an ethic of human autonomy which recognizes the binding character of the individual conscience and, potentially, even a duty to disobey unjust laws. It is true that what Thomas writes in his discussion of death penalty and persecution of heretics is simply disgusting, and yet we should blame Thomas the man, not Thomist ethical theory. Finally, Thomas’s ethics is not ethical ‘absolutism’, as both traditionalist Catholic theologians and secularist enemies of dogmatic morality tend to believe. It is instead an ethic of prudential judgment. Exceptions to this approach – or better results of logical fallacies – are such claims as the absolute character of negative precepts and of the existence of "intrinsically evil acts", claims that simply cease to make sense in the light of Thomas’s own distinction between human act and natural act, carrying consequences Thomas did not live long enough to draw or was not consistent enough to dare to draw. -/- 11. Francisco de Vitoria and casuistry. The first topic illustrated is the discussion about the notion of pura natura, namely the human condition after the original sin and before divine revelation. The core notion was already there in Aquinas but was later developed by Caietanus (Thomas de Vio) with a number of interesting implications: firstly a view of human nature as such much more positive than Augustine’s and his followers’ view, including both Calvinists and Jansenists; secondly, the implication that the philosopher’s morality, as opposed to the Christian’s morality, is a quite respectable kind of morality; thirdly, that theocracy and prosecution of the unfaithful lacked justification, with more far-fetching consequences than Aquinas himself had dared to draw. The second topic is casuistry, a new name for a comparatively older way of thinking, which was already there in late Stoicism and Cicero as well as in the Talmudic literature. This is an approach aimed at yielding probable enough solutions for doubtful cases even in absence of completely safe staring points. The genre developed from medieval reference books for confessors and became by the sixteenth-century a sophisticated tool-box for dealing with various fields of applied ethics. Francisco Vitoria, the main authority of Baroque Scholasticism, was a controversial figure, among the proponents of the new discipline of casuistry and a consistent proponent of more separation between the religious and the civil authority, stricter limits to the legitimacy of war, innate rights of non-Christian nations in the New World based on the notion of pura natura, providing a standard of ‘natural’ goodness, previous to revelation, on which the Indian nations were judged to live in a naturally good condition, provided with the institutions of family, justice, and religion had accordingly a right to full respect by Christian sovereigns. Bartolomé de Las Casas, arguing along similar lines, was the leader of a historical battle in defence of the rights of the Indios. -/- 12. Michel de Montaigne and the art of living. A short description of one of the Renaissance Phyrronism, one of the classical philosophies revived in the fifteenth and sixteenth century. Montaigne combines the sceptical epistemology with an understanding of ethics – indeed of philosophy as a whole – in terms of an art of living inspired by two basic ideas, sagesse, that is, practical wisdom as the only kind of rationality available after theology, science, and tradition have declared bankrupt, and an aesthetic ideal of self-transformation through the art of writing and introspection. -/- 13. Pierre Nicole and neo-Augustinianism. The chapter illustrates first the vicissitudes of Augustinianism newly born after the late medieval triumph of Thomist Aristotelianism in the alternative Protestant and Catholic versions processed by the Calvinists and the Jansenists. Then it illustrates the doctrines of Pierre Nicole, Blaise Pascal’s best disciple, on the impossibility of introspection, on the ubiquity of self-deception, on the incurably evil character of the passion of love, and on the two moralities, the one of the man of the world, the morality of honesty which is indispensable for granting peace and order but devoid of any true value for eternal salvation, since the same external behaviour may be prompted by opposite motivations, and the morality of charity, the only true one but also useless to society. The third topic is Pierre Malebranche’s view of self-deception as a ubiquitous phenomenon accounting for human action and responsibility and his reformulated theory of self-love, no less ubiquitous than for Nicole and yet not as incurably evil, given the distinction between morally indifferent and even necessary amour de soi and vicious amour proper, a distinction on which the whole of Rousseau’s moral and political theory rests. -/- 14. Samuel von Pufendorf and the new science of morality. The chapter is dedicated to the discovery of the idea of a ‘new moral science’. Hugo Grotius is discussed first highlighting the real character of his project, much closer to the Thomist idea of a natural law accessible to non-corrupted human reason when human beings are living in a state of pura natura. Then Hobbes’s combination of scepticism, voluntarism, and conventionalism is described and both the continuity with Grotius’s new science, in the search for non-revealed rational morality, and the break with him, in the adoption of voluntarism and refusal of an intellectualist view of natural law, are illustrated. Pufendorf’s work is illustrated as a synthesis of the two previous attempts and the – up to Schneewind underestimated – paradigmatic example of the new science of morality. -/- 15. Richard Cumberland and consequentialist voluntarism. The chapter gives an overview of eighteenth-century Anglican ethics, noticing how the Cambridge tradition gave special weight to natural theology as opposed to positive or revealed theology – and how two Cambridge fellows, John Gay and Thomas Brown, elaborated on Cumberland’s (and Malebranche’s, as well as Leibniz’s) strategy for finding a third way between intellectualist view and voluntarist view of the laws of nature. The result of their elaboration was a kind of a rational-choice account of the origins of natural laws, where a law-giver God chooses among a number possible sets of laws on a maximizing criterion, and God’s maximandum is happiness for his creatures. The chapter notices also how such a solution aimed at solving at once the problem of evil and that of the foundation of moral obligation by proving how God’s choice was justified as far as it was the one minimising the amount of suffering in the world. 16. Richard Price and intuitionism. The chapter describes first the doctrines of the Cambridge Platonists, an example of hyper-rationalist reaction to Calvinism. Secondly it describes the sophisticated and universally ignored – from Sidgwick to Anscombe –version of what was later labelled ‘ethical intuitionism’ – showing how it escapes familiar objections and misrepresentations of intuitionism – from Mill to Rawls – in grounding its argument on transcendental arguments while carefully avoiding recourse to introspection and psychological evidence, which has been taken as a too easy target by critics of intuitionism. Thirdly, the chapter discusses Whewell’s ‘philosophy of morality’, as opposed to ‘systematic morality’, not unlike Kant’s distinction between a pure and an empirical moral philosophy. Whewell worked out a systematization of traditional normative ethics as a first step before its rational justification; he believed that the point in the philosophy of morality is justifying a few rational truths about the structure of morality such as to rule hedonism, eudemonism, and consequentialism; yet a system of positive morality cannot be derived solely from such rational truths but requires consideration of the ongoing dialectics between idea and fact in historically given moralities. Whewell’s intuitionism turns out closer to Kantian ethics than commentators have made us believe until now, and quite different from what Sidgwick meant by intuitionism. -/- 17. Adam Smith and the morality of role-switch. The chapter describes first, Hutcheson’s attempt at basing the ‘new science’ of natural law on different bedrock than Pufendorf and the English Platonists, namely a moral sense, a faculty whose existence is assumed to be proved on an empirical basis. The second step is a reconstruction of Hume’s rejoinder in terms of a new science of man including morality on an ‘experimental’ basis, that is, a ‘Newtonian’ hypothetical-deductive approach, distinguished from Hutcheson’s allegedly uncritical descriptive approach to human nature. The third step is a reconstruction of Adam Smith theory of morality understood as emerging from a spontaneous interplay of exchanges of situations (the most basic meaning of the word ‘sympathy’ as construed by this author). -/- 18. Jeremy Bentham and utilitarianism. The bulk of the chapter is dedicated to the doctrines of Jeremy Bentham. The Enlightenment spirit that suggested the idea of a new morality, free from religion, is illustrated. The notion of utility is illustrated as well as the subsequent formulations of the principle of utility. The idea of felicific calculus is discussed, showing how its inner difficulties prompted several reformulations of the principle of utility in order to avoid undesirable implications of proposed formulations. The role of the thesis of spontaneous convergence between interest and duty is discussed, showing how it left numberless questions open, and the distinction between the virtues of prudence, justice and beneficence is described as a way out of the deadlocks of classical utilitarianism. After Bentham, Mill’s reformed utilitarianism is reconstructed, showing how it is a kind of mixed system – as closer to common sense as it gives up Bentham’s claims to consistency and simplicity – resulting as unintended consequences from the controversies in which Mill was too keen to engage. The hidden agenda of the controversy between Utilitarianism and Intuitionism, going beyond the image of the battle between Prejudice and Reason, is described, showing how both competing philosophical outlooks turn out to be more research programs than self-contained doctrinal bodies, and such programs appear to be implemented, and indeed radically transformed while in progress thanks to their enemies no less than to their supporters. -/- 19. Immanuel Kant, practical reason and judgment. The chapter argues that Kant took from Moses Mendelssohn the idea of a distinction between geometry of morals and a practical ethic. He was drastically misunderstood by his followers precisely on this point. He had learned from the sceptics and the Jansenists the lesson that men are prompted to act by deceptive ends, and he was aware that human actions are also empirical phenomena, where laws like the laws of Nature may be detected. His practical ethics made room for judgment as a holistic procedure for assessing the saliency of relevant moral qualities in one given situation; this procedure yields the same results as the geometry of morals does for abstract cases but does so immediately and without balancing conflicting duties with each other, since what makes for the salient quality of a situation is perceived from the very beginning. Kant's practical philosophy is richer than the received image, making room for an ‘empirical moral philosophy’ or moral anthropology including treatment of commerce, needs, value and price, happiness and well-being; the overall social theory and philosophy of history is less different from Adam Smith's than the received image makes believe; the paradox of happiness is central to Kant's philosophy; a distinction between happiness and well-being is clearly drawn; the distinction plays a basic role in establishing a link between the economic and the moral life. -/- 20. Georg Wilhelm Friedrich Hegel and the critique of abstract universalism. The chapter describes first the Romantic movement and the implications some of its concerns, rescuing passions, community, tradition, the individual as the bearer of a unique destiny, and the longing for organic unity between the individual, mankind and nature. Hegel’s contribution is discussed then, highlighting how, on the one hand, he shared a number of these concerns and on the other he had more rationalist leanings. The notion of morality is the pivotal point of the reconstruction, highlighting how Hegel construes this notion as a key to his own diagnosis of the malaise of modernity – the separation of individual and Gemeinschaft – and how his attack on Kant turns around this very idea. -/- 21. Friedrich Nietzsche against Christianity and the Enlightenment. The chapter illustrates first the idea of deconstruction of the back-world of values. Nietzsche claims to be legitimate heir of the French moralists, Leibniz, Kant and Hegel, in so far as he allegedly carries out to its deepest implications their discovery of what lies behind traditional naïve belief in the existence of an objective realm of values just waiting for description by the philosopher. The two exemplars form which genealogy draws inspiration are the classical philologist’s historical reconstructions of lost meanings and the chemist’s decomposition of elements. Then the genealogy of the notions of good and evil carried out in the first dissertation of Genealogy of morals is illustrated with its paradoxical conclusion that will to power is in fact the only ‘genuine’ kind of goodness. The third point illustrated is the dialectic of ascetism and self-realization with its ambiguous outcome. The suggested interpretation of such outcome is that Nietzsche’s normative ethics is a kind of virtue ethics taking an aesthetic ideal as a normative standard -/- 22. George Edward Moore and ideal utilitarianism. The chapter discusses the ideas of common sense and common-sense morality in Sidgwick. I argue that, far from aiming at overcoming common-sense morality, Sidgwick aimed purposely at grounding a consist code of morality by methods allegedly taken from the natural sciences to reach, also in ethics, the same kind of “mature” knowledge as in the natural sciences. His whole polemics with intuitionism was vitiated by the a priori assumption that the widespread ethos of the educated part of humankind, not the theories of the intuitionist philosophers, was what was worth considering as the expression of intuitionist ethics. In spite of a naïve positivist starting-point, Sidgwick was encouraged by his own approach in exploring the fruitfulness of coherentist methods for normative ethics. Thus, Sidgwick left an ambivalent legacy to twentieth-century ethics: the dogmatic idea of a “new” morality of a consequentialist kind, and the fruitful idea that we can argue rationally in normative ethics albeit without shared foundations. Then it reconstructs the background of ideas, concerns and intentions out of which Moore’s early essays, the preliminary version, and then the final version of Principia Ethica originated. I stress the role of religious concerns, as well as that of the Idealist legacy. I argue that PE is more a patchwork of rather diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. I add a comparison with Rashdall’s almost contemporary ethical work, suggesting that the latter defends the same general claims in a different way, one that manages to pave decisive objections in a more plausible way. I end by suggesting that the emergence of Analytic Ethics was a more ambiguous phenomenon than the received view would make us believe, and that the wheat (or some other gluten-free grain) of this tradition, that is, what logic can do for philosophy, should be separated from the chaff, that is, the confused and mutually incompatible legacies of Utilitarianism and Idealism. -/- 23. Edmund Husserl and the a-priori of action. The chapter illustrates first the idea of phenomenology and the Husserl’s project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the a priori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy carried out in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach’s theory of social acts as a key the grounding of norms, a view that basically sketches the very ideas ‘discovered’ later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section is dedicated to Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of ‘values’ – with surprising affinities with George E. Moore - than philosophers such as Max Scheler who claimed to Husserl’s legitimate heirs. -/- 24. Bertrand Russell and non-cognitivism. The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of ‘good’, its non-cognitive meaning, in a first phase identified with ‘emotive’ meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell’s ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of a rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson’s theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. Last of all, the discussion from the Forties about Hume’s law is described, mentioning Karl Popper’s argument and Richard Hare’s early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- 25. Elizabeth Anscombe and the revival of virtue ethics. The chapter discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. I argue that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. A short look at further developments in the neo-naturalist current is given trough a reconstruction of Philippa Foot’s and Peter Geach’s critiques to the naturalist-fallacy argument and Alasdair MacIntyre’s grand reconstruction of the origins and allegedly unavoidable failure of the Enlightenment project of an autonomous ethic. -/- 26. Richard Hare and neo-Utilitarianism. The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick’s and Moore’s fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine definitely refuted. A glimpse at this uproarious process is given through two examples. The first is Roy Harrod Wittgensteinian transformation of Utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This results in preference utilitarianism combined with a ‘Kantian’ version of rule utilitarianism. The second is Richard Hare’s two-level preference utilitarianism where act utilitarianism plays the function of eventual rational justification of moral judgments and rule-utilitarianism that of action-guiding practical device. -/- 27. Hans-Georg Gadamer and rehabilitation of practical philosophy. The post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named ‘Rehabilitation of practical philosophy’ is described. Among the actors of such rehabilitation there were a few of Heidegger’s most brilliant disciples, and Hans-Georg Gadamer is chosen as a paradigmatic example. His reading of Aristotle’s lesson I reconstructed, starting with Heidegger’s lesson but then subtly subverting its outcome thanks to the recovery of the central role of the notion of phronesis. -/- 28. Karl-Otto Apel and the revival of Kantian ethics. Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This started, instead than the rehabilitation of prudence, with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. An examination of his argument is some detail is offered, followed by a more cursory reconstruction of Jürgen Habermas’s elaboration on Apel’s theory. -/- 29. John Rawls and public ethics as applied ethics. Rawls’s distinction between a “political” and a “metaphysical” approach to one central part of ethical theory, namely the theory of justice, is interpreted as a formulation of the same basic idea at the root of both the principles approach and neo-casuistry, both discussed in the following chapter, namely that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls’ view never will be close – on the basic criteria for judgment. -/- 30. Beauchamp and Childress and bioethics as applied ethics. The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin’s new casuistry. -/- . (shrink)

The research presented in this paper was motivated by our aim to study a problem due to J. Bourgain [3]. The problem in question concerns the uniform boundedness of the classical separation rank of the elements of a separable compact set of the first Baire class. In the sequel we shall refer to these sets (separable or non-separable) as Rosenthal compacta and we shall denote by ∝(f) the separation rank of a real-valued functionfinB1(X), withXa Polish space. Notice that in (...) [3], Bourgain has provided a positive answer to this problem in the case ofKsatisfyingwithXa compact metric space. The key ingredient in Bourgain's approach is that whenever a sequence of continuous functions pointwise converges to a functionf, then the possible discontinuities of the limit function reflect a local ℓ1-structure to the sequence (fn)n. More precisely the complexity of this ℓ1-structure increases as the complexity of the discontinuities offdoes. This fruitful idea was extensively studied by several authors (c.f. [5], [7], [8]) and for an exposition of the related results we refer to [1]. It is worth mentioning that A.S. Kechris and A. Louveau have invented the rank rND(f) which permits the link between thec0-structure of a sequence (fn)nof uniformly bounded continuous functions and the discontinuities of its pointwise limit. Rosenthal'sc0-theorem [11] and thec0-index theorem [2] are consequences of this interaction.Passing to the case where either (fn)nare not continuous orXis a non-compact Polish space, this nice interaction is completely lost. (shrink)

For every$n\in \omega \setminus \{0,1\}$we introduce the following weak choice principle:$\operatorname {nC}_{<\aleph _0}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least n there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a selection function$f:\mathcal {G}\to \left [\bigcup \mathcal {G}\right ]^n$such that$f(F)\in [F]^n$for all$F\in \mathcal {G}$.Moreover, we consider the following choice principle:$\operatorname {KWF}^-:$For every infinite family$\mathcal {F}$of finite sets of size at least$2$there is an infinite subfamily$\mathcal {G}\subseteq \mathcal {F}$with a Kinna–Wagner selection function. That is, there is a function$g\colon \mathcal (...) {G}\to \mathcal {P}\left (\bigcup \mathcal {G}\right )$with$\emptyset \not =f(F)\subsetneq F$for every$F\in \mathcal {G}$.We will discuss the relations between these two choice principles and their relations to other well-known weak choice principles. Moreover, we will discuss what happens when we replace$\mathcal {F}$by a linearly ordered or a well-ordered family. (shrink)

