Metaphysical graphical structuralism is the view that at some fundamental level the world is a mathematical graph of nodes and edges. Randall Dipert has advanced a graphical structuralist theory of fundamental particulars and Alexander Bird has advanced a graphical structuralist theory of fundamental properties. David Oderberg has posed a powerful challenge to graphical structuralism: that it entails the absurd inexistence of the world or the absurd cessation of all change. In this paper I defend graphical structuralism. A sharper formulation, some (...) theorems about such structures, and careful attention to the interaction of metaphysical and mathematical features, shows that the absurdities depend on assumptions that are not essential to the view and brings to light a surprising fact about the necessary structure of fundamental properties. (shrink)

According to Bird’s Naïve Dispositional Monism, all properties are powers, and are individuated by their manifestations. Lowe has famously challenged the position with an individuation regress or circularity argument. Bird has then offered a structuralist side-step in the form of Structuralist Dispositional Monism, according to which powers are individuated through the unique position they occupy in an asymmetric power-structure. However, Structuralist Dispositional Monism has been argued to be just as problematic as Naïve Dispositional Monism, if not more so.I argue (...) that the debate is severely flawed to the extent that it relies on Lowe’s standard characterization of metaphysical individuation as a binary relation between objects. I will argue against this characterization in favor of a different one, either as a standard or sui generis explanatory relation of individuality facts. In the former case, Naïve Dispositional Monism is clear of all charges previously raised against it; whereas in the latter case, Structuralist Dispositional Monism works just fine; Structuralist Dispositional Monism may ultimately be argued to the be the superior option. Either way, the status of Dispositional Monism, vis à vis individuation circularities, is not as compromised as some have claimed—and Lowe’s intended way out (viz., allow for some non-power to eventually break the circularity) loses much of its appeal. (shrink)

Based on a unique data set on US direct microloans, we study the funding determinants of interest-free peer-to-peer crowdlending aimed at borrowers in the US. By performing logistic regressions on funding success and Tobit regressions on the reversed funding time, the existence of a social underwriting by a third-party trustee and information in the description texts fostering the investors’ trust are shown to be the main predictors of successful funding. Regarding social impact, the possibility to empower women and groups of (...) borrowers appeals to the investors, whereas empowerment of the family or community beyond the borrowers themselves appears to remain unappreciated. When examining the vulnerability of the borrowers as a predictor, the results manifest differences amongst the attitudes of the investors towards social impact. In the subsample of non-endorsed loans, the investors appear to prefer to support borrowers with an immigration background. In contrast, this is not the case with endorsed loans. (shrink)

This study examined cross-sectional links of the theistic and non-theistic sanctification of marriage and positive and negative religious coping with marital adjustment for 316 married Muslims from Iran. Perceiving marriage to be a manifestation of God and reflective of sacred qualities as well as engaging in positive and negative religious/spiritual coping strategies each uniquely contributed variance to marital adjustment, after controlling for each other and global indicators of devotion to Islam, and demographic variables. Specifically, theistic sanctification, non-theistic sanctification, and (...) positive r/s coping were uniquely tied to higher marital adjustment whereas negative r/s coping was uniquely tied to lower marital adjustment theistic in a hierarchical regression model with all primary variables and controls entered. These findings replicate and extend prior findings on the perceived sanctity of marriage with US samples of predominantly Christians to Muslims living in the Middle East, and offer novel cross-cultural insights into the possible roles that sanctification of marriage and r/s coping may play for marital well-being for non-distressed married Muslims. (shrink)

When the Canonical Ramsey’s Theorem by Erdős and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and McAloon. Taylor proved a “canonical” version of Hindman’s Theorem, analogous to the Canonical Ramsey’s Theorem. We introduce the restriction of Taylor’s Canonical Hindman’s Theorem to a subclass of the regressive functions, the $$\lambda $$ λ -regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of (...) this Regressive Hindman’s Theorem and of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that the well-ordering-preservation principle for base-$$\omega $$ ω exponentiation is reducible to this same principle by a uniform computable reduction. (shrink)