Ramsey’s theorem asserts that every k-coloring of $[\omega ]^n$ admits an infinite monochromatic set. Whenever $n \geq 3$, there exists a computable k-coloring of $[\omega ]^n$ whose solutions compute the halting set. On the other hand, for every computable k-coloring of $[\omega ]^2$ and every noncomputable set C, there is an infinite monochromatic set H such that $C \not \leq _T H$. The latter property is known as cone avoidance.In this article, we design a natural class of Ramsey-like (...) theorems encompassing many statements studied in reverse mathematics. We prove that this class admits a maximal statement satisfying cone avoidance and use it as a criterion to re-obtain many existing proofs of cone avoidance. This maximal statement asserts the existence, for every k-coloring of $[\omega ]^n$, of an infinite subdomain $H \subseteq \omega $ over which the coloring depends only on the sparsity of its elements. This confirms the intuition that Ramsey-like theorems compute Turing degrees only through the sparsity of its solutions. (shrink)

The aim of this exploratory study was to examine client demographics and expectations, reasons for use, sensations during treatment, and perceived outcomes of Pranic Healing, an energy healing system lacking in scientific documentation but whose use in the general population is becoming more widespread internationally. This study consisted of a cross-sectional survey of adults (18+ years of age) receiving care from 12 Pranic Healing practices in four different states in the U.S. (N = 179) completing online questionnaires. Closed-ended response (...) sets were analyzed descriptively, while qualitative data were analyzed using content analysis. Reasons to use the therapy included physical, mental/emotional, and metaphysical issues, dissatisfaction with conventional care, and overall well-being. Expectations of care included enhanced abilities, cure or relief, or unsure. Respondents were more likely to cite a specific problem from which they needed alleviation than to cite overall health or wellness as their goal. Sensations experienced were reported to be of a relaxing nature and not, as was hypothesized, of an energizing nature. Results show that those who use Pranic Healing fit the sociodemographic profile of CAM (complementary and alternative medicine) users in the United States, that their reasons for use are not homogeneous, and that preliminary descriptive data from a selective subsample of respondents indicated that some respondents are experiencing positive outcomes attributed to this modality. (shrink)

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate—a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is (...) some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is definitely true and those of which it is definitely false. Taking as primitive the operator ‘it is definitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is definitely true (or definitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (DΦ(x) ∧ D¬Φ(y)) → ¬R(x, y). Here ‘Φ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate—such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the definitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

We write$\mathcal {S}_n(A)$for the set of permutations of a setAwithnnon-fixed points and$\mathrm {{seq}}^{1-1}_n(A)$for the set of one-to-one sequences of elements ofAwith lengthnwherenis a natural number greater than$1$. With the Axiom of Choice,$|\mathcal {S}_n(A)|$and$|\mathrm {{seq}}^{1-1}_n(A)|$are equal for all infinite setsA. Among our results, we show, in ZF, that$|\mathcal {S}_n(A)|\leq |\mathrm {{seq}}^{1-1}_n(A)|$for any infinite setAif${\mathrm {AC}}_{\leq n}$is assumed and this assumption cannot be removed. In the other direction, we show that$|\mathrm {{seq}}^{1-1}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setAand the subscript$n+1$cannot be reduced ton. (...) Moreover, we also show that “$|\mathcal {S}_n(A)|\leq |\mathcal {S}_{n+1}(A)|$for any infinite setA” is not provable in ZF. (shrink)

Hume's law, that is, that moral claims cannot be inferred from exclusively nonmoral claims, is widely accepted by recent and contemporary philosophers, some exceptions being John Searle and A. N. Prior. Chapter 1 distinguishes three versions of the law: the formal version ), the conceptual version ), and the epistemic version ), all of which, according to Salwén, are true. When "valid inference" means "a sentence is a logical consequence of a set of sentences K iff there is no interpretation (...) under which all the sentences of K are true and x false", then the law is, HL: "For all valid arguments, K>X, and all moral expressions Ö, if Ö occurs nonvacuously in X, then Ö appears in K". When "valid inference" means an inference "such that the truth of the premise conceptually guarantees the truth of the conclusion", and when a bridge premise is a conditional sentence whose antecedent is a nonmoral sentence and whose consequence is a categorial norm or moral sentence, then the law reads, HL: "There are no analytic bridge sentences". Thus, HL implies, as against Searle, that the bridge premise, "If Jones has promised to pay Smith five dollars, then Jones ought to pay Smith five dollars," is false. Unlike either HL or HL, HL is about nonmoral reasons for holding moral beliefs. Thus, "HL implies that, say, the acceptance of 'Jones has promised to pay Smith five dollars' is a reason to accept 'Jones ought to pay Smith five dollars' only if it is accepted that promises ought to be kept". (shrink)

continent. 1.1 : 3-13. / 0/ – Introduction I want to propose, as a trajectory into the philosophically weird, an absurd theoretical claim and pursue it, or perhaps more accurately, construct it as I point to it, collecting the ground work behind me like the Perpetual Train from China Mieville's Iron Council which puts down track as it moves reclaiming it along the way. The strange trajectory is the following: Kant's critical philosophy and much of continental philosophy which has followed, (...) has been a defense against horror and madness. Kant's prohibition on speculative metaphysics such as dogmatic metaphysics and transcendental realism, on thinking beyond the imposition of transcendental and moral constraints, has been challenged by numerous figures proceeding him. One of the more interesting critiques of Kant comes from the mad black Deleuzianism of Nick Land stating, “Kant’s critical philosophy is the most elaborate fit of panic in the history of the Earth.” And while Alain Badiou would certainly be opposed to the libidinal investments of Land's Deleuzo-Guattarian thought, he is likewise critical of Kant's normative thought-bureaucracies: Kant is the one author for whom I cannot feel any kinship. Everything in him exasperates me, above all his legalism—always asking Quid Juris? Or ‘Haven’t you crossed the limit?’—combined, as in today’s United States, with a religiosity that is all the more dismal in that it is both omnipresent and vague. The critical machinery he set up has enduringly poisoned philosophy, while giving great succour to the academy, which loves nothing more than to rap the knuckles of the overambitious [….] That is how I understand the truth of Monique David-Menard’s reflections on the properly psychotic origins of Kantianism. I am persuaded that the whole of the critical enterprise is set up to to shield against the tempting symptom represented by the seer Swedenborg, or against ‘diseases of the head’, as Kant puts it. An entire nexus of the limits of reason and philosophy are set up here, namely that the critical philosophy not only defends thought from madness, philosophy from madness, and philosophy from itself, but that philosophy following the advent of the critical enterprise philosophy becomes auto-vampiric; feeding on itself to support the academy. Following Francois Laruelle's non-philosophical indictment of philosophy, we could go one step further and say that philosophy operates on the material of what is philosophizable and not the material of the external world. [1] Beyond this, the Kantian scheme of nestling human thinking between our limited empirical powers and transcendental guarantees of categorical coherence, forms of thinking which stretch beyond either appear illegitimate, thereby liquefying both pre-critical metaphysics and the ravings of the mad in the same critical acid. In rejecting the Kantian apparatus we are left with two entities – an unsure relation of thought to reality where thought is susceptible to internal and external breakdown and a reality with an uncertain sense of stability. These two strands will be pursued, against the sane-seal of post-Kantian philosophy by engaging the work of weird fiction authors H.P. Lovecraft and Thomas Ligotti. The absolute inhumanism of the formers universe will be used to describe a Shoggothic Materialism while the dream worlds of the latter will articulate the mad speculation of a Ventriloquil Idealism. But first we must address the relation of philosophy to madness as well as philosophy to weird fiction. /1/ – Philosophy and Madness There is nothing that the madness of men invents which is not either nature made manifest or nature restored. Michel Foucault. Madness and Civilization. The moment I doubt whether an event that I recall actually took place, I bring the suspicion of madness upon myself: unless I am uncertain as to whether it was not a mere dream. Arthur Schopenhauer. The World as Will and Idea, Vol. 3. Madness is commonly thought of as moving through several well known cultural-historical shifts from madness as a demonic or otherwise theological force, to rationalization, to medicalization psychiatric and otherwise. Foucault's Madness and Civilization is well known for orientating madness as a form of exclusionary social control which operated by demarcating madness from reason. Yet Foucault points to the possibility of madness as the necessity of nature at least prior to the crushing weight of the church. Kant’s philosophy as a response to madness is grounded by his humanizing of madness itself. As Adrian Johnston points out in the early pages of Time Driven pre-Kantian madness meant humans were seized by demonic or angelic forces whereas Kantian madness became one of being too human. Madness becomes internalized, the external demonic forces become flaws of the individual mind. Foucault argues that, while madness is de-demonized it is also dehumanized during the Renaissance, as madmen become creatures neither diabolic nor totally human reduced to the zero degree of humanity. It is immediately clear why for Kant, speculative metaphysics must be curbed – with the problem of internal madness and without the external safeguards of transcendental conditions, there is nothing to formally separate the speculative capacities for metaphysical diagnosis from the mad ramblings of the insane mind – both equally fall outside the realm of practicality and quotidian experience. David-Menard's work is particularly useful in diagnosing the relation of thought and madness in Kant's texts. David-Menard argues that in Kant's relatively unknown “An Essay on the Maladies of the Mind” as well as his later discussion of the Seer of Swedenborg, that Kant formulates madness primarily in terms of sensory upheaval or other hallucinatory theaters. She writes: “madness is an organization of thought. It is made possible by the ambiguity of the normal relation between the imaginary and the perceived, whether this pertains to the order of sensation or to the relations between our ideas” Kant's fascination with the Seer forces Kant between the pincers of “aesthetic reconciliation” – namely melancholic withdrawal – and “a philosophical invention” – namely the critical project. Deleuze and Guattari's schizoanalysis is a combination and reversal of Kant's split, where an aesthetic over engagement with the world entails prolific conceptual invention. Their embrace of madness, however, is of course itself conceptual despite all their rhizomatic maneuvers. Though they move with the energy of madness, Deleuze and Guattari save the capacity of thought from the fangs of insanity by imbuing materiality itself with the capacity for thought. Or, as Ray Brassier puts it, “Deleuze insists, it is necessary to absolutize the immanence of this world in such a way as to dissolve the transcendent disjunction between things as we know them and as they are in themselves”. That is, whereas Kant relied on the faculty of judgment to divide representation from objectivity Deleuze attempts to flatten the whole economy beneath the juggernaut of ontological univocity. Speculation, as a particularly useful form of madness, might fall close to Deleuze and Guattari’s shaping of philosophy into a concept producing machine but is different in that it is potentially self destructive – less reliant on the stability of its own concepts and more adherent to exposing a particular horrifying swath of reality. Speculative madness is always a potential disaster in that it acknowledges little more than its own speculative power with the hope that the gibbering of at least a handful of hysterical brains will be useful. Pre-critical metaphysics amounts to madness, though this may be because the world itself is mad while new attempts at speculative metaphysics, at post-Kantian pre-critical metaphysics, are well aware of our own madness. Without the sobriety of the principle of sufficient reason we have a world of neon madness: “we would have to conceive what our life would be if all the movements of the earth, all the noises of the earth, all the smells, the tastes, all the light – of the earth and elsewhere, came to us in a moment, in an instant – like an atrocious screaming tumult of things”. Speculative thought may be participatory in the screaming tumult of the world or, worse yet, may produce its spectral double. Against theology or reason or simply commonsense, the speculative becomes heretical. Speculation, as the cognitive extension of the horrorific sublime should be met with melancholic detachment. Whereas Kant's theoretical invention, or productivity of thought, is self -sabotaging, since the advent of the critical project is a productivity of thought which then delimits the engine of thought at large either in dogmatic gestures or non-systematizable empirical wondrousness. The former is celebrated by the fiction of Thomas Ligotti whereas the latter is espoused by the tales of H.P. Lovecraft. /2/ – Weird Fiction and Philosophy. Supernatural horror, in all its eerie constructions, enables a reader to taste treats inconsistent with his personal welfare. Thomas Ligotti Songs of a Dead Dreamer. I choose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve,momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which forever imprison us and frustrate our curiosity about the infinite cosmic spaces beyond the radius of our sight and analysis H.P. Lovecraft. “Notes on Writing Weird Fiction” Lovecraft states that his creation of a story is to suspend natural law yet, at the same time, he indexes the tenuousness of such laws, suggesting the vast possibilities of the cosmic. The tension that Lovecraft sets up between his own fictions and the universe or nature is reproduced within his fictions in the common theme of the unreliable narrator; unreliable precisely because they are either mad or what they have witnessed questions the bounds of material reality. In “The Call of Cthulhu” Lovecraft writes: The most merciful thing in the world, I think, is the inability of the human mind to correlate all its contents. We live on a placid island of ignorance in the midst of black seas of infinity, and it was not meant that we should voyage far. The sciences, each straining in its own direction, have hitherto harmed us little; but some day the piecing together of dissociated knowledge will open up such terrifying vistas of reality, and of our frightful position therein, that we shall either go mad from the revelation or flee from the deadly light into the peace and safety of a new dark age. Despite Lovecraft's invocations of illusion, he is not claiming that his fantastic creations such as the Old Ones are supernatural but, following Joshi, are only ever supernormal. One can immediately see that instead of nullifying realism Lovecraft in fact opens up the real to an unbearable degree. In various letters and non-fictional statements Lovecraft espoused strictly materialist tenets, ones which he borrowed from Hugh Elliot namely the uniformity of law, the denial of teleology and the denial of non-material existence. Lovecraft seeks to explore the possibilities of such a universe by piling horror upon horror until the fragile brain which attempts to grasp it fractures. This may be why philosophy has largely ignored weird fiction – while Deleuze and Guattari mark the turn towards weird fiction and Lovecraft in particular, with the precursors to speculative realism as well as contemporary related thinkers have begun to view Lovecraft as making philosophical contributions. Lovecraft's own relation to philosophy is largely critical while celebrating Nietzsche and Schopenhauer. This relationship of Lovecraft to philosophy and philosophy to Lovecraft is coupled with Lovecraft's habit of mercilessly destroying the philosopher and the figure of the academic more generally in his work, a destruction which is both an epistemological destruction and an ontological destruction. Thomas Ligotti's weird fiction which he has designated as a kind of “confrontational escapism” might be best described in the following quote from one of his shortstories, “The human phenomenon is but the sum of densely coiled layers of illusion each of which winds itself on the supreme insanity. That there are persons of any kind when all there can be is mindless mirrors laughing and screaming as they parade about in an endless dream”. Whereas Lovecraft's weirdness draws predominantly from the abyssal depths of the uncharted universe, Ligotti's existential horror focuses on the awful proliferation of meaningless surfaces that is, the banal and every day function of representation. In an interview, Ligotti states: We don't even know what the world is like except through our sense organs, which are provably inadequate. It's no less the case with our brains. Our whole lives are motored along by forces we cannot know and perceptions that are faulty. We sometimes hear people say that they're not feeling themselves. Well, who or what do they feel like then? This is not to say that Ligotti sees nothing beneath the surface but that there is only darkness or blackness behind it, whether that surface is on the cosmological level or the personal. By addressing the implicit and explicit philosophical issues in Ligotti's work we will see that his nightmarish take on reality is a form of malevolent idealism, an idealism which is grounded in a real, albeit dark and obscure materiality. If Ligotti's horrors ultimately circle around mad perceptions which degrade the subject, it takes aim at the vast majority of the focus of continental philosophy. While Lovecraft's acidic materialism clearly assaults any romantic concept of being from the outside, Ligotti attacks consciousness from the inside: Just a little doubt slipped into the mind, a little trickle of suspicion in the bloodstream, and all those eyes of ours, one by one, open up to the world and see its horror [...] Not even the solar brilliance of a summer day will harbor you from horror. For horror eats the light and digests it into darkness. Clearly, the weird fiction of Lovecraft and Ligotti amount to a anti-anthrocentric onslaught against the ramparts of correlationist continental philosophy. /3/ – Shoggothic Materialism or the Formless Formless protoplasm able to mock and reflect all forms and organs and processes—viscous agglutinations of bubbling cells—rubbery fifteen-foot spheroids infinitely plastic and ductile—slaves of suggestion, builders of cities—more and more sullen, more and more intelligent, more and more amphibious, more and more imitative—Great God! What madness made even those blasphemous Old Ones willing to use and to carve such things? H.P. Lovecraft. “At the Mountains of Madness” On the other hand, affirming that the universe resembles nothing and is only formless amounts to saying that the universe is something like a spider or spit. Georges Bataille. “Formless”. The Shoggoths feature most prominently in H.P. Lovecraft's shortstory “At the Mountains of Madness” where they are described in the following manner: It was a terrible, indescribable thing vaster than any subway train – a shapeless congeries of protoplasmic bubbles, faintly self -luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter. The term is a litmus test for materialism itself as the Shoggoth is an amorphous creature. The Shoggoths were living digging machines bio engineered by the Elder Things, and their protoplasmic bodies being formed into various tools by their hypnotic powers. The Shoggoths eventually became self aware and rose up against their masters in an ultimately failed rebellion. After the Elder Ones retreated into the oceans leaving the Shoggoths to roam the frozen wastes of the Antarctic. The onto-genesis of the Shoggoths and their gross materiality, index the horrifyingly deep time of the earth a concept near and dear to Lovecraft's formulation of horror as well as the fear of intelligences far beyond, and far before, the ascent of humankind on earth and elsewhere. The sickly amorphous nature of the Shoggoths invade materialism at large, where while materiality is unmistakably real ie not discursive, psychological, or otherwise overly subjectivist, it questions the relation of materialism to life. As Eugene Thacker writes: The Shoggoths or Elder Things do not even share the same reality with the human beings who encounter them—and yet this encounter takes place, though in a strange no-place that is neither quite that of the phenomenal world of the human subject or the noumenal world of an external reality. Amorphous yet definitively material beings are a constant in Lovecraft's tales. In his tale “The Dream-Quest of Unknown Kadatth” Lovecraft describes Azathoth as, “that shocking final peril which gibbers unmentionably outside the ordered universe,” that, “last amorphous blight of nethermost confusion which blashphemes and bubbles at the centre of all infinity,” who, “gnaws hungrily in inconceivable, unlighted chambers beyond time”. Azathoth's name may have multiple origins but the most striking is the alchemy term azoth which is both a cohesive agent and a acidic creation pointing back to the generative and the decayed. The indistinction of generation and degradation materially mirrors the blur between the natural and the unnatural as well as life and non-life. Lovecraft speaks of the tension between the natural and the unnatural is his short story “The Unnameable.” He writes, “if the psychic emanations of human creatures be grotesque distortions, what coherent representation could express or portray so gibbous and infamous a nebulousity as the spectre of a malign, chaotic perversion, itself a morbid blasphemy against Nature?”. Lovecraft explores exactly the tension outlined at the beginning of this chapter, between life and thought. At the end of his short tale Lovecraft compounds the problem as the unnameable is described as “a gelatin—a slime—yet it had shapes, a thousand shapes of horror beyond all memory”. Deleuze suggests that becoming-animal is operative throughout Lovecraft's work, where narrators feel themselves reeling at their becoming non-human or of being the anomalous or of becoming atomized. Following Eugene Thacker however, it may be far more accurate to say that Lovecraft's tales exhibit not a becoming-animal but a becoming-creature. Where the monstrous breaks the purportedly fixed laws of nature, the creature is far more ontologically ambiguous. The nameless thing is an altogether different horizon for thought. The creature is either less than animal or more than animal – its becoming is too strange for animal categories and indexes the slow march of thought towards the bizarre. This strangeness is, as aways, some indefinite swirling in the category of immanence and becoming. Bataille begins “The Labyrinth” with the assertion that being, to continue to be, is becoming. More becoming means more being hence the assertion that Bataille's barking dog is more than the sponge. This would mean that the Shoggotth is altogether too much being, too much material in the materialism. Bataille suggests that there is an immanence between the eater and the eaten, across the species and never within them. That is, despite the chaotic storm of immanence there must remain some capacity to distinguish the gradients of becoming without reliance upon, or at least total dependence upon, the powers of intellection to parse the universe into recognizable bits, properly digestible factoids. That is, if we undo Deleuze's aforementioned valorization of sense which, for his variation of materialism, performed the work of the transcendental, but refuse to reinstate Kant's transcendental disjunction between thing and appearance, then it must be a quality of becoming-as-being itself which can account for the discernible nature of things by sense. In an interview with Peter Gratton, Jane Bennett formulates the problem thusly: What is this strange systematicity proper to a world of Becoming? What, for example, initiates this congealing that will undo itself? Is it possible to identify phases within this formativity, plateaus of differentiation? If so, do the phases/plateaus follow a temporal sequence? Or, does the process of formation inside Becoming require us to theorize a non-chronological kind of time? I think that your student’s question: “How can we account for something like iterable structures in an assemblage theory?” is exactly the right question. Philosophy has erred too far on the side of the subject in the subject-object relation and has furthermore, lost the very weirdness of the non-human. Beyond this, the madness of thought need not override. /4/ - Ventriloquial Idealism or the Externality of Thought My aim is the opposite of Lovecraft's. He had an appreciation for natural scenery on earth and wanted to reach beyond the visible in the universe. I have no appreciation for natural scenery and want the objective universe to be a reflection of a character. Thomas Ligotti. “Devotees of Decay and Desolation.” Unless life is a dream, nothing makes sense. For as a reality, it is a rank failure [….] Horror is more real than we are. Thomas Ligotti. “Professor Nobody's Little Lectures on Supernatural Horror”. Thomas Ligotti's tales are rife with mannequins, puppets, and other brainless entities which of replace the valorized subject of philosophy – that of the free thinking human being. His tales such as “The Dream of the Manikin” aim to destroy the rootedness of consciousness. James Trafford has connected the anti-egoism of Ligotti to Thomas Metzinger – where the self is at best an illusion and we plead desperately for someone else to acknowledge that we are real. Trafford has stated it thus, “Life is played out as an inescapable puppet show, an endless dream in which the puppets are generally unaware that they are trapped within a mesmeric dance of whose mechanisms they know nothing and over which they have no control”. An absolute materialism, for Ligotti, implies an alienation of the idea which leads to a ventriloquil idealism. As Ligotti notes in an interview, “the fiasco and nightmare of existence, the particular fiasco and nightmare of human existence, the sense that people are puppets of powers they cannot comprehend, etc.” And then further elaborates that,“[a]ssuming that anything has to exist, my perfect world would be one in which everyone has experienced the annulment of his or her ego. That is, our consciousness of ourselves as unique individuals would entirely disappear”. The externality of the idea leads to the unfortunate consequence of consciousness eating at itself through horror which, for Ligotti, is more real than reality and goes beyond horror-as-affect. Beyond this, taking together with the unreality of life and the ventriloquizing of subjectivity, Ligotti's thought becomes an idealism in which thought itself is alien and ultimately horrifying. The role of human thought and the relation of non-relation of horror to thought is not completely clear in Ligotti's The Conspiracy Against the Human Race. Ligotti argues in his The Conspiracy Against the Human Race,that the advent of thought is a mistake of nature and that horror is being in the sense that horror results from knowing too much. Yet, at the same time, Ligotti seems to suggest that thought separates us from nature whereas, for Lovecraft, thought is far less privileged – mind is just another manifestation of the vital principal, it is just another materialization of energy. In his brilliant “Prospects for Post-Copernican Dogmatism” Iain Grant rallies against the negative definition of dogmatism and the transcendental, and suggests that negatively defining both over-focuses on conditions of access and subjectivism at the expense of the real or nature. With Schelling, who is Grant's champion against the subjectivist bastions of both Fichte and Kant, Ligotti's idealism could be taken as a transcendental realism following from an ontological realism. Yet the transcendental status of Ligotti's thought move towards a treatment of the transcendental which may threaten to leave beyond its realist ground. Ligotti states: Belief in the supernatural is only superstition. That said, a sense of the supernatural, as Conrad evidenced in Heart of Darkness, must be admitted if one's inclination is to go to the limits of horror. It is the sense of what should not be- the sense of being ravaged by the impossible. Phenomenally speaking, the super-natural may be regarded as the metaphysical counterpart of insanity, a transcendental correlative of a mind that has been driven mad. Again, Ligotti equates madness with thought, qualifying both as supernatural while remaining less emphatic about the metaphysical dimensions of horror. The question becomes one of how exactly the hallucinatory realm of the ideal relates to the black churning matter of Lovecraft's chaos of elementary particles. In his tale “I Have a Special Plan for This World” Ligotti formulates thus: A: There is no grand scheme of things. B: If there were a grand scheme of things, the fact – the fact – that we are not equipped to perceive it, either by natural or supernatural means, is a nightmarish obscenity. C: The very notion of a grand scheme of things is a nightmarish obscenity. Here Ligotti is not discounting metaphysics but implying that if it does exist the fact that we are phenomenologically ill-equipped to perceive that it is nightmarish. For Ligotti, nightmare and horror occur within the circuit of consciousness whereas for Lovecraft the relation between reality and mind is less productive on the side of mind. It is easier to ascertain how the Kantian philosophy is a defense against the diseases of the head as Kant armors his critical enterprise from too much of the world and too much of the mind. The weird fiction of both Lovecraft and Ligotti demonstrates that there is too much of both feeding into one another in a way that corrodes the Kantian schema throughly, breaking it down into a dead but still ontologically potentiated nigredo. The haunting, terrifying fact of Ligotti's idealism is that the transcendental motion which brought thought to matter, while throughly material and naturalized, brings with it the horror that thought cannot be undone without ending the material that bears it either locally or completely. Thought comes from an elsewhere and an elsewhen being-in-thought. The unthinkable outside thought is as maddening as the unthought engine of thought itself within thought which doesn't exist except for the mind, the rotting décor of the brain. /5/ - Hyperstitional Transcendental Paranoia or Self -Expelled Thought Weird fiction has been given some direct treatment in philosophy in the mad black Deleuzianism of Nick Land. Nick Land along with others in the 1990s created the Cyber Culture Research Unit as well as the research group Hyperstition. The now defunct hyperstitional website, an outgrowth of the Cyber Culture Research Unit, defined hyperstition in the following fourfold: 1-Element of effective culture that makes itself real. 2-Fictional quantity functional as a time-traveling device. 3-Coincidence intensifier. 4-Call to the Old Ones. The distinctively Lovecraftian character of hyperstition is hard to miss as is its Deleuzo-Guattarian roots. In the opening pages of A Thousand Plateaus Deleuze and Guattari write, “We have been criticized for over-quoting literary authors. But when one writes, the only question is which other machine the literary machine can be plugged into”. The indisinction of literature and philosophy mirrors the mess of being and knowing as post-correlationist philosophy, where philosophy tries to make itself real where literature, especially the weird, aims itself at the brain-circuit of horror. The texts of both Lovecraft and Ligotti work through horror as epistemological plasticity meeting with proximity as well as the deep time of Lovecraft and the glacially slow time of paranoia in Ligotti. Against Deleuze, and following Brassier, we cannot allow the time of consciousness, the Bergsonian time of the duree, to override natural time, but instead acknowledge that it is an unfortunate fact of existence as a thinking being. Horror-time, the time of consciousness, with all its punctuated moments and drawn out terrors, cannot compare to the deep time of non-existence both in the unreachable past and the unknown future. The crystalline cogs of Kant's account of experience as the leading light for the possibility of metaphysics must be throughly obliterated. His gloss of experience in Prolegomena to any Future Metaphysics could not be more sterile: Experience consists of intuitions, which belong to the sensibility, and of judgments, which are entirely a work of the understanding. But the judgments which the understanding makes entirely out of sensuous intuitions are far from being judgments of experience. For in the one case the judgment connects only the perceptions as they are given in sensuous intuition [....] Experience consists in the synthetic connection of appearances in consciousness, so far as this connection is necessary. Here it is difficult to dismiss the queasiness that Kant's legalism induces upon sight for both Badiou and David-Menard. Kant's thought becomes, as Foucault says when reflecting on Sade's text in relation to nature, “the savage abolition of itself”. For Badiou, Kant's philosophy simply closes off too much of the outside, freezing the world of thought in an all too limited formalism. Critical philosophy is simply the systematized quarantine on future thinking, on thinking which would threaten the formalism which artificially grants thought its own coherency in the face of madness. Even the becoming-mad of Deleuze, while escaping the rumbling ground, makes grounds for itself, mad grounds but grounds which are thinkable in their affect. The field of effects allows for Deleuze's aesthetic and radical empiricism, in which effects and/or occasions make up the material of the world to be thought as a chaosmosis of simulacra. Given a critique of an empiricism of aesthetics, of the image, it may be difficult to justify an attack on Kantian formalism with the madness of literature, which does not aim to make itself real but which we may attempt to make real. That is, how do Lovecraft's and Ligotti's materials, as materials for philosophy to work on, differ from either the operative formalisms of Kant or the implicitly formalized images of Deleuzian empiricism? It is simply that such texts do not aim to make themselves real, and make claims to the real which are more alien to us than familiar, which is why their horror is immediately more trustworthy. This is the madness which Blanchot discusses in The Infinite Conversation through Cervantes and his knight – the madness of book-life, of the perverse unity of literature and life a discussion which culminates in the discussion of one of the weird's masters, that of Kafka. The text is the knowing of madness, since madness, in its moment of becoming-more-mad, cannot be frozen in place but by the solidifications of externalizing production. This is why Foucault ends his famous study with works of art. Furthermore extilligence, the ability to export the products of our maligned brains, is the companion of the attempts to export, or discover the possibility of intelligences outside of our heads, in order for philosophy to survive the solar catastrophe. To borrow again from Deleuze, writing is inseparable from becoming. The mistake is to believe that madness is reabsorbed by extilligence, by great works, or that it could be exorcised by the expelling of thought into the inorganic or differently organic. Going out of our heads does not guarantee we will no longer mean we cannot still go out of our minds. This is simply because of the outside, of matter, or force, or energy, or thing-in-itself, or Schopenhauerian Will. In Lovecraft’s “The Music of Erich Zahn” an “impoverished student of metaphysics” becomes intrigued by strange viol music coming from above his room. After meeting the musician the student discovers that each night he plays frantic music at a window in order to keep some horridness at bay, some “impenetrable darkness with chaos and pandemonium”. The aesthetic defenses provided by the well trained brain can bear the hex of matter for so long, the specter of unalterability within it which too many minds obliterate, collapsing everything before the thought of thought as thinkable or at least noetically mutable on our own terms. Transcendental paranoia is the concurrent nightmare and promise of Paul Humphrey's work, of being literally out of our minds. It is the gothic counterpart of thinking non-conceptually but also of thinking never belonging to any instance of purportedly solid being. As Bataille stated, “At the boundary of that which escapes cohesion, he who reflects within cohesion realizes there is no longer any room for him” Thought is immaterial only to the degree that it is inhuman, it is a power that tries, always with failure, to ascertain its own genesis. Philosophy, if it can truly return to the great outdoors, if it can leave behind the dead loop of the human skull, must recognize not only the non-priority of human thought, but that thought never belongs to the brain that thinks it, thought comes from somewhere else. To return to the train image from the beginning “a locomotive rolling on the surface of the earth is the image of continuous metamorphosis” this is the problem of thought, and of thinking thought, of being no longer able to isolate thought, with only a thought-formed structure. [1] One of the central tenets of Francois Laruelle's non-philosophy is that philosophy has traditionally operated on material already presupposed as thinkable instead of trying to think the real in itself. Philosophy, according to Laruelle, remains fixated on transcendental synthesis which shatters immanence into an empirical datum and an a prori factum which are then fused by a third thing such as the ego. For a critical account of Laruelle's non-philosophy see Ray Brassier's Nihil Unbound. (shrink)

We examine the reverse mathematical strength of a variation of Hindman’s Theorem (HT) constructed by essentially combining HT with the Thin Set Theorem to obtain a principle that we call thin-HT. This principle states that every coloring c:N→N has an infinite set S⊆N whose finite sums are thin for c, meaning that there is an i with c(s)≠i for all nonempty sums s of finitely many distinct elements of S. We show that there is a computable instance of (...) thin-HT such that every solution computes ∅′, as is the case with HT, as shown by Blass, Hirst, and Simpson (1987). In analyzing this proof, we deduce that thin-HT implies ACA0 over RCA0+IΣ20. On the other hand, using Rumyantsev and Shen’s computable version of the Lovász Local Lemma, we show that there is a computable instance of the restriction of thin-HT to sums of exactly 2 elements such that any solution has diagonally noncomputable degree relative to ∅′. Hence there is a computable instance of this restriction of thin-HT with no Σ20 solution. (shrink)