In this paper we present a collection of results related to the comparability of summands property of regressive isols. We show that if an infinite regressive isol has comparability of summands, then every predecessor of the isol has a weak comparability of summands property. Recently R. Downey proved that there exist regressive isols that are both hyper-torre and cosimple. There is a surprisingly close connection between non-recursive recursively enumerable sets and particular retraceable sets and regressive isols. We apply the (...) class='Hi'>theorem of Downey to show that among the regressive isols that are related to recursively enumerable sets there are some with a new property. (shrink)

For al-Urmawī, the soul is an essence that governs the parts of our body to move both naturally and voluntarily. Cognitive actions in the body is also by means of the soul. This essence is the same in each of us. Every one of us necessarily knows he or she is one person. This is what referred as 'I' or 'you'. al-Urmawī argues that the thing that consists of the soul and body must be one single living being. If not, (...) then it would be necessary to talk about two separate substances that do not have any relation between them. According to al-Urmawī, the reasoning soul (al-nasf al-nāṭiqah) continues to exist and reason after the degeneration of the body. According to him, perceptions about sensibles are in three parts; sensory perception, imaginary perception, and intellectual perception. For him, the perceiving faculty perceives either particulars or universals. The faculty that perceives the particulars consists of the external senses. According to al-Urmawī, inner senses either only perceive or both perceive and govern what is perceived together. Sirājuddīn al-Urmawī also asserts that knowledge consists of concepts (tasawwur) and assents (tasdīq). So, knowledge occurs either as in the form of a concept or a judgement (ḥukm). According to al-Urmawī, the imaginative faculty is also active in the formation of knowledge. He mentions intuition as an alternative way of obtaining knowledge. He states that any information that human beings do not possess can be obtained through pre-possessed information. This can only happen by transferring from a ready mind. This mental transfer and leap occur in two directions. The first manifests itself as an effort to reach more information by navigating between meanings using the imaginative faculty. The goal is to reach the middle term. First, what to be reached is determined, and then the mind is directed to the hidden antecedent. He explains that knowledge must be in harmony with the extramental world. According to him, information must be in complete harmony with the perceived object outside. He stipulated that the extramental object must be in a state of complete conformity with its image in the mind to be able to speak of that particular knowledge. He thinks like Ibn Sīnā that knowledge is generated in the mind as a form. He indicates that the shape-giver, Gabriel, who gives the forms clearly, plays an active and dominant role in the production of knowledge in the soul. Sirājuddīn al-Urmawī mentions necessary (ḍarūrī) and acquired (kasbī) knowledge in many passages in his commentary on Ishārāt; and accepted both these types of knowledge. According to him, necessary prime knowledge (awwaliyāt) are the means that lead to acquired knowledge. He shows that the abstraction of mental existence is brought about by reason as a result of complete abstraction and he, following Ibn Sīnā, separates sense perception from the inner perception with precise lines. Since, according to him, external senses cannot perform abstraction. Al-Urmawī thinks that the definition i.e. conception must precede the assent and syllogism and each of these is either necessary or acquired. Acquired knowledge is also derived from the necessary knowledge as a result of intellectual effort. Otherwise, there will be either infinite regression or vicious circle. As Sirājuddīn al-Urmawī’s also holds the idea that, al-‘ārif al-mutanazzih (a knowledgeable purified person) who mature himself with meditation and purification (riyāḍah), can reach knowledge as well through inspiration and unveiling (ilhām and kashf). This particular ‘ārif has a bright rank and higher degree that is unique to them, which also is free and isolated from bodily interests, bonds and situations. Over and above, this happens before the ultimate disconnection between the body and the soul. (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)