Architecture and Deconstruction Case of Peter Eisenman and Bernard Tschumi -/- Introduction Towards deconstruction in architecture Intensive relations between philosophical deconstruction and architecture, which were present in the late 1980s and early 1990s, belong to the past and therefore may be described from a greater than before distance. Within these relations three basic variations can be distinguished: the first one, in which philosophy of deconstruction deals with architectural terms but does not interfere with real architecture, the second one, in which (...) a collaboration between Jacques Derrida and a group of architects interested in his concepts is commenced, and the third one, in which completed or only designed objects or new concepts of deconstruction created by architects gain their supremacy over philosophy. The following book analyses these three possible ways, first of all with the reference to Peter Eisenman and Bernard Tschumi. -/- Peter Eisenman -/- Misreading… and Other Errors -/- The issue of relations between Peter Eisenman’s work and philosophy of deconstruction may be referred to his activity more than ten years preceding his direct collaboration with Jacques Derrida (in 1985) and organisation of the exhibition Deconstructivist Architecture at Museum of Modern Art in New York (in 1988). As soon as at the stage of designing the first houses (House I-III, 1967-1970), which almost entirely inscribed in formalistic aesthetics of Modernism, the architect analysed the problem of architecture dependence on its assumptions. All his later designs may be treated as consequence of this initial interest in relations between practice and theory, and at the same time as an introduction to manipulations later on led at the level of metaphysics of architecture. Beginning with the issue of presence, considered in comments to House VI (1972), the number of ideas having their analogies in philosophy of deconstruction increased. The text entitled The End of the Classical: The End of the Beginning, The End of the End (1984), in which Eisenman criticised questions of representation in architecture, its delusive strive for truth and comparably unattainable attempts at ultimate definition of elementary rules, should be acclaimed the breaking point. This attitude was extended by numerous strategies disturbing architecture rules defined at metaphysical level in an essay Moving Arrows, Eros, and Other Errors: an Architecture of Absence (1986). The issue of Eisenman’s passage from formalism to deconstruction has already been much discussed in the literature (Rosalind Krauss, Thomas Patin among others), still it should be mentioned that the threads similar to Derrida’s concept included in Eisenman’s writing reveal untranslatability of architecture and philosophy. -/- Choral Works or Separate tricks -/- In 1985-1986 a series of seven disputes between Jacques Derrida and Peter Eisenman took place. The pretext for them were designs concerning Parc de la Villette in Paris. The situation of many months of collaboration between a notable philosopher of the second half of the 20th c. and an architect that already had a huge theoretical oeuvre, ended up with a publication of a large volume entitled Chora L Works and it became at the same time a vast study area for historians of contemporary architecture and philosophers. Derrida’s contribution to concept works were his considerations over the idea of chôra, the properties related to this concept were about to be reflected in shapes of the park. Therefore, Chora L Works became an example of the abilities of contemporary art, both in its capability of translation from philosophical ideas to artistic forms and its resistance to tradition of representing in architecture some phenomena and values originating outside this discipline. In the final period of their collaboration both interlocutors started to polemicise with each other more decidedly, what became a separate part of their thought exchange. The exchange of letters between Derrida and Eisenman at the turn of 1989 ended up the period of their direct contacts, nevertheless, at this time precisely a large group of experts in issues of deconstruction joined the discussion and extended the revealed in the former dispute problems into more than ten years of further considerations and publications. Except for a long text by Jeffrey Kipnis, who had participated in the meetings of the philosopher and the architect, there appeared also comments of researchers of artistic theories (K. Michael Hays, Thomas Patin), philosophers (Andrew Benjamin), and even experts in Greek literature (Maria Theodorou or Ann Bergren). Following these debates a contemporary reflection on architecture has saturated with indeed numerous concepts originating in philosophy of deconstruction. -/- Architecture which imitates mute philosophy -/- The series of Jacques Derrida and Peter Eisenman meetings, which took place in the period of 1985-1987, induced many authors to make comments. Some of them (Jeffrey Kipnis, Ann Bergren, Maria Theodorou) developed the subject of chôra which was introduced to the discussion by Derrida. The problem that was about to be solved was the question of tying up the concept of chôra with architecture, including Eisenman’s architecture and the series of meetings within frames of Chora L Works project. Kipnis on this occasion paid attention to chôra and its character of anachronia which infects any being created within chôra. In other words any event has its counterpart (analogon) in another, earlier event. He demonstrated the similarity of structure of many events and statements from the times of Derrida and Eisenman’s meetings to the almost identical behaviour of figures in Plato’s dialogue Timaeus. The loss of beginning present in this phenomenon was appropriate to both features of chôra and the effects of typical analyses of philosophy of deconstruction. Bergren’s analyses focused on accentuating gender of chôra, which, according to this author, had been neglected hitherto in discussions. She collated chôra descriptions with characteristics of women in myths, early Greek epic and philosophy and she arrived at a conclusion that chôra has features of a single woman and a married one at the same time. And yet Theodorou’s studies showed that in the Homeric epics chôra is not treated as an idea but is related with single things and events. The other part of the comments (represented by Andrew Benjamin and K. Michael Hays’ utterances) concerns Eisenman’s attitude to tradition which was treated as a variety of iteration understood philosophically. Benjamin commenced his considerations at the point of closeness between a definition of tradition and a concept of chôra understood as perpetuation (placement). A problematic issue was for him Eisenman’s complex relation to tradition based on its contest and affirmation at the same time. Overcoming the simple subordination to tradition – according to Benjamin – was based on awareness of the role of repetition in culture not known before. Hays made an attempt to explain the pleasure and torment of repetition with the support of Sigmund Freud and Roland Barthes’ concepts. According to Hays repetitions are attempts of a single being to a certain primal state perceived as free of any tension. In a similar way Rosalind Krauss explained a motif of a grate present in Modernistic art and also exceptionally frequent in Eisenman’s work. -/- Annex Architecture is still writing Balzac novels. Peter Eisenman and literature -/- Architecture’s approach to writing, script or literature, present within Peter Eisenman’s work, is an exceptional phenomenon, furthermore a complex one. The article considers four possible relations. The first one relates to Eisenman’s characteristics as a person extremely gifted with the ability to wordplay, which very ‘play’ reveals skills to create architectural images. In the second approach the attention has been paid to Eisenman’s interests – in the first period of his oeuvre – in linguistic works by Noam Chomsky and his transformational-generative grammar. The third kind of relations applied to overcoming the need for autonomy of architecture (and of modernist aesthetics at the same time) and renew interests in questions of meaning in architecture. The fourth sort of relations occurred when Eisenman started to create reflections of historic or literary narrations in architecture – ‘stone stories’ and architectural fictions of their kind. -/- Bernard Tschumi -/- From perversion to deconstruction In Bernard Tschumi’s writings from the 1970s and 1980s we can find a transposition of important threads of post-structuralist ideas deriving from Georges Bataille, Roland Barthes and Jacques Derrida’s works. The analysis of the architect’s writings also shows roots in Phillippe Sollers, Michel Foucault and Denis Hollier’s works. The analysis of borrowed elements from the beginnings of Tschumi’s theoretical activity may be helpful in explaining the contents of his later writings motre inspired by philosophy of deconstruction. The set of his earliest views was inspired by Marxism, Neo Marxism and French Structuralism, mainly by the writings of Henri Levebre and Guy Debord. From the thought of Levebre Tschumi took interest for city as not only a question of urbanistics but also a political issue. From Debord’s concepts he borrowed a conviction about the role of situational violation for changes in the society structure. Some of these beliefs were preserved in his own concepts of architecture as an event. From this period derived also his will to change conservative elements of social structure not by means of political revolution but of theoretical and creative activity. Tschumi acknowledged that the effective way of the proceedings towards achieving his aims would be accepting the role of both a critical intellectualist and architecture expert who would not hide away his left-wing orientation. The speculations defined by the architect as ‘revolting analyses’ were about to characterise contradictions which tear the society apart, penetrate architecture and constitute the basis of culture. Spreading away of the conscience of false assumptions hidden away in various disciplines could have weakened cohesion of a conservative society and influence the will to change among the elites. This way the beginnings of political revolution were rooted in philosophy of architecture. In 1977 Tschumi published his text entitled The Pleasure of Architecture inspired by Roland Barthes’s The Pleasure of the Text, it also included some concepts derived from Georges Bataille and Jacques Derrida. First of all the author used Barthes’s concept which made an assumption that literary activity is pervaded by the spirit of resistance towards social rules, and Tschudi transferred this remark onto architecture. From the ideas of Bataille, acquainted via Holier’s work, he derived his belief that two concepts of space, a conceptual one (defined as Pyramid) and a sensual one (defined as Labirynth), not losing their distinct features, they join in the concept of experienced space which exceeds contradictions. The exceeding itself was defined as the basic rule of architecture and it was referred to situations in which architecture not only negates social needs, but also disavows its own tradition. Crossing the borders applies not only to political issues or permanent rules of the very discipline but also interfering with other fields (especially literature and film). The fact that architecture is associated with organising events turned Tschumi’s attention to questions of violence that result from upsetting architectural order of a given building by its users and the one hand, and on the other from forcing the users to specific acts imposed by this very order. The analysis of the concepts used by Tschumi in his early writings indicates that they are close to definitions that would occur in his reflection in the following years influenced by philosophy of deconstruction. -/- Approaching deconstruction Tschumi in his theories developed in the 1980s presumed that the current social world had undergone a deep process of decay, and the reaction against which ought to be based on ordering-up actions, and also preserving the main outline of disintegration of the whole and its elements in the state of conflict. The statements concerning the nature of the contemporary to Tschumi social relations were applied by him to the world of architecture, this led him to coming up with designing strategies that took into consideration the destabilised character of conditions in which works of architecture were created. New ways of conduct invented by Tschumi drew their inspiration from literature and research on literature, psychoanalysis, structural linguistics, structuralism and post structuralism, and eventually also deconstruction philosophy. The proposed methods were opposed by their author both to functionalism continuity trends and postmodern architecture. Tschumi’s proposals contradicted any forms of conservatism or traditionalism in political sphere as well as in reference to tendencies in architecture. They were not simple contradictions of social or architectural rules, they intrude them from the inside, weaken or escalate the already existing incongruities, they move the boundaries between the areas. Revolutionary illusions about the possibility of radical changes were replaced with strategies which completed, tainted or test former rules in the series of formal games of permutation and combination. Quite different from avant-garde formalism Tschumi’s games were not about maintaining the autonomy of a given area, but on the contrary – polluting it with other areas’ influences. Tschumi enjoyed demonstrating illusions of architecture concerning simple relations between form and function, or between form and meaning. Making use of Freud, Lacan and Foucault’s research he introduced a category of “madness” into architecture allowing an observation that the recognised norms are nothing but merely ones of many possible principles of behaviour, and their recognised status resulted from unjustified hindering innovativeness which is crucial for architecture. To reborn architecture’s capability of changing Tschumi also made use of Barthes’s discoveries concerning rules of narration and works by writers who applied in their writing knowledge on linguistics. Making a work’s author unclear by various mechanical transformations of its elements was however apparent only, and formal rigours imposed on the process of designing liberated possibilities difficult to obtain in more traditional creative action. Another mode of acting introduced by Tschumi was combining his work of elements deriving from outside architecture; joining space records with notation of motion and events accompanying architectural objects among others. These architectural and extra-architectural elements were not unified, on the contrary their heterogenous and conflictual character was stressed. This is how shock, anxiety and instability, typical for live in great metropolises, infiltrated architecture. Taking some ideas of deconstruction philosophy as a pattern Tschumi also took into critical consideration in his essays traditional in architecture oppositions between form and figuration, or theory and practice. By combining various inspirations he eventually worked out an idea of architectural event, which he understood as a series of actions contesting its own field, redefining its sources, principles and elements. An event, understood in this way, was not so much producing works as rather creating conditions of their production and at the same time designing the society different from a hierarchic one. -/- Park of deconstruction Among numerous philosophical strategies of deconstruction most frequently used was questioning the practice of strong opposition of two reasons. In many cases Bernard Tschumi’s writings just consider functioning of the conflict juxtaposition of the ideas of structure and ornament or theory and practice in history of architecture. Violation of traditional relations between terms of this kind, both old and modern, raised Jacques Derrida’s objections, when he was induced for the first time to co-operate with architects’ milieu. During this long lasting thought exchange the philosopher eventually acknowledged Bernard Tschumi’s arguments for reasoning the encroachment of architecture’s fundamental rules. Deconstruction applied in architecture was not a simple transposition or analogy of practices that had been applied by philosophy of deconstruction. We may even say that considering architectural terms became an important formula of deconstruction. Architecture understood in philosophical way became something beyond the practice and theory of its own discipline, a sort of metaphysics of both philosophy and architecture. The deliberate encroachment of simplicity of dividing architecture into theory and practice, for the first time became a clear aim for Tschumi in his drawings and texts entitled The Manhattan Transcripts. The contents of this series of works was a record of characteristic features of this New York district in such a way that not only objects were the subject of the record but also relations between objects, people and events. The record was about to take into consideration a conflict character of elements of this representation and at the same time to avoid applying to them the rule of mimetism. The record became a form of reflection over the very record by an increased control over the ways of representation. Architecture which was considered in the The Manhattan Transcripts was not directed to fulfill the needs of inhabitation or production, it was rather related with hitherto usually marginalised liminal situations: building ostentatiously big monuments, religious cult, war etc. Architecture operating in these relations focused also the attention on the included in it continuous tendency to overpass its own restrictions, the role of violence as its not recognised factor, or the meaning of excess and shock in its operation. Architecture moving from reason towards madness became even more visible in the design of Parisian Parc de la Villette, whose pavilions were defined as folies (in French it means both small park buildings and follies). The park was supposed to be on the one hand a reflection of traditional society disintegration while on the other it questioned basic rules of producing a work of architecture. The traditional rules of designing, based on ordering up, were replaced with the strategies of dysfunction and dissociation. In Tschumi’s opinion methods of this kind may be equivalent of what Derrida named différance. Instead of aiming at mergence, any diversity, plays or variations were strengthen. Tschumi’s texts, in which he explained his attitude, were completed by Derrida’s extent statement entitled Point de folie – Maintenant l’architecture. Derrida’s article is the most significant of all his statements on architecture as a form of thinking and activity. According to the philosopher, architecture should divide space (in French defined as espacement), what enables both thinking and action – it arranges the space of an event. Tschumi’s buildings, defined as folies, in an essential way destabilise any created order, and at the same time they refresh it. Derrida’s statement suggests that architecture may become both metaphor of an order merging a language or a society but also of inner forces which deconstruct and reconstruct it. Therefore architecture is at the same time a construction, a deconstruction and a reconstruction. Parc de la Villette stands out in this system with its attempt to step beyond the scheme of an easy repetition and its heading for chances of achieving more radical otherness. -/- Conclusion Destruction as construction. Paradoxes of deconstruction in architecture -/- Scepticism about persistence and common importance of fundamental values of human culture evinced in philosophers and writers’ works as early as in Greek antiquity, nevertheless it was not expressed so strongly as in the second half of the 20th century. Especially in Heidegger’s work Being and Time (although originated in 1927, still influential in all later philosophy) the following states were characterised: the state of losing the ground (Abgrund), of being out of sight (Unheimlichkeit) and of being out of dwelling (Un-zuhause-sein) – as the basis of self-confidence of conscious being there (Dasein). The entire criticism of philosophy of home and dwelling draws the inspiration from this early writing of the German philosopher, it combines crisis of basic terms of metaphysics with social conditions which are dictated by living in large metropolis. The crisis of both metaphysical foundation and home appears to be similar to the situation of weakening the relations between a man and his dwelling in extensively expanding cities. Whereas philosophy, as well as many disciplines of social sciences, have diagnosed for a long time the destabilisation of fundamental ideas of Western culture and crucial changes in the ways of dwelling, architecture itself occurred to be “the last fortress of metaphysics” (J. Derrida). Among contemporary architects, Peter Eisenman and Bernard Tschumi were the ones who engaged most decidedly in the issues of critical analysis of architecture foundation and its social role. Both the architects noticed new formulas of contemporary social and individual existence, tremendously different from the entire history, and at the same time they affirmed lack of adequacy of architecture concepts to new situations. Both Eisenman and Tschumi used to describe the existing architecture as a tool for consolidation of highly integrated and hierarchised societies, and also as a discipline extremely uncoincidental with the current character of social life based on ideas of freedom and diversity. The means to transform architecture and make a factor of further social changes out of it, was a concept that accentuated revealing the inner contradictions of this discipline, and considering them in designing strategies. Eisenman’s activity, in regard of what has just been noticed, was focused on questioning the basic rules of traditionally comprehended architecture, especially the rule of purpose. The American architect noticed that the concept of architecture as fulfilment the need of location, hides away the fact that the location has to be constantly reconsidered, and hence it is overtaken by change (dislocation). Therefore new concept of architecture propounded architectural activity to translocate the concept of location – more than before – but also to change its status perpetually. Such comprehended architecture should claim, as its main purpose, the constant revision of this purpose and create itself anew permanently. Even Eisenman’s earliest designs of houses nos. I-IV broke with such values as the sense of safety, closeness and familiarity, and just on the contrary they accentuated senses of strangeness, homelessness and loss of confidence. The contradictions within architecture noticed by Tschumi referred to combination of intellectual and sensual values in architecture, when their non-appropriation was defeated by an additional condition, namely the way of experience based on pleasure of excess, marked by insanity. The features of folly were especially visible in his designs of gardens, where the order of planning was mixed with sensual experience introduced by particular elements (both the ones created by nature, and the buildings defined as folies). Parc de la Villette designed by the French architect in Paris put in question not only the common understanding of purpose in architecture but also the ideas of order and integrity, as its plan was based on the combination of independent layers with records of grids of points, various lines and planes. The architecture that collides inadequate elements with each other was supposed to be a kind of an event with no beginning and no end. The architecture treated as an event became a form of a space weakened articulation that maintains its diversity and lack of accordance of the elements building it up. The analyses of Eisenman and Tschumi’s theoretical writings indicate how much the aims of architecture have actually changed; instead of supporting social persistence, the architecture is rather intensifying contradictions, and instead of providing people with the sense of safety, it sublimes danger. From simple acts of defamiliarisation, increasing the distance to itself and enhancing the role of theory, through discomfort, anxiety, not feeling someone at home, weirdness, excess, shock and violence, architecture reached the edge of stability and uncertainty, only to make an attempt at penetrating what is impossible and unutterable, and recording what cannot become the subject of any records. -/- . (shrink)

We say that a real X is n-generic relative to a perfect tree T if X is a path through T and for all $\Sigma _{n}^{0}(T)$ sets S, there exists a number k such that either X|k ∈ S or for all σ ∈ T extending X|k we have σ ∉ S. A real X is n-generic relative to some perfect tree if there exists such a T. We first show that for every number n all but countably many reals (...) are n-generic relative to some perfect tree. Second, we show that proving this statement requires ZFC− + "∃ infinitely many iterates of the power set of ω". Third, we prove that every finite iterate of the hyperjump. ${\cal O}^{(n)}$ , is not 2-generic relative to any perfect tree and for every ordinal α below the least λ such that supβ<i (βth admissible) = λ, the iterated hyperjump ${\cal O}^{(\alpha)}$ is not 5-generic relative to any perfect tree. Finally, we demonstrate some necessary conditions for reals to be 1-generic relative to some perfect tree. (shrink)

We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy ≠ 0). Theorem (...) 2. If R is a prime ring with an infinite center and R admits elimination of quantifiers, then R is an algebraically closed field. Let A be the class of finite fields. Let B be the class of 2 × 2 matrix rings over a field with a prime number of elements. Let C be the class of rings of the form $GF(p^n) \bigoplus GF(p^k)$ such that either n = k or g.c.d. (n, k) = 1. Let D be the set of ordered pairs (f, Q) where Q is a finite set of primes and f: Q → A ∪ B ∪ C such that the characteristic of the ring f(q) is q. Finally, let E be the class of rings of the form $\bigoplus_{q \in Q}f(q)$ for some (f, Q) in D. Theorem 3. Let R be a finite ring without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R belongs to E. Theorem 4. Let R be a ring with the descending chain condition of left ideals and without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R is an algebraically closed field or R belongs to E. In contrast to Theorems 2 and 4, we have Theorem 5. If R is an atomless p-ring, then R is finite, commutative, has no nonzero trivial ideals and admits elimination of quantifiers, but is not prime and does not have the descending chain condition. We also generalize Theorems 1, 2 and 4 to alternative rings. (shrink)

Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. If x is an element of X, let $B_n (x)$ be the ball of radius n around x. Suppose that X is infinite, connected and of bounded degree. A first-order sentence ϕ in the language of X is almost surely true (resp. a. s. false) for finite substructures of X if for every x ∈ X, the fraction of substructures of $B_n (...) (x)$ satisfying ϕ approaches 1 (resp. 0) as n approaches infinity. Suppose further that, for every finite substructure, X has a disjoint isomorphic substructure. Then every ϕ is a. s. true or a. s. false for finite substructures of X. This is one form of the geometric zero-one law. We formulate it also in a form that does not mention the ambient infinite structure. In addition, we investigate various questions related to the geometric zero-one law. (shrink)

We examine how degrees of computably enumerable equivalence relations under computable reduction break down into isomorphism classes. Two ceers are isomorphic if there is a computable permutation of ω which reduces one to the other. As a method of focusing on nontrivial differences in isomorphism classes, we give special attention to weakly precomplete ceers. For any degree, we consider the number of isomorphism types contained in the degree and the number of isomorphism types of weakly precomplete ceers contained in the (...) degree. We show that the number of isomorphism types must be 1 or ω, and it is 1 if and only if the ceer is self-full and has no computable classes. On the other hand, we show that the number of isomorphism types of weakly precomplete ceers contained in the degree can be any member of $[0,\omega ]$. In fact, for any $n \in [0,\omega ]$, there is a degree d and weakly precomplete ceers ${E_1}, \ldots,{E_n}$ in d so that any ceer R in d is isomorphic to ${E_i} \oplus D$ for some $i \le n$ and D a ceer with domain either finite or ω comprised of finitely many computable classes. Thus, up to a trivial equivalence, the degree d splits into exactly n classes.We conclude by answering some lingering open questions from the literature: Gao and Gerdes [11] define the collection of essentially FC ceers to be those which are reducible to a ceer all of whose classes are finite. They show that the index set of essentially FC ceers is ${\rm{\Pi }}_3^0$-hard, though the definition is ${\rm{\Sigma }}_4^0$. We close the gap by showing that the index set is ${\rm{\Sigma }}_4^0$-complete. They also use index sets to show that there is a ceer all of whose classes are computable, but which is not essentially FC, and they ask for an explicit construction, which we provide.Andrews and Sorbi [4] examined strong minimal covers of downwards-closed sets of degrees of ceers. We show that if $\left$ is a uniform c.e. sequence of non universal ceers, then $\left\{ {{ \oplus _{i \le j}}{E_i}|j \in \omega } \right\}$ has infinitely many incomparable strong minimal covers, which we use to answer some open questions from [4].Lastly, we show that there exists an infinite antichain of weakly precomplete ceers. (shrink)

Philosophers disagree about whether vagueness requires us to admit truth-value gaps, about whether there is a gap between the objects of which a given vague predicate is true and those of which it is false on an appropriately constructed sorites series for the predicate---a series involving small increments of change in a relevant respect between adjacent elements, but a large increment of change in that respect between the endpoints. There appears, however, to be widespread agreement that there is (...) some sense in which vague predicates are gappy which may be expressed neutrally by saying that on any appropriately constructed sorites series for a given vague predicate there will be a gap between the objects of which the predicate is denitely true and those of which it is denitely false. Taking as primitive the operator ‘it is denitely the case that’, abbreviated as ‘D’, we may stipulate that a predicate F is denitely true (or denitely false) of an object just in case ‘DF (a)’, where a is a name for the object, is true (or false) simpliciter.1 This yields the following conditional formulation of a ‘gap principle’: (D Φ (x) ∧ D¬ Φ (y)) → ¬R(x, y). Here ‘ Φ ’ is to be replaced with a vague predicate, while ‘R’ is to stand for a sorites relation for that predicate: a relation that can be used to construct a sorites series for the predicate---such as the relation of being just one millimetre shorter than for the predicate ‘is tall’. Disagreements about the sense in which it is correct to say that vague predicates are gappy can then be recast as disagreements about how to understand the denitely operator. One might give it, for example, a pragmatic construal such as ‘it would not be misleading to assert that’; or an epistemic construal such as ‘it is known that’ or ‘it is knowable that’; or a semantic construal such as ‘it is true that’. (shrink)

This article enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: Allxareyand Somexarey, There are at least as manyxasy, and There are morexthany. Herexandyrange over subsets (not elements) of a giveninfiniteset. Moreover,xandymay appear complemented (i.e., as$\bar{x}$and$\bar{y}$), with the natural meaning. We formulate a logic for our language that is based on the classical syllogistic. The main result is a (...) soundness/completeness theorem. There are efficient algorithms for proof search and model construction. (shrink)

Given two infinite binary sequences A,B we say that B can compress at least as well as A if the prefix-free Kolmogorov complexity relative to B of any binary string is at most as much as the prefix-free Kolmogorov complexity relative to A, modulo a constant. This relation, introduced in Nies [14] and denoted by A≤LKB, is a measure of relative compressing power of oracles, in the same way that Turing reducibility is a measure of relative information. The equivalence classes (...) induced by ≤LK are called LK degrees and there is a least degree containing the oracles which can only compress as much as a computable oracle, also called the ‘low for K’ sets. A well-known result from Nies [14] states that these coincide with the K-trivial sets, which are the ones whose initial segments have minimal prefix-free Kolmogorov complexity. We show that with respect to ≤LK, given any non-trivial sets X,Y there is a computably enumerable set A which is not K-trivial and it is below X,Y. This shows that the local structures of and Turing degrees are not elementarily equivalent to the corresponding local structures in the LK degrees. It also shows that there is no pair of sets computable from the halting problem which forms a minimal pair in the LK degrees; this is sharp in terms of the jump, as it is known that there are sets computable from which form a minimal pair in the LK degrees. We also show that the structure of LK degrees below the LK degree of the halting problem is not elementarily equivalent to the or structures of LK degrees. The proofs introduce a new technique of permitting below a set that is not K-trivial, which is likely to have wider applications. (shrink)

We study the proof-theoretic strength and effective content of the infinite form of Ramsey's theorem for pairs. Let RT n k denote Ramsey's theorem for k-colorings of n-element sets, and let RT $^n_{ denote (∀ k)RT n k . Our main result on computability is: For any n ≥ 2 and any computable (recursive) k-coloring of the n-element sets of natural numbers, there is an infinite homogeneous set X with X'' ≤ T 0 (n) . Let IΣ n and BΣ (...) n denote the Σ n induction and bounding schemes, respectively. Adapting the case n = 2 of the above result (where X is low 2 ) to models of arithmetic enables us to show that RCA 0 + IΣ 2 + RT 2 2 is conservative over RCA 0 + IΣ 2 for Π 1 1 statements and that $RCA_0 + I\Sigma_3 + RT^2_{ , is Π 1 1 -conservative over RCA 0 + IΣ 3 . It follows that RCA 0 + RT 2 2 does not imply BΣ 3 . In contrast, J. Hirst showed that $RCA_0 + RT^2_{ does imply BΣ 3 , and we include a proof of a slightly strengthened version of this result. It follows that $RT^2_{ is strictly stronger than RT 2 2 over RCA 0. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE PROBLEM OF THING AND OBJECT IN MARITAIN JOHN c. CAHALAN Methuen, Massachusetts I N THE essay, "Critical Realism," Jacques Maritain said, "The problem of thing and object is the crux of the problem of realism." 1 Since then, the distinction between thing and object has received little attention, except for some helpful discussions by Yves Simon. Either Maritain and Simon were very mistaken, or we have been missing (...) something very important. This study will attempt to explain the importance of the thing/object distinction by showing how it applies to a wide range of questions about human knowledge, from the nature of metaphysics to the problem of conceptual relativity in the philosophy of science and hermeneutics. Skeptics and idealists grant that our awareness has objects. Skeptics question whether we can make extramentally existing things objects of awareness as they are. Idealists deny that things have an existence other than being objects of awareness.2 Maritain considered the presuppositions of calling something an " object " of awareness: what are we doing when we call something an object of awareness and what conditions are necessary for knowing that something is such an object. He found that the conditions necessary for knowing that something is an object of awareness provide the basis for refutations of skepticism and 1 Jacques Maritain, The Degrees of Knowledge, trans. Gerald B. Phelan (New York: Scribners, 1959) 107 (translation corrected). Hereafter, I refer to this work as DK, followed by a page number. 2 Maritain uses " idealism " for both ways of denying that we directly attain extramental existents, that is, for any position holding that we must begin from awareness of our mental states. 21 22 JOHN C. CAHALAN idealism. But his analysis also gives us a tool, the distinction between things as things and things as objects, capable of illuminating many other epistemological problems. I will begin by explaining the thing/object distinction and how it enables us to refute idealism. Then, I will apply the distinction to problems concerning the knowledge of being in metaphysics. Next, I will show how the distinction reveals, for the first time, the nature of that " conformity" between the mind and things which we call truth. Finally, I will apply the distinction to the problems of skepticism and conceptual relativity. I How do the conditions required for knowing that something is an object enable us to defend realism? We can ask epistemological questions because we are reflexively aware of our own awareness. The reality we call "awareness" is a way of relating to terms that we call its "objects." "Object" is a relational term here; to call something an "object" of awareness is to describe it as a term of a knowledge relation (where " knowledge " means cognition in general, not just knowledge of truth). " We must distinguish," Maritain says, "between the thing as thingas existing or able to exist for itself-and the thing as objectwhen it is set before the faculty of knowing and made present to it" (DK, 91). "The object is the correlative of a knowing subject... which precisely takes the name 'object' from the fact that it is presented to the mind" (DK, 93; my emphasis). When we describe something as known, conceived, imagined, heard, referred to, expressed, meant, thought about, remembered, etc., we are describing it as an object, in Maritain's sense. The subjectobject polarity is a fundamental fact that reflexive self-awareness reveals to us: A state of awareness has an object that is distinct from itself at least to the extent that the term of any relation is distinct from the relation, and just as we can describe awareness as a relation to something, we can describe that something as a term of a relation of awareness, an object. But we cannot describe objects solely as objects; for whatever we are first aware of, we must be aware of other than as an ob- THING AND OBJECT IN MARITAIN 23 ject. To be an object is to be a term of a knowledge relation; consequently, to be aware that X is an object is to have a knowledge relation whose term is the existence of a knowledge relation to X. But what are... (shrink)

Let us define the intuitionistic part of a classical theory T as the intuitionistic theory whose proper axioms are identical with the proper axioms of T. For example, Heyting arithmetic HA is the intuitionistic part of classical Peano arithmetic PA. It's a well-known fact, proved by Heyting and Myhill, that ZF is identical with its intuitionistic part. In this paper, we mainly prove that TT, Russell's Simple Theory of Types, and NF, Quine's "New Foundations," are not equal to (...) their intuitionistic part. So, an intuitionistic version of TT or NF seems more naturally definable than an intuitionistic version of ZF. In the first section, we present a simple technique to build Kripke models of the intuitionistic part of TT (with short examples showing bad properties of finite sets if they are defined in the usual classical way). In the remaining sections, we show how models of intuitionistic NF 2 and NF can be obtained from well-chosen classical ones. In these models, the excluded middle will not be satisfied for some non-stratified sentences. (shrink)