Dirac’s identification of the quantum analog of the Poisson bracket with the commutator is reviewed, as is the threat of self-inconsistent overdetermination of the quantization of classical dynamical variables which drove him to restrict the assumption of correspondence between quantum and classical Poisson brackets to embrace only the Cartesian components of the phase space vector. Dirac’s canonical commutation rule fails to determine the order of noncommuting factors within quantized classical dynamical variables, but does imply the quantum/classical correspondence of Poisson brackets (...) between any linear function of phase space and the sum of an arbitrary function of only configuration space with one of only momentum space. Since every linear function of phase space is itself such a sum, it is worth checking whether the assumption of quantum/classical correspondence of Poisson brackets for all such sums is still self-consistent. Not only is that so, but this slightly stronger canonical commutation rule also unambiguously determines the order of noncommuting factors within quantized dynamical variables in accord with the 1925 Born-Jordan quantization surmise, thus replicating the results of the Hamiltonian path integral, a fact first realized by E.H. Kerner. Born-Jordan quantization validates the generalized Ehrenfest theorem, but has no inverse, which disallows the disturbing features of the poorly physically motivated invertible Weyl quantization, i.e., its unique deterministic classical “shadow world” which can manifest negative densities in phase space. (shrink)

Martin’s conjecture is an attempt to classify the behavior of all definable functions on the Turing degrees under strong set theoretic hypotheses. Very roughly it says that every such function is either eventually constant, eventually equal to the identity function or eventually equal to a transfinite iterate of the Turing jump. It is typically divided into two parts: the first part states that every function is either eventually constant or eventually above the identity function and the second part states that (...) every function which is above the identity is eventually equal to a transfinite iterate of the jump. If true, it would provide an explanation for the unique role of the Turing jump in computability theory and rule out many types of constructions on the Turing degrees.In this thesis, we will introduce a few tools which we use to prove several cases of Martin’s conjecture. It turns out that both these tools and these results on Martin’s conjecture have some interesting consequences both for Martin’s conjecture and for a few related topics.The main tool that we introduce is a basis theorem for perfect sets, improving a theorem due to Groszek and Slaman. We also introduce a general framework for proving certain special cases of Martin’s conjecture which unifies a few pre-existing proofs. We will use these tools to prove three main results about Martin’s conjecture: that it holds for regressive functions on the hyperarithmetic degrees, that part 1 holds for order preserving functions on the Turing degrees, and that part 1 holds for a class of functions that we introduce, called measure preserving functions.This last result has several interesting consequences for the study of Martin’s conjecture. In particular, it shows that part 1 of Martin’s conjecture is equivalent to a statement about the Rudin-Keisler order on ultrafilters on the Turing degrees. This suggests several possible strategies for working on part 1 of Martin’s conjecture, which we will discuss.The basis theorem that we use to prove these results also has some applications outside of Martin’s conjecture. We will use it to prove a few theorems related to Sacks’ question about whether it is provable in $\mathsf {ZFC}$ that every locally countable partial order of size continuum embeds into the Turing degrees. We will show that in a certain extension of $\mathsf {ZF}$, this holds for all partial orders of height two, but not for all partial orders of height three. Our proof also yields an analogous result for Borel partial orders and Borel embeddings in $\mathsf {ZF}$, which shows that the Borel version of Sacks’ question has a negative answer.We will end the thesis with a list of open questions related to Martin’s conjecture, which we hope will stimulate further research.prepared by Patrick Lutz.E-mail: [email protected]. (shrink)

We prove a uniqueness theorem showing that, subject to certain natural constraints, all 'no collapse' interpretations of quantum mechanics can be uniquely characterized and reduced to the choice of a particular preferred observable as determine (definite, sharp). We show how certain versions of the modal interpretation, Bohm's 'causal' interpretation, Bohr's complementarity interpretation, and the orthodox (Dirac-von Neumann) interpretation without the projection postulate can be recovered from the theorem. Bohr's complementarity and Einstein's realism appear as two quite different (...) proposals for selecting the preferred determinate observable--either settled pragmatically by what we choose to observe, or fixed once and for all, as the Einsteinian realist would require, in which case the preferred observable is a 'beable' in Bell's sense, as in Bohm's interpretation (where the preferred observable is position in configuration space). (shrink)

Many existence propositions in constructive analysis are implied by the lesser limited principle of omniscience LLPO; sometimes one can even show equivalence. It was discovered recently that some existence propositions are equivalent to Bouwer's fan theorem FAN if one additionally assumes that there exists at most one object with the desired property. We are providing a list of conditions being equivalent to FAN, such as a unique version of weak König's lemma. This illuminates the relation between FAN and LLPO. (...) Furthermore, we give a short and elementary proof of the fact that FAN is equivalent to each positive valued function with compact domain having positive infimum. (shrink)

We show that the Bub-Clifton uniqueness theorem (1996) for 'no collapse' interpretations of quantum mechanics can be proved without the 'weak separability' assumption.