continent. 2.2 (2012): 155–158 Michel Serres. Biogea . Trans. Randolph Burks. Minneapolis: Univocal Publishing. 2012. 200 pp. | ISBN 9781937561086 | $22.95 Conveying to potential readers the significance of a book puts me at risk of glad handing. It’s not in my interest to laud the undeserving, especially on the pages of this journal. This is not a sales pitch, but rather an affirmation of a necessary work on very troubled terms: human, earth, nature, and the problematic world we made. (...) It is this world that aspirates the silence (so to speak), and therefore the subject which, along with the development of the “made world” exports the excess augmentation of the cosmically missing, this silence of the natural, et cetera. Had we learned from Locke that lesson of “labor,” to consume what we need… but perhaps we need more than what matters? Serres’ Biogea has several functions on this manner, if it is indeed a book to be consumed. First, readers searching for novelistic entertainment have a place to dwell. Biogea deserves a place in your back pocket; biographical generosity and poetic fluidity should satisfy most textual fetishes. For lay philosophers who want to refresh their acumen, Biogea deserves a place on the book shelf, one already reads a sorely needed postmodern tune-up here. Serres’ style is clearly French; he leaves few cheese crumbs on his words, rather preciseness and breathing in the work give way to a sweeping manner that breaks the narrative line of sight. A circular narrative and anachronistic fragmentation of terms allows an abyssal atmosphere to swell, if only to pump into the book the externality of its broader text. Biogea aspires to a higher standard and the book, at times, is thinking this negentropic problem too. Univocal, the publisher, has crafted a book appropriate for the hands to hold and the translations are an achievement of an otherwise difficult writer to translate. Terms are the conditions of a broader text. It is important to note that Serres’ content is as much a thinking of terminal ports. There is a regard for the transportation technology of the written word. For me, this is the mark of genius, a craftiness that tells of a book device that I may trust. Serres is an accomplished thinker and a necessary voice to check the putative trendiness of anti-postmodernist and market-driven theory of endless cultural liquidation. Offering interventions on subjectivity as an open system we are given a chance to affirm the human, not merely to discard it, but to engage its poetic image emotion, the calibratory silent sense of the analogic world; the terms on which we base our efforts. 1 The human is the center of its own negation, constantly mediating it. Something deeper at stake appears in the work then, and it is quite obvious from the onset. Certainly, a book is an intensification of possible text and those who brought this actual book into existence have captured a rarity in regards to the subject matter and artistic accomplishment. I mentioned terms as conditions, so let us understand Biogea as bio-yea, a yes to bios . An affirmation of living and accepting presence for all of its defiance of images, words, and things temporal. Therefore Serres’ existence and its existants plays parts; out of linearity and still like a porous bone pumping blood it manufactures into the fleshy life it becomes. Starting from a man named silence chaos emerges, or the man “Old Taciturn” takes up a journey anticipating a great flood. In other words, a development akin to the one in Genesis. In dealing with this ancestral occupation, fusing Genesis with contemporary philosophical terms, Serres initiates this anachronistic fragmentation under the forming subjectivity of his own autobiography. This mutation in the open system is precisely one of Serres’ terms. There an abyss is at work, stated, but also measured by heels on the ground—the abyss dispatching earthen tensions, that which plays our tunes, that which we abide by and recognize in volcanoes, rivers, oceans, earthquakes and weaponry in the battles of the world. Set in later stages of the book, such tensions are harnessed through scientific principles in an attempt to unify the terms of natural force if only to terminate the world. Thus the elevation of the earth into the world is clearly set forth. Here already, and few pages in, a resonance is set forth under appellations such as the river Garonne, a subjectivity as much as it is inhuman, the river is the inhuman that makes us human. I get the sense that Serres is taking up a challenge issued by Wallace Stevens; namely, that the great poems of heaven and hell have been written, but that only the poem of the earth has resisted composition. 2 On this level we cannot avoid the killing factor of silence, given that our cognition blocks its pure, radical obliteration. Thus a silence of attunement to the earth is in a novel dialectic of the rithmic and rhythm. A technological world, a triumph of termination is set forth. If a text imposes its will given the reader who authorizes it, it is made to convey or convect a presupposition to a reader or its inhabitant(s). Text is therefore both, in-content, contenting, contentedness, and in reading it, a way to navigate self-destruction (dis-content). Here then would one note that the “inhuman” reveals itself, “an aperiodic rhythm of lovers and beloved…the sea as our friend…but as our enemy…maternal vivifying sea.” The sea is an open book, or vaginal birth canal, where the engagement of text comes forth: “…woman sea, open vulva.” One sees like the sea, but only after it, when the uninhabitable truth of inhabiting it switches the polarity of the sailors soul: “I was seeing like the sea” (9-11). In other words, we are invited to embrace the nonsense of the visible. At this point I am taken to Jean-François Lyotard’s work The Inhuman , specifically the first entry on negentropy that would be congruent with Serres’ thematic. 3 The human being exports, deports, or transplants its relation through text, through the system— and this is its sense or relation to silence, to music. Unaware of Serres’ proximity to this work, the concept of gender interrelation as regards a solar catastrophe runs clear. It would be, on this basis, that Serres references his peers, the other texts that, as mentioned above, are discarded in philosophy today. For students of philosophy what we have here is perhaps a gift, a needed project. If silence and death are at work, there is a political valence to deal with, and here, much like the domain of the text and the dominion of the reader, we confront the world of natural, fluid violence. The anti-postmodernist critique is in part based on a weak idea that the loss of ideology, of a world vision, motivates the “correlationist” project. 4 Serres seems to offer another way to view this when he notes that whereas persons “sometimes kill,” it is clearly “the collective” that “always kills” (17). What is the collective today, if not an organizing function we never see yet acts in its favor in the name of truth? One feels a sense of enigma here, if only to link to what Stevens remarked of communism as a “grubby faith,” providing this applies for capitalism as well, namely any ideology of progress overly interested in absolutes. Here we get the sense that the inhuman, silence, this type of killing, always killing, could not be matched by human-made, political dynamos. Or that if it comes to an equilibrium, a catastrophe is never too far from us to read with our heels. We are left to note that the forces of nature presuppose and permeate political systems, the more these systems obtain force, the more the system takes upon itself the proper name of nature that motivates its dissemination, albeit falsely. This note, that in an age of ecocide and technological captivity (sustainability and transparency) political regimes won’t grow our soul-learning ears any larger than our tongues, stands clear to us. The promise of technological desubjectification is here pushed aside. Regarding politics, Serres illustrates this fact: Where did this corpse come from? Who was it? Who killed it? I don’t know. I won’t try to find out. I refuse to get vengeance for it. And I only see Garonne. For our victims, today, are the rivers, too. Their waters have irrigated my life, enchanted my thought, invigorated my body; I’ve known them to be threatening, untamable, as dangerous as the sea when it rages. Yes, murderous. They decided to control their courses; dams, sometimes senseless, destroying sites and valleys, reduced entire populations to servile displacements; programs for the irrigation of thirsty farmland, often beneficial of course, completed their drying up.(22) Serres enters into his idea concerning the captivity of language from the natural into a world system: For thousands of years, we have been licking things with our tongues, covering and daubing them so as to appropriate things for ourselves. If language boils down to a convention, this convention took place between the speakers without consulting the thing named, become as a result the property of those who covered it in this way with their drawn or voiced productions. Malfeasance analyzes these acts of appropriation. Thus every inert object, every living thing as well, sleeps under the covers of signs, a little in the way that, today, a thousand posters shouting messages and ugly riots of color drown, with their filthy flood, the landscapes, or better, exclude them from perception because the meaning, almost nil, of this false language and these base images forms an irresistible source of attraction to our neurons and eyes. This appropriation covers the world’s beauty with ugliness. (38-39) Technological concealment coming to bear, we begin to get a sense of another commentary on the condition of sensing, driving home the necessity of a text dealing with such subject matter to be what its terms insist. Thus toward new openings: The new opening. As low beneath our feet as you like, the Biogea opens us to another space, high enough for us to be able to acquire a wisdom there, that of redeveloping this same place differently from our fathers, this place that’s still politically cut up by old hatreds, beneath the flood of tears and blood that we call history. Without this soft place, spiritually very old, but newly conceived in this way, without the juridical construction of a common good, opposed to our filthy ownership, I don’t see how our planet, hard, will survive. Hardness that depends on a softness, material belonging that depends on this temporary rented location (51). Serres enters into a summit on the content and the structure of his work. Archimedes is brought in with the concept of three volcanoes. Meaning fire, but as well earth, water, air. For it was Archimedes’ war machines that sought to lift the earth, thus bringing in the question of principles of science: “can a principle be invented while controlling its consequences?” (66-7). May the earth be put in a sentence, terminated by terminology, appellations, gone wild? By means of these element-dominating laws, this old physicist began to tear nature away from the ancient myths; by a strange return, today we’re plunging our successes back into the anxieties and terrors from which that ancient physics was born. Yes, our new history of science and technology is plunging, today, as though in a loop, into the fundamental human myths from which Empedocles’ first laws came. A major progression and a regression on the nether side of the origins. Consequently, the contemporary time requires that we try to return to that unity in which the principles of hate and love are at the same time human, living, inert and global. We will never attain a deontology of our knowledge and actions without thinking the subjective, the objective, the collective, and the cognitive all together simultaneously. Here, hate and love are the result of these four components.(71) Working then on the concept of fire-starting mirrors to the atomic annihilation of the Second War, Serres works into the subjectivity in question on the matter of rhythm—say rithmic— precisely at that point: Knowledge is changing today. The all-political is dying; the monarchy of the sciences said to be hard is coming to a close. The science of the things of the world will have to communicate just as much as the things of the world do, which do it much better than humans do, who don’t always want to do it. Let’s celebrate two changes this morning. The first one strikes a new blow to our narcissism. No, knowledge and the world don’t resemble our analytical enjoyments of refined cutting up, of endless debates and of exclusions full of hate. They, on the contrary, form a bloc and a sum, alliance and alloys. Uniting the fields of knowledge among themselves the way the things are connected among themselves, the second newness puts into place sets united by interlacing, webs and simplexes that combine with the things of the world, themselves combined, the combined knowledge that understands them.(130-1) Biogea closes on its opening flood thematic, approaching the initial telos of Genesis. Here the trees are brought into a position with atmosphere, the opaque abyssal reservoir, the tomb of the sun, sea in the polarity of the earthen heaven and hell. The poem of the earth then is silent but deadly, indeed, as funny as that phrase is, mainly a tomb gas. The meaning of the living and the non-meaning of things converge in the muteness of the world; this meaning and non-meaning plunge there and come out, the ultimate eddy. Mundus patet: through a fissure, through an opening, a fault, a cleft come noises, calls as small as these apertures. I’m listening, attentive, I’m translating, I’m advancing in the scaled-down meaning and science. Mundus patet: should the world open greatly, it will launch me into its silence. The totality remains silent. Knowledge expanded in elation. White origin of meaning, fountain of joy. (198) Final Remarks One test of a review is the long term trajectory the referee thinks the book will have. I see Serres’ text lending greatly into the vision of Biogea . In fact, in the vision of the novel inquiries of Stephen Jay Gould’s work there is something to be thought on the level of the individual and the species; namely, that humanity and its uniqueness is in its deferral, its thinking and naming, a thinking surrounded by silence that filters into everything, that pulls us through the world, the kinetic pulse we recognize, and all of that we cleave away in the base philosophical maxim of difference itself. Unique individuals are spatial creatures: we dwell, and we ought to get good at it. Yet this is an imaginative space that, if you are crazy enough to believe it, de-term-ine the conditions of its own terms. That is why we are not merely creating spaces on the acceleration of time, or so this ignoramus thinks, to accidentally transcend. Imagination already has this insatiable silence that we drink up and fail to manifest. Space is timeless. The imagination itself, shared by humans for themselves, their objects, and the species as a whole, is a non-defined space of relation; a whole human trajectory as part of nature, and part of worlds that are the other side of thinking nature, the consequence of it, at least our attempt to do so. Our survival is based on our deliberation, our caution, our natural deconstructive sense toward this silence that is already part of the song, sung, singing of this century without end. Good books will let us inhabit this space and recognize a form of life. Serres’ text moves toward dwelling, as noted, in masterful and accessible ways. The pitched battles are the falling replays of anemic and dead politics. As soon as we realize there is humanity, we may be able to enjoy the end of it, our inhuman capability of listening to silence. NOTES 1. See Michel Serres. The Parasite . Minneapolis: University of Minnesota Press. 2007. 2. Wallace Stevens, “Imagination as Value” [ca. 1945], in Collected Poetry and Prose . New York: The Library of America. 1997. 724-39. 3. Jean-François Lyotard. The Inhuman: Reflections on Time . Trans. Geoffrey Bennington & Rachel Bowlby. Stanford, CA: Stanford University Press. 1992. 4. See the introduction: Quentin Melliassoux. After Finitude: An Essay on the Necessity of Contingency . Trans. Ray Brassier. New York: Continuum. 2008. EDITOR'S NOTE: This review was updated on August 8, 2012. Substantial edits include block quotes from the book under review as well as the inclusion of comments from the author. (shrink)

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

The structure of traditional fiction is essentially linear or serial. No matter how complex a given work may be, it presents information to its reader successively, one element at a time, in a sequence determined by its author. By contrast, interactive fiction is parallel in structure or, more accurately, dendritic or tree-shaped. Not one, but several possible courses of action are open to the reader. Further, which one actually happens depends largely, though not exclusively, upon the reader’s own choices. To (...) be sure, the author is still in overall control, since it is she who has set up the particular nexus of events, but the route up the narrative tree, the actual sequence of events, is generally affected, if not completely determined, by the reader’s responses to that particular reader’s specific situation. In an adventure, the sequence of action frequently depends upon the reader’s decision to go in one geographical direction rather than another. In the eliza sample, the content of the “story” depends on such particulars as whether this reader has a brother or not, whether she fears her father, and why she has consulted the terminal. In general, the text presented to the eliza-reader depends on what that reader has already said and how the computer has interpreted and stored it, and this is generally true of interactive fiction.Further, interactive fiction is, in principle , open-ended—infinite. A conversation with eliza could go on for as long as one with Woody Allen’s psychoanalyst—in principle, forever. It has no necessary terminus. The program will go one writing texts and answers on the screen as long as the reader or player chooses to supply responses. Further, the computer can act as a metafictional narrator like John Barth or Thomas Pynchon who can create a story within a story or a story that generates another story within itself which generates another story within itself and so on, fictions dizzying and dazzling. One senses one’s essential humanity wobbling in the midst of the infinite paradoxes of existence and meaning. Anthony J. Niesz, assistant professor of German at Yale University, is the author of Dramaturgy in German Drama: From Gryphius to Goethe . He is interested in the phenomenon of the meta-theater, especially in seventeenth- and eighteenth-century German drama, as well as in the literature and cultural policies of the German Democratic Republic. Norman N. Holland is Milbauer Eminent Scholar at the University of Florida. He is the author of Laughing and The I. (shrink)

Let T and T1 be tournaments with n elements, E a basis for T, E′ a basis for T′, and k ≥ 3 an integer. The dual of T is the tournament T” of basis E defined by T = T for all x, y ε E. A hemimorphism from T onto T′ is an isomorphism from T onto T” or onto T. A k-hemimorphism from T onto T′ is a bijection f from E to E′ such that for (...) any subset X of E of order k the restrictions T/X and T1/f are hemimorphic. The set of hemimorphisms of T onto itself has group structure, this group is called the group of hemimorphisms of T. In this work, we study the restrictions to n – 2 elements of a tournament with n elements. In particular, we prove: Let k ≥ 3 be an integer, T a tournament with n elements, where n ≥ k + 5. Then the following statements are equivalent: All restrictions of T to subsets with n – 2 elements are k-hemimorphic. All restrictions of T to subsets with n – 2 elements are 3-hemimorphic. All restrictions of T to subsets with n – 2 elements are hemimorphic. All restrictions of T to subsets with n – 2 elements are isomorphic, Either T is a strict total order, or the group of hemimorphisms of T is 2-homogeneous. (shrink)

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some given criteria. In order to obtain a better accuracy for the plithogenic aggregation operators in the plithogenic set, and for (...) a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween each attribute value and the dominant (most important) attribute value. The plithogenic intersection and union are linear combinations of the fuzzy operators tnorm and tconorm, while the plithogenic complement, inclusion (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees. This article offers some examples and applications of these new concepts in our everyday life. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:498 BOOK REVIEWS generations of theologians across denominational lines. Both Placher and Hunsinger at the end of their essays choose quotations from within Frei's own writings to give a synoptic portrait of the man and his work. Placher chooses a remark about Niebuhr's sense of vocation as a theologian (20), and Hunsinger one about knowledge of that seemingly elusive reality, a person's identity (257). However one might come away (...) from this challenging collection of essays, further confused or more enlightened, more in agreement or disagreement, I think every reader will recognize the coincidence of intellectual perspicuity and generosity with passionate faith. Regis College, Toronto School of Theology Toronto, Ontario, Canada GEORGE P. SCHNER, S.J. Reasoned Faith. Edited by ELEONORE STUMP. Ithaca, N.Y.: Cornell University Press, 1993. Pp. x + 364. As the editor remarks in her "Introduction," it is not so long ago that the analytical philosophy of religion consisted very largely of discussions of the meaningfulness of religious language, and of arguments about the existence of God. Nowadays it is more adventurous, ranging over such topics as creation, providence, and God's responsibility for sin. According to Robert Merrihew Adams, the statement "truth is subjectivity," though one of the most famous, is also one of the most misunderstood in Kierkegaard's writings. He argues that, taken in context within the Concluding Unscientifu: Postscript, the statement is by no means incompatible with the objective truth of religious belief. From the point of view of the Postscript, a member of an idolatrous community who prays to her God with "the entire passion of the infinite" has more of the truth than one who prays in a false spirit from within Christendom; but this implies that the latter does have some truth. Whatever the deficiencies in her faith, she is clearly admitted to be in possession of the true concept of God objectively speaking (223 ). Adams maintains, quite rightly in the reviewer's opinion, that the Postscript is excessively pessimistic about the integration of the ideals of subjectivity and objectivity, of passionate commitment on the one side and rational assessment of evidence on the other, in religious faith (21). A useful distinction is made by Scott MacDonald between "occurrent" and "dispositional" belief; this seems to resolve some of the more puzzling paradoxes about the relation of the more cognitive and propositional side of faith to other aspects which may be thought essential to it. The demons alluded to by St. James (2:19) might believe dispositionally that their highest fulfillment BOOK REVIEWS 499 was to be found in obeying the divine will, and so performing acts of charity and service to other creatures. But to avoid the inconvenience of acting in such a way, they could think of God occurrently as just a powerful being who makes burdensome demands (55). For MacDonald, the cognitive component of faith has only two elements, belief that certain propositions are true, and belief that the kind of response of the will which is also essential to faith may be grounded on these (56). "We can make sense of Christian faith if we think of it simply as belief that Christianity is true plus an appropriate volitional response to that truth" (69). Against mainline Christian accounts like those of Augustine and Aquinas, he sees no good reason to suppose that one cannot have faith in propositions for which one has conclusive proof, but only in those for which one's justification is relatively weak. He provides interesting grounds for contradiction of a view which has been expounded by both Robert Adams and John Hick, that only such uncertainty can ground the trust which is essential to the relationship which human beings ought to have to God (59). "My ability to love and trust my wife, to commit myself without reservation to her well-being and to the goals and purposes we have chosen as definitive of our common life seem in no way dependent on my being uncertain about what she is like or what she will do" (60). On the question of how faith ought to be related to the demands of reason, Robert Audi remarks that, up to the middle 1970s... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:"A Mark ofthe Growing Mind is Veneration of Objects" (Ludwig Wittgenstein) Fay Horton Sawyier Introduction In book 1 of the Treatise,1 Hume directs his attention to two sets of concepts; one of these sets is what I think of as the "basic epistemological set" and the other as the "basic metaphysical or ontological set." Except for the idea of personal identity, the First Inquiry2 addresses the same arrays of (...) concerns. Within the "epistemological set" we find discussions ofknowledge, belief, origin of ideas, etc.; within the "metaphysical set"are seen space, time, identity, cause and effect, uniformity ofnature, external objects and so on.3 For the first (epistemological) set, Hume constructs a mode of analysis which depends crucially on the provenance of an idea or concept. Thatis, asit does forarthistorians today, authenticityortruth depends on how the thingin question came intoyour possession. Hume announces not only that every simple idea depends on and comes from its simple impression, but that the full understandingofa complexidea requires first factoring it into its simple components and then tracing them back to their impressions. Understanding is, so to speak, like displaying the family tree. It turns out that all of the members of the "metaphysical" set have dubious parentage. Even if one grants the accuracy and adequacy of Hume's factoring, we are left facing his demonstrations that for each metaphysical concept there are at least some elements with no clear ancestry from single impressions. In this wayHume directs our attention tohis questforhow suchideas(or such elements withinideas) are ever come by. Why do we attribute identity? Howcanwe assume thereisanecessary connection and apower? What can possibly bring us to imagine, even, that anything can be independent ofour perceptions? And so on. All ofthis is not only at the heart ofthe Humean enterprise inbook 1 ofthe Treatise ami theFirstInquiry butis well-known to anyone even modestly familiar with Hume's writings. The result of his powerful analyses is that these mysterious, illegitimate elements in the metaphysical concepts are generated within subjects exposed to repeated instances of, for example, pairings in time or place, similar sightings after temporal lapses and so on. The processes by which we Volume XVIII Number 2 315 FAY HORTON SAWYIER construct our categories as well as the elements out ofwhich we make them areimportantandin these cases were shown tobe developmental or time-dependent.4 Furthermore, since these processes and these resultant conceptshavebeen shown tohave been generated by us, they are uniquely quaUfied to demonstrate the nature of human nature, which was, after all, the subject ofthe Treatise? Having reminded ourselves ofthese extremely general features of Hume's exposition, I want now to isolate and to highlight some particular and peculiar features. 1.The subject upon whose mind or sensibilities paired and repeated events are presumed to impinge and by whose consequent conditioning these otherwise inexplicable concepts can be understood is always an adult male.6 2.The presentingsituation which is presumed to arise and repeatfor this adult male is always hypothetical and never observed. 3.Thisman'sconstructionofanyoneofthese concepts (like necessary connection) is always as his solution to a logical problem, his way-out ofa mental awkwardness or unease. 4.These adult male concept generators and logical problem solvers neverseem to doanything but sitstill and look around themselves.7 The fundamental character ofmy inquiry can be understood as a search for the (presumably deleterious) consequences of the four particular features noted above. Since the lives and experiences of young children are neglected and since acquisition of the basic metaphysical set is always initiated in early childhood, one may well hypothesize that Hume's results will be damaged or skewed. Intuitively, this would seem to be an obvious inference, but proof is needed that in some cases Hume did indeed misconstrue certain basic concepts and that the central factor in his shortfall was his neglect of the child's experience of concept development and acquisition. By contrast, his contemporary, Thomas Reid, remarked, "Could we obtain a distinct and full history of all that hath passed in the mind ofa child from thebeginning ofUfe and sensation, till it grows to the use ofreason... this would be a treasury of natural history, which would probably give... (shrink)