In this article we analyze the claim that a probabilistic interpretation of the infinite epistemic regress problem leads to a unique solution, the so called “completion” of the regress. This claim is implicitly based on the assumption that the standard Kolmogorov axioms of probability theory are suitable for describing epistemic probability. This assumption, however, has been challenged in the literature, by various authors. One of the alternatives that have been suggested to replace the Kolmogorov axioms in case of (...) an epistemic interpretation of probability, are belief functions, introduced by Shafer in 1976. We show that when one uses belief functions to describe the infinite epistemic regress problem, it is no longer the case that the solution is unique. We also argue that this complies with common sense. (shrink)

If M is a countable transitive model of $ZFC+MA_{\aleph_{1}}$ , then for every real x there is a unique shortest iteration $j: M \rightarrow N$ with $x \in N$ , or none at all.

The evolution of the human mind through natural selection mandates that our conscious experiences are causally potent in order to leave a tangible impact upon the surrounding physical world. Any attempt to construct a functional theory of the conscious mind within the framework of classical physics, however, inevitably leads to causally impotent conscious experiences in direct contradiction to evolution theory. Here, we derive several rigorous theorems that identify the origin of the latter impasse in the mathematical properties of ordinary differential (...) equations employed in combination with the alleged functional production of the mind by the brain. Then, we demonstrate that a mind--brain theory consistent with causally potent conscious experiences is provided by modern quantum physics, in which the unobservable conscious mind is reductively identified with the quantum state of the brain and the observable brain is constructed by the physical measurement of quantum brain observables. The resulting quantum stochastic dynamics obtained from sequential quantum measurements of the brain is governed by stochastic differential equations, which permit genuine free will exercised through sequential conscious choices of future courses of action. Thus, quantum reductionism provides a solid theoretical foundation for the causal potency of consciousness, free will and cultural transmission. (shrink)

The existence and uniqueness of a maximum point for a continuous real—valued function on a metric space are investigated constructively. In particular, it is shown, in the spirit of reverse mathematics, that a natural unique existence theorem is equivalent to the fan theorem.

The tridecompositional uniqueness theorem of Elby and Bub (1994) shows that a wavefunction in a triple tensor product Hilbert space has at most one decomposition into a sum of product wavefunctions with each set of component wavefunctions linearly independent. I demonstrate that, in many circumstances, the unique component wavefunctions and the coefficients in the expansion are both hopelessly unstable, both under small changes in global wavefunction and under small changes in global tensor product structure. In my opinion, this means (...) that the theorem cannot underlie lawlike solutions to the problems of the interpretation of quantum theory. I also provide examples of circumstances in which there are open sets of wavefunctions containing no states with various decompositions. (shrink)

The paper aims to elucidate in better detail than before the dispute about whether or not dispositional monism—the view that all basic properties are pure powers—entails a vicious infinite regress. Particular focus is on Alexander Bird's and George Molnar's attempts to show that the arguments professing to demonstrate a vicious regress are inconclusive because they presuppose what they aim to prove, notably that powers are for their nature dependent on something else. I argue that Bird and Molnar are (...) mistaken. It is true that dispositional monism is popularly assumed to characterize powers as dependent entities, but this is not what the arguments aim to prove. They merely aim to demonstrate that it would be absurd to assume that all properties are dependent in this way. Finally, it is argued that there is an unresolved tension in Bird's and Molnar's accounts of powers. They characterize them as being for their nature dependent on the manifestations that they are for, and yet ontologically independent of those same manifestations. Until that tension is resolved, their accounts are not equipped to remove the threat of vicious regress. (shrink)

La régression est un concept connoté de façon souvent négative et elle est souvent uniquement perçue dans sa valeur descriptive et phénoménologique. Dans cet article sur la thérapie de couple, l’auteur distingue les états régressés, sur lesquels s’ancre en partie la constitution du couple, et le processus régressif, qui a lieu au cours de la thérapie. Le thérapeute de couple doit être sensible à ce processus tant dans la compréhension qu’il aura des étapes de la thérapie que dans sa propre (...) position psychique interne. (shrink)

In this work we propose an encoding of Reiter’s Situation Calculus solution to the frame problem into the framework of a simple multimodal logic of actions. In particular we present the modal counterpart of the regression technique. This gives us a theorem proving method for a relevant fragment of our modal logic.