Pierre de Fermat is known as the inventor of modern number theory. He invented–improved many methods useful in this discipline. Fermat often claimed to have proved his most difficult theorems thanks to a method of his own invention: the infinite descent. He wrote of numerous applications of this procedure. Unfortunately, he left only one almost complete demonstration and an outline of another demonstration. The outline concerns the theorem that every prime number of the form 4n + 1 is the (...) sum of two squares. In this paper, we analyse a recent proof of this theorem. It is interesting because: it follows all the elements of which Fermat wrote in his outline; it represents a good introduction to all logical nuances and mathematical variants concerning this method of which Fermat spoke. The assertions by Fermat will also be framed inside their historical context. Therefore, the aims of this paper are related to the history of mathematics and to the logic of proof-methods. (shrink)

Table of contentsI1 Proceedings of the 4th World Conference on Research IntegrityConcurrent Sessions:1. Countries' systems and policies to foster research integrityCS01.1 Second time around: Implementing and embedding a review of responsible conduct of research policy and practice in an Australian research-intensive universitySusan Patricia O'BrienCS01.2 Measures to promote research integrity in a university: the case of an Asian universityDanny Chan, Frederick Leung2. Examples of research integrity education programmes in different countriesCS02.1 Development of a state-run “cyber education program of research ethics” in (...) KoreaEun Jung Ko, Jin Sun Kwak, TaeHwan Gwon, Ji Min Lee, Min-Ho LeeCS02.3 Responsible conduct of research teachers’ training courses in Germany: keeping on drilling through hard boards for more RCR teachersHelga Nolte, Michael Gommel, Gerlinde Sponholz3. The research environment and policies to encourage research integrityCS03.1 Challenges and best practices in research integrity: bridging the gap between policy and practiceYordanka Krastev, Yamini Sandiran, Julia Connell, Nicky SolomonCS03.2 The Slovenian initiative for better research: from national activities to global reflectionsUrsa Opara Krasovec, Renata SribarCS03.3 Organizational climate assessments to support research integrity: background of the Survey of Organizational Research Climate and the experience with its use at Michigan State UniversityBrian C. Martinson, Carol R. Thrush, C.K. Gunsalus4. Expressions of concern and retractionsCS04.1 Proposed guidelines for retraction notices and their disseminationIvan Oransky, Adam MarcusCS04.2 Watching retractions: analysis of process and practice, with data from the Wiley retraction archivesChris Graf, Verity Warne, Edward Wates, Sue JoshuaCS04.3 An exploratory content analysis of Expressions of ConcernMiguel RoigCS04.4 An ethics researcher in the retraction processMichael Mumford5. Funders' role in fostering research integrityCS05.1 The Fonds de Recherche du Québec’s institutional rules on the responsible conduct of research: introspection in the funding agency activitiesMylène Deschênes, Catherine Olivier, Raphaëlle Dupras-LeducCS05.2 U.S. Public Health Service funds in an international setting: research integrity and complianceZoë Hammatt, Raju Tamot, Robin Parker, Cynthia Ricard, Loc Nguyen-Khoa, Sandra TitusCS05.3 Analyzing decision making of funders of public research as a case of information asymmetryKarsten Klint JensenCS05.4 Research integrity management: Empirical investigation of academia versus industrySimon Godecharle, Ben Nemery, Kris Dierickx5A: Education: For whom, how, and what?CS05A.1 Research integrity or responsible conduct of research? What do we aim for?Mickey Gjerris, Maud Marion Laird Eriksen, Jeppe Berggren HoejCS05A.2 Teaching and learning about RCR at the same time: a report on Epigeum’s RCR poll questions and other assessment activitiesNicholas H. SteneckCS05A.4 Minding the gap in research ethics education: strategies to assess and improve research competencies in community health workers/promoteresCamille Nebeker, Michael Kalichman, Elizabeth Mejia Booen, Blanca Azucena Pacheco, Rebeca Espinosa Giacinto, Sheila Castaneda6. Country examples of research reward systems and integrityCS06.1 Improving systems to promote responsible research in the Chinese Academy of SciencesDing Li, Qiong Chen, Guoli Zhu, Zhonghe SunCS06.4 Exploring the perception of research integrity amongst public health researchers in IndiaParthasarathi Ganguly, Barna Ganguly7. Education and guidance on research integrity: country differencesCS07.1 From integrity to unity: how research integrity guidance differs across universities in Europe.Noémie Aubert Bonn, Kris Dierickx, Simon GodecharleCS07.2 Can education and training develop research integrity? The spirit of the UNESCO 1974 recommendation and its updatingDaniele Bourcier, Jacques Bordé, Michèle LeducCS07.3 The education and implementation mechanisms of research ethics in Taiwan's higher education: an experience in Chinese web-based curriculum development for responsible conduct of researchChien Chou, Sophia Jui-An PanCS07.4 Educating principal investigators in Swiss research institutions: present and future perspectivesLouis Xaver Tiefenauer8. Measuring and rewarding research productivityCS08.1 Altimpact: how research integrity underpins research impactDaniel Barr, Paul TaylorCS08.2 Publication incentives: just reward or misdirection of funds?Lyn Margaret HornCS08.3 Why Socrates never charged a fee: factors contributing to challenges for research integrity and publication ethicsDeborah Poff9. Plagiarism and falsification: Behaviour and detectionCS09.1 Personality traits predict attitude towards plagiarism of self and others in biomedicine: plagiarism, yes we can?Martina Mavrinac, Gordana Brumini, Mladen PetrovečkiCS09.2 Investigating the concept of and attitudes toward plagiarism for science teachers in Brazil: any challenges for research integrity and policy?Christiane Coelho Santos, Sonia VasconcelosCS09.3 What have we learnt?: The CrossCheck Service from CrossRefRachael LammeyCS09.4 High p-values as a sign of data fabrication/falsificationChris Hartgerink, Marcel van Assen, Jelte Wicherts10. Codes for research integrity and collaborationsCS10.1 Research integrity in cross-border cooperation: a Nordic exampleHanne Silje HaugeCS10.3 Research integrity, research misconduct, and the National Science Foundation's requirement for the responsible conduct of researchAaron MankaCS10.4 A code of conduct for international scientific cooperation: human rights and research integrity in scientific collaborations with international academic and industry partnersRaffael Iturrizaga11. Countries' efforts to establish mentoring and networksCS11.1 ENRIO : a network facilitating common approaches on research integrity in EuropeNicole FoegerCS11.2 Helping junior investigators develop in a resource-limited country: a mentoring program in PeruA. Roxana Lescano, Claudio Lanata, Gissella Vasquez, Leguia Mariana, Marita Silva, Mathew Kasper, Claudia Montero, Daniel Bausch, Andres G LescanoCS11.3 Netherlands Research Integrity Network: the first six monthsFenneke Blom, Lex BouterCS11.4 A South African framework for research ethics and integrity for researchers, postgraduate students, research managers and administratorsLaetus OK Lategan12. Training and education in research integrity at an early career stageCS12.1 Research integrity in curricula for medical studentsGustavo Fitas ManaiaCS12.2 Team-based learning for training in the responsible conduct of research supports ethical decision-makingWayne T. McCormack, William L. Allen, Shane Connelly, Joshua Crites, Jeffrey Engler, Victoria Freedman, Cynthia W. Garvan, Paul Haidet, Joel Hockensmith, William McElroy, Erik Sander, Rebecca Volpe, Michael F. VerderameCS12.4 Research integrity and career prospects of junior researchersSnezana Krstic13. Systems and research environments in institutionsCS13.1 Implementing systems in research institutions to improve quality and reduce riskLouise HandyCS13.2 Creating an institutional environment that supports research integrityDebra Schaller-DemersCS13.3 Ethics and Integrity Development Grants: a mechanism to foster cultures of ethics and integrityPaul Taylor, Daniel BarrCS13.4 A culture of integrity at KU LeuvenInge Lerouge, Gerard Cielen, Liliane Schoofs14. Peer review and its role in research integrityCS14.1 Peer review research across disciplines: transdomain action in the European Cooperation in Science and Technology “New Frontiers of Peer Review ”Ana Marusic, Flaminio SquazzoniCS14.2 Using blinding to reduce bias in peer reviewDavid VauxCS14.3 How to intensify the role of reviewers to promote research integrityKhalid Al-Wazzan, Ibrahim AlorainyCS14.4 Credit where credit’s due: professionalizing and rewarding the role of peer reviewerChris Graf, Verity Warne15. Research ethics and oversight for research integrity: Does it work?CS15.1 The psychology of decision-making in research ethics governance structures: a theory of bounded rationalityNolan O'Brien, Suzanne Guerin, Philip DoddCS15.2 Investigator irregularities: iniquity, ignorance or incompetence?Frank Wells, Catherine BlewettCS15.3 Academic plagiarismFredric M. Litto16. Research integrity in EuropeCS16.1 Whose responsibility is it anyway?: A comparative analysis of core concepts and practice at European research-intensive universities to identify and develop good practices in research integrityItziar De Lecuona, Erika Löfstrom, Katrien MaesCS16.2 Research integrity guidance in European research universitiesKris Dierickx, Noémie Bonn, Simon GodecharleCS16.3 Research Integrity: processes and initiatives in Science Europe member organisationsTony Peatfield, Olivier Boehme, Science Europe Working Group on Research IntegrityCS16.4 Promoting research integrity in Italy: the experience of the Research Ethics and Bioethics Advisory Committee of the Consiglio Nazionale delle Ricerche Cinzia Caporale, Daniele Fanelli17. Training programs for research integrity at different levels of experience and seniorityCS17.1 Meaningful ways to incorporate research integrity and the responsible conduct of research into undergraduate, graduate, postdoctoral and faculty training programsJohn Carfora, Eric Strauss, William LynnCS17.2 "Recognize, respond, champion": Developing a one-day interactive workshop to increase confidence in research integrity issuesDieter De Bruyn, Bracke Nele, Katrien De Gelder, Stefanie Van der BurghtCS17.4 “Train the trainer” on cultural challenges imposed by international research integrity conversations: lessons from a projectJosé Roberto Lapa e Silva, Sonia M. R. Vasconcelos18. Research and societal responsibilityCS18.1 Promoting the societal responsibility of research as an integral part of research integrityHelene IngierdCS18.2 Social responsibility as an ethical imperative for scientists: research, education and service to societyMark FrankelCS18.3 The intertwined nature of social responsibility and hope in scienceDaniel Vasgird, Stephanie BirdCS18.4 Common barriers that impede our ability to create a culture of trustworthiness in the research communityMark Yarborough19. Publication ethicsCS19.1 The authors' forum: A proposed tool to improve practices of journal editors and promote a responsible research environmentIbrahim Alorainy, Khalid Al-WazzanCS19.2 Quantifying research integrity and its impact with text analyticsHarold GarnerCS19.3 A closer look at authorship and publication ethics of multi- and interdisciplinary teamsLisa Campo-Engelstein, Zubin Master, Elise Smith, David Resnik, Bryn Williams-JonesCS19.4 Invisibility of duplicate publications in biomedicineMario Malicki, Ana Utrobicic, Ana Marusic20. The causes of bad and wasteful research: What can we do?CS20.1 From countries to individuals: unravelling the causes of bias and misconduct with multilevel meta-meta-analysisDaniele Fanelli, John PA IoannidisCS20.2 Reducing research waste by integrating systems of oversight and regulationGerben ter Riet, Tom Walley, Lex Marius BouterCS20.3 What are the determinants of selective reporting?: The example of palliative care for non-cancer conditionsJenny van der Steen, Lex BouterCS20.4 Perceptions of plagiarism, self-plagiarism and redundancy in research: preliminary results from a national survey of Brazilian PhDsSonia Vasconcelos, Martha Sorenson, Francisco Prosdocimi, Hatisaburo Masuda, Edson Watanabe, José Carlos Pinto, Marisa Palácios, José Lapa e Silva, Jacqueline Leta, Adalberto Vieyra, André Pinto, Mauricio Sant’Ana, Rosemary Shinkai21. Are there country-specific elements of misconduct?CS21.1 The battle with plagiarism in Russian science: latest developmentsBoris YudinCS21.2 Researchers between ethics and misconduct: A French survey on social representations of misconduct and ethical standards within the scientific communityEtienne Vergès, Anne-Sophie Brun-Wauthier, Géraldine VialCS21.3 Experience from different ways of dealing with research misconduct and promoting research integrity in some Nordic countriesTorkild VintherCS21.4 Are there specifics in German research misconduct and the ways to cope with it?Volker Bähr, Charité22. Research integrity teaching programmes and their challengesCS22.1 Faculty mentors and research integrityMichael Kalichman, Dena PlemmonsCS22.2 Training the next generation of scientists to use principles of research quality assurance to improve data integrity and reliabilityRebecca Lynn Davies, Katrina LaubeCS22.3 Fostering research integrity in a culturally-diverse environmentCynthia Scheopner, John GallandCS22.4 Towards a standard retraction formHervé Maisonneuve, Evelyne Decullier23. Commercial research and integrityCS23.1 The will to commercialize: matters of concern in the cultural economy of return-on-investment researchBrian NobleCS23.2 Quality in drug discovery data reporting: a mission impossible?Anja Gilis, David J. Gallacher, Tom Lavrijssen, Malwitz David, Malini Dasgupta, Hans MolsCS23.3 Instituting a research integrity policy in the context of semi-private-sector funding: an example in the field of occupational health and safetyPaul-Emile Boileau24. The interface of publication ethics and institutional policiesCS24.1 The open access ethical paradox in an open government effortTony SavardCS24.2 How journals and institutions can work together to promote responsible conductEric MahCS24.3 Improving cooperation between journals and research institutions in research integrity casesElizabeth Wager, Sabine Kleinert25. Reproducibility of research and retractionsCS25.1 Promoting transparency in publications to reduce irreproducibilityVeronique Kiermer, Andrew Hufton, Melanie ClyneCS25.2 Retraction notices issued for publications by Latin American authors: what lessons can we learn?Sonia Vasconcelos, Renan Moritz Almeida, Aldo Fontes-Pereira, Fernanda Catelani, Karina RochaCS25.3 A preliminary report of the findings from the Reproducibility Project: Cancer biologyElizabeth Iorns, William Gunn26. Research integrity and specific country initiativesCS26.1 Promoting research integrity at CNRS, FranceMichèle Leduc, Lucienne LetellierCS26.2 In pursuit of compliance: is the tail wagging the dog?Cornelia MalherbeCS26.3 Newly established research integrity policies and practices: oversight systems of Japanese research universitiesTakehito Kamata27. Responsible conduct of research and country guidelinesCS27.1 Incentives or guidelines? Promoting responsible research communication through economic incentives or ethical guidelines?Vidar EnebakkCS27.3 Responsible conduct of research: a view from CanadaLynn PenrodCS27.4 The Danish Code of Conduct for Research Integrity: a national initiative to promote research integrity in DenmarkThomas Nørgaard, Charlotte Elverdam28. Behaviour, trust and honestyCS28.1 The reasons behind non-ethical behaviour in academiaYves FassinCS28.2 The psychological profile of the dishonest scholarCynthia FekkenCS28.3 Considering the implications of Dan Ariely’s keynote speech at the 3rd World Conference on Research Integrity in MontréalJamal Adam, Melissa S. AndersonCS28.4 Two large surveys on psychologists’ views on peer review and replicationJelte WichertsBrett Buttliere29. Reporting and publication bias and how to overcome itCS29.1 Data sharing: Experience at two open-access general medical journalsTrish GrovesCS29.2 Overcoming publication bias and selective reporting: completing the published recordDaniel ShanahanCS29.3 The EQUATOR Network: promoting responsible reporting of health research studiesIveta Simera, Shona Kirtley, Eleana Villanueva, Caroline Struthers, Angela MacCarthy, Douglas Altman30. The research environment and its implications for integrityCS30.1 Ranking of scientists: the Russian experienceElena GrebenshchikovaCS30.4 From cradle to grave: research integrity, research misconduct and cultural shiftsBronwyn Greene, Ted RohrPARTNER SYMPOSIAPartner Symposium AOrganized by EQUATOR Network, Enhancing the Quality and Transparency of Health ResearchP1 Can we trust the medical research literature?: Poor reporting and its consequencesIveta SimeraP2 What can BioMed Central do to improve published research?Daniel Shanahan, Stephanie HarrimanP3 What can a "traditional" journal do to improve published research?Trish GrovesP4 Promoting good reporting practice for reliable and usable research papers: EQUATOR Network, reporting guidelines and other initiativesCaroline StruthersPartner Symposium COrganized by ENRIO, the European Network of Research Integrity OfficersP5 Transparency and independence in research integrity investigations in EuropeKrista Varantola, Helga Nolte, Ursa Opara, Torkild Vinther, Elizabeth Wager, Thomas NørgaardPartner Symposium DOrganized by IEEE, the Institute of Electrical and Electronics EngineersRe-educating our author community: IEEE's approach to bibliometric manipulation, plagiarism, and other inappropriate practicesP6 Dealing with plagiarism in the connected world: An Institute of Electrical and Electronics Engineers perspectiveJon RokneP7 Should evaluation of raises, promotion, and research proposals be tied to bibliometric indictors? What the Institute of Electrical and Electronics Engineers is doing to answer this questionGianluca SettiP8 Recommended practices to ensure conference content qualityGordon MacPhersonPartner Symposium EOrganized by the Committee on Freedom and Responsibility in the Conduct of Science of ICSU, the International Council for ScienceResearch assessment and quality in science: perspectives from international science and policy organisationsP9 Challenges for science and the problems of assessing researchEllen HazelkornP10 Research assessment and science policy developmentCarthage SmithP11 Research integrity in South Africa: the value of procedures and processes to global positioningRobert H. McLaughlinP12 Rewards, careers and integrity: perspectives of young scientists from around the worldTatiana Duque MartinsPartner Symposium FOrganized by the Online Resource Center for Ethics Education in Engineering and Science / Center for Engineering, Ethics, and Society of the National Academy of EngineeringP13 Research misconduct: conceptions and policy solutionsTetsuya Tanimoto, Nicholas Steneck, Daniele Fanelli, Ragnvald Kalleberg, Tajammul HusseinPartner Symposium HOrganized by ORI, the Office of Research Integrity; Universitas 21; and the Asia Pacific Research Integrity NetworkP14 International integrity networks: working together to ensure research integrityPing Sun, Ovid Tzeng, Krista Varantola, Susan ZimmermanPartner Symposium IOrganized by COPE, the Committee on Publication EthicsPublication without borders: Ethical challenges in a globalized worldP15 Authorship: credit and responsibility, including issues in large and interdisciplinary studiesRosemary ShinkaiPartner Symposium JOrganized by CITI, the Cooperative Institutional Training InitiativeExperiences on research integrity educational programs in Colombia, Costa Rica and PeruP16 Experiences in PeruRoxana LescanoP17 Experiences in Costa RicaElizabeth HeitmanP18 Experiences in ColumbiaMaria Andrea Rocio del Pilar Contreras NietoPoster Session B: Education, training, promotion and policyPT.01 The missing role of journal editors in promoting responsible researchIbrahim Alorainy, Khalid Al-WazzanPT.02 Honorary authorship in Taiwan: why and who should be in charge?Chien Chou, Sophia Jui-An PanPT.03 Authorship and citation manipulation in academic researchEric Fong, Al WilhitePT.04 Open peer review of research submission at medical journals: experience at BMJ Open and The BMJTrish GrovesPT.05 Exercising authorship: claiming rewards, practicing integrityDésirée Motta-RothPT.07 Medical scientists' views on publication culture: a focus group studyJoeri Tijdink, Yvo SmuldersPoster Session B: Education, training, promotion and policyPT.09 Ethical challenges in post-graduate supervisionLaetus OK LateganPT.10 The effects of viable ethics instruction on international studentsMichael Mumford, Logan Steele, Logan Watts, James Johnson, Shane Connelly, Lee WilliamsPT.11 Does language reflect the quality of research?Gerben ter Riet, Sufia Amini, Lotty Hooft, Halil KilicogluPT.12 Integrity complaints as a strategic tool in policy decision conflictsJanneke van Seters, Herman Eijsackers, Fons Voragen, Akke van der Zijpp and Frans BromPoster Session C: Ethics and integrity intersectionsPT.14 Regulations of informed consent: university-supported research processes and pitfalls in implementationBadaruddin Abbasi, Naif Nasser AlmasoudPT.15 A review of equipoise as a requirement in clinical trialsAdri LabuschagnePT.16 The Research Ethics Library: online resource for research ethics educationJohanne Severinsen, Espen EnghPT.17 Research integrity: the view from King Abdulaziz City for Science and TechnologyDaham Ismail AlaniPT. 18 Meeting global challenges in high-impact publications and research integrity: the case of the Malaysian Palm Oil BoardHJ. Kamaruzaman JusoffPT.19 University faculty perceptions of research practices and misconductAnita Gordon, Helen C. HartonPoster Session D: International perspectivesPT.21 The Commission for Scientific Integrity as a response to research fraudDieter De Bruyn, Stefanie Van der BurghtPT. 22 Are notions of the responsible conduct of research associated with compliance with requirements for research on humans in different disciplinary traditions in Brazil?Karina de Albuquerque Rocha, Sonia Maria Ramos de VasconcelosPT.23 Creating an environment that promotes research integrity: an institutional model of Malawi Liverpool Welcome TrustLimbanazo MatandikaPT.24 How do science policies in Brazil influence user-engaged ecological research?Aline Carolina de Oliveira Machado Prata, Mark William NeffPoster Session E: Perspectives on misconductPT.26 What “causes” scientific misconduct?: Testing major hypotheses by comparing corrected and retracted papersDaniele Fanelli, Rodrigo Costas, Vincent LarivièrePT.27 Perception of academic plagiarism among dentistry studentsDouglas Leonardo Gomes Filho, Diego Oliveira GuedesPT. 28 a few bad apples?: Prevalence, patterns and attitudes towards scientific misconduct among doctoral students at a German university hospitalVolker Bähr, Niklas Keller, Markus Feufel, Nikolas OffenhauserPT. 29 Analysis of retraction notices published by BioMed CentralMaria K. Kowalczuk, Elizabeth C. MoylanPT.31 "He did it" doesn't work: data security, incidents and partnersKatie SpeanburgPoster Session F: Views from the disciplinesPT.32 Robust procedures: a key to generating quality results in drug discoveryMalini Dasgupta, Mariusz Lubomirski, Tom Lavrijssen, David Malwitz, David Gallacher, Anja GillisPT.33 Health promotion: criteria for the design and the integrity of a research projectMaria Betânia de Freitas Marques, Laressa Lima Amâncio, Raphaela Dias Fernandes, Oliveira Patrocínio, and Cláudia Maria Correia Borges RechPT.34 Integrity of academic work from the perspective of students graduating in pharmacy: a brief research studyMaria Betânia de Freitas Marques, Cláudia Maria Correia Borges Rech, Adriana Nascimento SousaPT.35 Research integrity promotion in the Epidemiology and Health Services, the journal of the Brazilian Unified Health SystemLeila Posenato GarciaPT.36 When are clinical trials registered? An analysis of prospective versus retrospective registration of clinical trials published in the BioMed Central series, UKStephanie Harriman, Jigisha PatelPT.37 Maximizing welfare while promoting innovation in drug developmentFarida LadaOther posters that will be displayed but not presented orally:PT.38 Geoethics and the debate on research integrity in geosciencesGiuseppe Di Capua, Silvia PeppoloniPT.39 Introducing the Professionalism and Integrity in Research Program James M. DuBois, John Chibnall, Jillon Van der WallPT.40 Validation of the professional decision-making in research measureJames M. DuBois, John Chibnall, Jillon Van der Wall, Raymond TaitPT.41 General guidelines for research ethicsJacob HolenPT. 42 A national forum for research ethicsAdele Flakke Johannessen, Torunn EllefsenPT.43 Evaluation of integrity in coursework: an approach from the perspective of the higher education professorClaudia Rech, Adriana Sousa, Maria Betânia de Freitas MarquesPT.44 Principles of geoethics and research integrity applied to the European Multidisciplinary Seafloor and Water Column Observatory, a large-scale European environmental research infrastructureSilvia Peppoloni, Giuseppe Di Capua, Laura BeranzoliF1 Focus track on improving research systems: the role of fundersPaulo S.L. Beirão, Susan ZimmermanF2 Focus track on improving research systems: the role of countriesSabine Kleinert, Ana MarusicF3 Focus track on improving research systems: the role of institutionsMelissa S. Anderson, Lex Bouter. (shrink)