La régression est un concept connoté de façon souvent négative et elle est souvent uniquement perçue dans sa valeur descriptive et phénoménologique. Dans cet article sur la thérapie de couple, l’auteur distingue les états régressés, sur lesquels s’ancre en partie la constitution du couple, et le processus régressif, qui a lieu au cours de la thérapie. Le thérapeute de couple doit être sensible à ce processus tant dans la compréhension qu’il aura des étapes de la thérapie que dans sa propre (...) position psychique interne. (shrink)

According to a standard characterization of dispositions, when a disposition is activated by a stimulus, a manifestation of that disposition typically occurs. For example, when flammable gasoline encounters a spark in an oxygen-rich environment, the manifestation of flammability—combustion—occurs. In the dispositions/powers literature, it is common to assume that a manifestation is an effect of a disposition being activated. (I use “disposition” and “power” interchangeably). I address two questions in this chapter: Could all manifestations be effects that involve things acquiring only (...) dispositional properties? And, is thinking of manifestations as contributions to effects preferable to thinking of them as effects? I defend negative responses to both questions. If all properties are dispositional, as the pandispositionalists claim, then any time the activation of a disposition results is something acquiring a new property, it results in something acquiring another disposition. Some worry that a vicious regress ensues (Swinburne, 1980; Bird, 2007a, 2007b: 132-46). While I believe that regress arguments can be addressed, my worry is that, on the pandispositionalist view, manifestations become unobservable. Thinking of manifestations as effects is problematic in cases where what actually occurs is not the kind of effect that the power is a power for, but rather a complex interaction of various powers. Because of this, some prefer to think of manifestations as contributions to effects (Molnar, 2003: 194-8; Mumford, 2009). I argue against this proposal on the ground that it introduces mysterious new entities into our ontology. In the end, the most plausible view is that a single kind of power can have different kinds of effects, some of which involve the instantiation of non-dispositional properties. I proceed as follows. In the first section of this chapter, I show that the philosophical concept of a manifestation is the concept of an effect. In the second section, I argue against the claim that all manifestations involve instantiations of only dispositional properties. In the third section, I argue against the view that manifestations are contributions rather than effects. (shrink)

Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a (...) frame iff this frame contains at least an infinite walk which has an arbitrarily large depth. We thus get that $\lambda^n$ has a degree of paradoxicality no more than $\lambda^m$ iff the multiplicity of 2 in the (unique) prime factorisation of $n$ is no more than that in the prime factorisation of $m$; and all tranfinite $\lambda^\alpha$ has the same degree of paradoxcality but has a higher degree of paradoxicality than any $\lambda^n$. (shrink)

Drawing on the so-called “doctrinal paradox”, List and Pettit (2002) have shown that, given an unrestricted domain condition, there exists no procedure for aggregating individual sets of judgments over multiple interconnected propositions into corresponding collective ones, where the procedure satisfies some minimal conditions similar to the conditions of Arrow’s theorem. I prove that we can avoid the paradox and the associated impossibility result by introducing an appropriate domain restriction: a structure condition, called unidimensional alignment, is shown to open up (...) a possibility result, similar in spirit to Black’s median voter theorem. Specifically, I prove that, given unidimensional alignment, propositionwise majority voting is the unique procedure for aggregating individual sets of judgments into collective ones in accordance with the above mentioned minimal conditions. (shrink)

For thousands of years, religion through the universal system of its values ​​actively influenced the formation of the worldview in all its most important aspects, including in purely scientific, helping or, conversely, interfering with the actualization of the spiritual and practical potential of culture. And although intensive scientific and technological development significantly influenced the fate of religion itself, leading to a "re-evaluation" of its individual values, the latter did not lose their own, without exaggeration, a leading role in the life (...) of man and society. The question of the meaning of religious values, their unique significance, is still important. It is possible that even today it is even more relevant than in previous years. (shrink)

It is folklore that if a continuous function on a complete metric space has approximate roots and in a uniform manner at most one root, then it actually has a root, which of course is uniquely determined. Also in Bishop's constructive mathematics with countable choice, the general setting of the present note, there is a simple method to validate this heuristic principle. The unique solution even becomes a continuous function in the parameters by a mild modification of the uniqueness (...) hypothesis. Moreover, Brouwer's fan theorem for decidable bars turns out to be equivalent to the statement that, for uniformly continuous functions on a compact metric space, the crucial uniform “at most one” condition follows from its non-uniform counterpart. This classification in the spirit of the constructive reverse mathematics, as propagated by Ishihara and others, sharpens an earlier result obtained jointly with Berger and Bridges. (shrink)

Discussions of Ryle’s regress argument against the “intellectualist legend” have largely focused on whether it is effective against a certain view about knowledge how, namely, the view that knowledge how is a species of propositional knowledge. This is understandable, as this is how Ryle himself framed the issue. Nevertheless, this focus has tended to obscure some different concerns which are no less pressing—either for Ryle or for us today. More specifically, I argue that a version of Ryle’s regress (...) confronts any view according to which the intelligence manifested in action must be inherited from purely inner mental causes. I recommend an alternative account of the metaphysics of intelligent action, which avoids this commitment. (shrink)

According to Ernst Gombrich, cartoons provide us the chance to “study the use of symbols in a circumscribed context [and] find out what role the image may play in the household of our mind” (Gombrich 1973, 190). This paper looks at some underexplored implications and outcomes of Ernst Gombrich’s conceptual schemata when such a schemata is applied to cartoons. While we might easily avoid defamatory reference when picking out a subject in writing or speech, cartoon depictions, especially those unaccompanied by (...) speech bubbles or captions, often rely on a visual symbolism typified by the warping of some features the removal of others, and the manifestation of some visual trope or other, more easily lend themselves to defamatory reference. While harms to the referent are many in cases of defamatory cartoons, this paper focuses on the harms to the viewers of such cartoons by the depicter’s message and mode of representation, unique to the cartoon form. I will focus on the harms of misinformation of the viewer by the visual schemata (Gombrich 1960) present in certain cartoons, and the way this misinformative visual schemata (Ibid) may also restrict the possibility of conceptual revisions in its viewership. Harms of this kind come out uniquely in cartoons via norms of cartooning (as a particularly stylized and symbolic mode of visual representation) and the norms of interaction employed in the act of viewing a cartoon. As we’ll see in our case study of the infamous Jyllands Posten cartoons of Muhammad the Prophet, even in cases where a cartoon representation bears no visual similarity to its referent, viewers can easily and reliably pick out the referent by calling to mind, in our focal case, the defamatory stereotypes, stock figures and icons inextricably linked with the referent. I argue that the damage to viewers of these sorts of depictions lies not in the fact that the viewer manages to pick out the intended referent of the depiction but what tools they use to pick out the referent and how such tools of reference (mis)inform their understanding of the referent they’ve picked out. (shrink)

A minimal theorem in a logic L is an L-theorem which is not a non-trivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal implicational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicational theorem A in intuitionistic logic has a unique -normal proof in NJ (...) whenever A is provable without non-prime contraction. The non-prime contraction rule in NJ is the implication introduction rule whose cancelled assumption differs from a propositional variable and appears more than once in the proof. Our result improves the known partial positive solutions to Komori's problem. Also, we present another simple example of a minimal implicational theorem in intuitionistic logic which does not have a unique -normal proof in NJ. (shrink)

An automatic theorem prover for a proof system in the style of dual tableaux for the relational logic associated with modal logic K has been introduced. Although there are many well-known implementations of provers for modal logic, as far as we know, it is the first implementation of a specific relational prover for a standard modal logic. There are two main contributions in this paper. First, the implementation of new rules, called (k1) and (k2), which substitute the classical relational (...) rules for composition and negation of composition in order to guarantee not only that every proof tree is finite but also to decrease the number of applied rules in dual tableaux. Second, the implementation of an order of application of the rules which ensures that the proof tree obtained is unique.As a consequence, we have implemented a decision procedure for modal logic K. Moreover, this work would be the basis for successive extensions of this logic, such as T, B and S4. (shrink)

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios.