For a set x, let ${\cal S}\left$ be the set of all permutations of x. We prove in ZF several results concerning this notion, among which are the following: For all sets x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{{\cal S}_{{\rm{fin}}}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into ${{\cal S}_{{\rm{fin}}}}\left$, where ${{\cal S}_{{\rm{fin}}}}\left$ denotes the set of all permutations of x which move only finitely many elements. For all (...) sets x such that ${\cal S}\left$ is Dedekind infinite, $\left| {{\rm{seq}}\left} \right| < \left| {{\cal S}\left} \right|$ and there are no finite-to-one functions from ${\cal S}\left$ into seq, where seq denotes the set of all finite sequences of elements of x. For all infinite sets x such that there exists a permutation of x without fixed points, there are no finite-to-one functions from ${\cal S}\left$ into x. For all sets x, $|{[x]^2}| < \left| {{\cal S}\left} \right|$. (shrink)

Given a sequence of sets An⊆{0,…,n−1}, the Furstenberg correspondence principle provides a shift-invariant measure on2N that encodes combinatorial information about infinitely many of the An's. Here it is shown that this process can be inverted, so that for any such measure, ergodic or not, there are finite sets whose combinatorial properties approximate it arbitarily well. The finite approximations are obtained from the measure by an explicit construction, with an explicit upper bound on how large n has to be to (...) yield a sufficiently good approximation. We draw conclusions for computable measure theory, and show, in particular, that given any computable shift-invariant measure on 2N, there is a computable element of 2N that is generic for the measure. We also consider a generalization of the correspondence principle to countable discrete amenable groups, and once again provide an effective inverse. (shrink)

Abstract A Note to Cogito Les Jones Blackburn College Previous submissions include -Intention, interpretation and literary theory, a first lookWittgenstein and St Augustine A DiscussionAreas of Interest – History of Western Philosophy, Miscellaneous Philosophy, European A Note on Cogito Descartes' brilliance in driving out doubt, and proving the existence of himself as a thinking entity, is well documented. Sartre's critique (or maybe extension) is both apposite and grounded and takes these enquiries on to another level. Let's take a look. 'I (...) think' somehow, for all its power, lacks something. What? Consider what one does when thinking (difficult, but we can try). Implicit in the word 'think', in fact the very essence of the word 'think', is that activity is going on, and if such activity is going on then it must be going on about something, an object, an emotion, a problem,or maybe some dreamlike state, but common to all these is that something is going on. Is that really so? Well, if that wasn't so we would be able to think in a pure state, wouldn't we? But what does a pure state of 'thinking' mean? It can't mean that there isnothing there, because if there were nothing there then no thinking would be taking place. Can it mean that we are thinking of nothing? Well no, because if we are thinking of nothing then we are thinking of something, we are contemplating the notion, or the nature, of nothing. In fact, one can argue that if we talk of something, inthis case nothing or nothingness, then in our head we have some notion of what that is, i.e. something exists in the mind for it to come out of our mouths. Thinking is a recognition of something outside the individual, for the very act of direction, which isan indispensable part of thinking, recognises, must recognise, that there are things to address outside the individual. Something else to bear in mind. According to Sartre human beings are condemned to freedom. Why condemned? Human beings did not choose to be born, but the act ofbeing born also imparts the freedom of which Sartre speaks. Freedom is something which we parrot off as being a sine qua non for the human condition. I believe that's true, but freedom in this sense isn't without its consequences for the individual humanbeing, for individual human beings handle freedom differently. To some it enables them to fly, to others it imparts immense pressures, anguish, heartbreak, unhappiness can all be associated with such freedom. Each individual is responsible for his destiny, for his direction. If someone says that God impelled him, that individual chose his or her God, and chose to obey his or her God. This believer has to sift through the multitude of things that his or her God desire of him or her. All this is fine, so long as we acknowledge what is going on here. Belief in God is, by definition, a belief. Belief, following Wittgenstein, is a language game with its rules and its boundaries. The essential feature of religion as language game are its boundaries, which can be summed up in the word belief. OK, belief has its practises which are its constituent parts, but belief is the boundary between religion and other language games, as the proof constituents are different. Our world is determined by the language used to describe everything that goes on within it. The boundaries of our world are set by the language we use. This might be better put as language gives access to ever expending boundaries. Ever expanding boundaries are only possible by ever expanding thought, and ever expanding thought is only possible by ever expanding directions to our thought brought about through language. It is a fact taken that to be conscious is to think. How could this be otherwise? Consciousness without thought just does not make sense. Imagine a state of consciousness without directional thought. What would it be like? It would be something never experienced, completely out of our understanding. Why? Because understanding itself is a directional thought process. If we say we are going outside our understanding then that is a world of void, and a world of void does not exist. Can such a world be contemplated in our thinking? Well, yes, but then it requires thinking, and thinking requires direction, and such direction requires language. Why does direction require language? Because there is no other way for human beings to articulate a directional thought. Could one point at an image without language? Well, one could have an image in mind, but the essence of saying something about it, of descriptive power, brings us back to the essence, to the power of language to direct. So what of this language of which we speak? Wittgenstein's private language argument points us towards the notion that language itself constantly develops and redevelops through human interaction. Descarte's cogito implies that thinking rules out doubt of one's own existence. But such thinking, to be valid, to make sense, to direct, must develop in a language that has developed, has been verified, by a plurality, by a plurality whose essence is social. Correct use of language symbols, i.e. words, requires that we verify and reverify the accuracy of such symbols. How do we do that? We do that in constant usage, in constant interaction, with other human beings. An individual using a private language could not be understood by others, his symbol system has not been verified by others, his meanings may not be your meanings. It follows from what we have said above that language is constructed, and is continually constructed, in a social context. Given our previous thoughts regarding verification this could not be otherwise. Language has a normative form. All language users are required, by their very use of the language, to verify the use of terms, grammar etc etc. As Wittgenstein cites (appropriately) games as a model, let us take a look. If I play e.g. Ludo, I am governed by the rules. It is not just that I may play dishonestly, for if I were to play at all that very dishonesty, to count as Ludo, would have to be rule governed. The rules of Ludo are Ludo, they are the essence and the constitution of it. Wittgenstein, particularly in his later writings, interweaves many concepts, and connects them in different and sometimes rather elusive ways. Wittgenstein sees concepts like emotions, sentiments and experiences in these interweaving maps. Of course these can be regarded as psychological concepts ** Language can be considered in another but related way, as embodying the elements of a cultural heritage. Language was seen as embodying the notion of higher culture in the arts, architecture etc. Over recent decades this has tended to shift to consider less tangible benefits, such things as oral traditions, cultural values and cultural identity. So language enables us to explore, through the achievements of past generations, cultural mores that may have laid unchallenged for many years. Many of these values and mores may be seen as independent of the language by which they are transmitted, but still this monumental accomplishment of mankind i.e. language, enables man to explore, to modify, to codify, to extend the boundaries of human experience. There are therefore massive implications for our Note on Cogito of Wittgenstein's work. Following Wittgenstein emotions and other psychological concepts can be termed depth grammar, and are distinguished by the fact that the third person of the present is recognised by observation, the first person is not. Taking Wittgenstein's well known pain example the sentence 'He is in pain' is a third person statement of an observational nature. The sentence 'I am in pain' is not derived from observation but from experience, it is an expression of that experience, it's essence is the experience. The asymmetry consists in the fact that predicting psychological attributes of others is warranted by what they do and say. By contrast, the use of such statements in the first person present tense does not rest on one's observation of one's own behaviour. (Hacker 2010:287) p 9 According to Wittgenstein 'I am in pain' is more like a cry of pain, an expression of pain, than a report of some pain. Of course this appertains for other similar statements. 'I feel good' etc. (shrink)

For a set x, let S(x) be the set of all permutations of x. We prove by the method of permutation models that the following statements are consistent with ZF: (1) There is an infinite set x such that |p(x)|<|S(x)|<|seq^1-1(x)|<|seq(x)|, where p(x) is the powerset of x, seq(x) is the set of all finite sequences of elements of x, and seq^1-1(x) is the set of all finite sequences of elements of x without repetition. (2) There is a Dedekind (...) infinite set x such that |S(x)|<|[x]^3| and such that there exists a surjection from x onto S(x). (3) There is an infinite set x such that there is a finite-to-one function from S(x) into x. (shrink)