We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms (...) are necessary to prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma. (shrink)

We prove that in IST, Nelson's internal set theory, the Uniqueness and Collection principles, hold for all (including external) formulas. A corollary of the Collection theorem shows that in IST there are no definable mappings of a set X onto a set Y of greater (not equal) cardinality unless both sets are finite and #(Y) ≤ n #(X) for some standard n. Proofs are based on a rather general technique which may be applied to other nonstandard structures. In particular (...) we prove that in a nonstandard model of PA, Peano arithmetic, every hyperinteger uniquely definable by a formula of the PA language extended by the predicate of standardness, can be defined also by a pure PA formula. (shrink)

In this paper, Anselm’s argument for the uniqueness of God or, more precisely, something through which everything that exists has its being is reconstructed. A first reading of the argument leads to a preliminary reconstruens with one major weakness, namely the incompleteness of a central case distinction. In the successful attempt to construct a more tenable reconstruens some additional premises which are deeply rooted in an Anselmian metaphysics are identified. Anselm’s argument seems to depend on premises such as that if (...) two things have the same nature, then there is one common thing from which they have this nature and in virtue of which they exist. Furthermore it appears that infinite regresses are excluded by the premise that if everything that exists is through something, then there is something through which it is “most truly”. (shrink)

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the (...) formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection. (shrink)

Au terme d'une longue recherche en quête du sens de l'art et de son mystère au coeur de nos vies, ce bref essai voudrait revenir sur le point central de jointure entre apparence et apparition qu'on peut désigner sous l'expression de manifestation esthétique. Interrogation ultime que soulève tout grand créateur d'une oeuvre d'art digne de ce nom, à savoir porteuse d'un contenu de vérité authentique. Ainsi du doute de Cézanne hanté au dire de Merleau-Ponty par le soupçon de l'échec de (...) la peinture à conjurer l'illusion des images - ou encore de l'angoisse de Schoenberg à la poursuite d'une musique qui soit espérance messianique (ce que J S Bach déjà avait poursuivi au sommet toute sa vie). Question éminemment philosophique méditée depuis toujours par les plus grands penseurs. Ainsi, au confluent du néo-platonisme et du christianisme, la lecture augustinienne de Plotin ; en plein âge baroque, l'analyse kantienne décisive du sublime au principe de l'imagination esthétique, et, à l'aurore de notre modernité du XXe siècle, l'invocation de Walter Benjamin à "l'aura, l'unique apparaître d'un lointain". (shrink)

In lieu of an abstract, here is a brief excerpt of the content:ManifestsRachel Blau Duplessis (bio)O great classic cadences of English poetry We blush to hear thee lie Above thy deep and dreamless.—Denise Riley, Mop Mop GeorgetteThat tall white pasture clump that we call cow parsnip, Queen Anne’s lace magnified, are, in Latin, umbellifers, a flat-topped or rounded flower cluster. But sometimes people call them “umbrella flowers.” This work is closer to umbrella flowers than to umbellifers, down there on the (...) ground with bricolaged theorizing practices, folk etymologies, my poetry, and intransigent details. That was a tribute to the essay as woodsy ramble [Good xii and x].And to the essay as personal—a way of marking and mocking the professional codes and impersonal solemnities of the representation of thought. If saying “I” like a heroine will adequately undermine unsituated false universals, I’ll say “I” yes I will. “I” will report that in 1966 or so I diminished all the way down to a scant handful of one-line poems, and to gnomic statements, barely effective. The kind of development they needed was not rhetorical but historical.I, Lady, you are my true love’s lady. You stand in the middle of the room, Sunlight streaming around you. Sunlight takes hold of the seeds in you And wets them. I want to hold myself to you, But you are myself. Can I?This 1966 fragment issues directly from, and is a preternatural reminder of a passionate problematic—questions of gender, in relation to an engagement with poetry, poetry figured as a set of psychosocial and intellectual institutions imbuing a practice of writing in lines. This fragment knew and represented issues, points of political and cultural contradiction about the construction of authorship and the poetic career before their maker could see them as such. The fragment was a cognitive act, not just in autobiography. It functioned as a probe of a situation then almost invisible and always underacknowledged; to have understood it then, one would have needed the cultural apparatus precipitated (though not elaborated) by a social movement—second wave feminism, something that had not yet occurred.Despite mirroring each other in a dramatic hinged appositive, with Lady as hinge (“I, Lady, you”), the female “I” is separated by the very concept “Lady” from her addressee, one traditional addressee of poems, the female “you.” “Lady” is both hinge and barrier; she belongs to “my true love”—a charming and smug ballad turn, filled with idealizations of class and sexuality. Yet the “I” wants to hold this “you” figure to herself, actualizing in female-to-female attraction the long half-life of a Petrarchan structure of feeling in order to create female authorship. Now that gesture could be interpreted as desire (in a [End Page 31] lesbian, matrifocal, or preoedipal plot), or as self-aggrandizing forms of egoistic desire. Is the desired embrace regressive? immature? narcissistic? self-serving? greedy? masturbatory? (all these having been thought of as bad attitudes with a bad press—one might now wonder). Fueled by an ambisexual or polysexual suggestiveness, the poem makes a wobbly declaration of vocation in its desire to embrace singular, hieratic woman herself, yourself, myself. Yet as pronouns multiply, a serious problem is accosted. “But you are myself. Can I?”The fragment stops, startled, where the cultural problem began. Authorship was compromised and almost aborted; in any event, these issues, which seemed to me, in my (then commonplace) ignorance of female cultural production, to have no analogues, pointed me toward total blockage. The “can I” is not simply a personal questioning of my own powers, but concerns general contingencies of gender and female place in culture, a then invisible social horizon. Am “I” forbidden to poetry by one—but one key—law of poetry—the cult of the idealized female? Should “Lady” be ditched totally? or examined? both? and how to poke at a Petrarchanism that seems utterly belated, never uniformly hegemonic, and not, after all, the whole content of poetry? (As I bear down upon it, it recedes, is evasive.) Yet any number of writers do take “Lady” for granted as one of the institutional assumptions of poetry. Many male writers get to say Lady early and often... (shrink)

We study experimentally in the laboratory the situation when individuals have to report their private information about a variable to a public authority that then makes inference about the true values given a known variable using a regression technique. It is assumed that individuals prefer this predicted value to be as close as possible to their true value. Consistent with the theoretical literature, we show that subjects misrepresent their private information more when an ordinary least squares regression is implemented than (...) when the so-called resistant line estimator is employed. The latter extends the median voter theorem to the two-dimensional setting and belongs to the family of robust estimation techniques. In fact, we find that OLS involves serious biases but the RL estimation is empirically unbiased. Furthermore, subjects never earn less when the RL is applied. (shrink)

We prove the following main theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality μ. Let μ be a cardinal above the the Löwenheim‐Skolem number of the class. If is μ‐Galois‐stable, has no μ‐Vaughtian Pairs, does not have long splitting chains, and satisfies locality of splitting, then any two ‐limits over M, for, are isomorphic over M.

This paper investigates the role of conditionals in hypothetical reasoning and rational decision making. Its main result is a proof of a representation theorem for preferences defined on sets of sentences (and, in particular, conditional sentences), where an agent’s preference for one sentence over another is understood to be a preference for receiving the news conveyed by the former. The theorem shows that a rational preference ordering of conditional sentences determines probability and desirability representations of the agent’s degrees (...) of belief and desire that satisfy, in the case of non-conditional sentences, the axioms of Jeffrey’s decision theory and, in the case of conditional sentences, Adams’ expression for the probabilities of conditionals. Furthermore, the probability representation is shown to be unique and the desirability representation unique up to positive linear transformation. (shrink)