Online research in philosophy

The Gödelian symphony -- Foundations and paradoxes -- This sentence is false -- The liar and Gödel -- Language and metalanguage -- The axiomatic method or how to get the non-obvious out of the obvious -- Peano's axioms -- And the unsatisfied logicists, Frege and Russell -- Bits of set theory -- The abstraction principle -- Bytes of set theory -- Properties, relations, functions, that is, sets again -- Calculating, computing, enumerating, that is, the notion of algorithm -- Taking numbers (...) as sets of sets -- It's raining paradoxes -- Cantor's diagonal argument -- Self-reference and paradoxes -- Hilbert -- Strings of symbols -- In mathematics there is no ignorabimus -- Gödel on stage -- Our first encounter with the incompleteness theorem -- And some provisos -- Gödelization, or say it with numbers! -- TNT -- The arithmetical axioms of tnt and the standard model N -- The fundamental property of formal systems -- The Gödel numbering -- And the arithmetization of syntax -- Bits of recursive arithmetic -- Making algorithms precise -- Bits of recursion theory -- Church's thesis -- The recursiveness of predicates, sets, properties, and relations -- And how it is represented in typographical number theory -- Introspection and representation -- The representability of properties, relations, and functions -- And the Gödelian loop -- I am not provable -- Proof pairs -- The property of being a theorem of TNI (is not recursive!) -- Arithmetizing substitution -- How can a TNT sentence refer to itself? -- Fixed point -- Consistency and omega-consistency -- Proving G1 -- Rosser's proof -- The unprovability of consistency and the immediate consequences of G1 and -- G2 -- Technical interlude -- Immediate consequences of G1 and G2 -- Undecidable1 and undecidable 2 -- Essential incompleteness, or the syndicate of mathematicians -- Robinson arithmetic -- How general are Gödel's results? -- Bits of turing machine -- G1 and G2 in general -- Unexpected fish in the formal net -- Supernatural numbers -- The culpability of the induction scheme -- Bits of truth (not too much of it, though) -- The world after Gödel -- Bourgeois mathematicians! : the postmodern interpretations -- What is postmodernism? -- From Gödel to Lenin -- Is biblical proof decidable? -- Speaking of the totality -- Bourgeois teachers! -- (un)interesting bifurcations -- A footnote to Plato -- Explorers in the realm of numbers -- The essence of a life -- The philosophical prejudices of our times -- From Gödel to Tarski -- Human, too human -- Mathematical faith -- I'm not crazy! -- Qualified doubts -- From gentzen to the dialectica interpretation -- Mathematicians are people of faith -- Mind versus computer : Gödel and artificial intelligence -- Is mind (just) a program? -- Seeing the truth and going outside the system -- The basic mistake -- In the haze of the transfinite -- Know thyself : Socrates and the inexhaustibility of mathematics -- Gödel versus wittgenstein and the paraconsistent interpretation -- When geniuses meet -- The implausible Wittgenstein -- There is no metamathematics -- Proof and prose -- The single argument -- But how can arithmetic be inconsistent? -- The costs and benefits of making Wittgenstein plausible. (shrink)

Despite Wittgensein's anti-foundationalist stance, clearly expressed in his claim that philosophy is an activity of analyzing language, his philosophy is based on peculiar conceptual scheme. The post-Wittgensteinian philosophy uses this scheme as Wittgenstein had recommended: as an instrument ("ladder") that helps by forming good taste for judging. The latter is used by solving problems of science and life.

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses the semantic paradoxes, and how they arise as diagonal arguments and fixed point theorems in logic, computability theory, complexity theory and formal language theory.

According to several commentators, Kurt Godel's incompleteness discoveries were assimilated promptly and almost without objection by his contemporaries - - a circumstance remarkable enough to call for explanation. Careful examination reveals, however, that there were doubters and critics, as well as defenders and rival claimants to priority. In particular, the reactions of Carnap, Bernays, Zermelo, Post, Finsler, and Russell, among others, are considered in detail. Documentary sources include unpublished correspondence from Godel's Nachlass.

This paper will apply post-structural semiotic theories to study the texts of Gödel's first incompleteness theorem. I will study the texts’ own articulations of concepts of ‘meaning’, analyze the mechanisms they use to sustain their senses of validity, and point out how the texts depend (without losing their mathematical rigor) on sustaining some shifts of meaning. I will demonstrate that the texts manifest semiotic effects, which we usually associate with poetry and everyday speech. I will conclude with an analysis (...) of how the picture I paint relates to an ethics of mathematical production. (shrink)

A quantum key distribution scheme whose security depends on the features of pre- and post-selected quantum states is described.

The burgeoning literature on jus post bellum has repeatedly reaffirmed three positions that strike me as deeply implausible: that in the aftermath of wars, compensation should be a priority; that we should likewise prioritize punishing political leaders and war criminals even in the absence of legitimate multilateral institutions; and that when states justifiably launch armed humanitarian interventions, they become responsible for reconstructing the states into which they have intervened – the so called “Pottery Barn” dictum, “You break it, you own (...) it.” Against these common positions, this chapter argues that compensation should be subordinate to reconstruction, with resources going where they are most needed and can do the most good, rather than to the most aggrieved. Just punishment, meanwhile, presupposes just multilateral institutions – the victor cannot be trusted to mete out punishment fairly. And just interveners, who have already taken on such a heavy burden, are entitled to expect the international community to contribute to reconstruction after they have made the first and vital steps. After presenting each of these objections in greater depth, the chapter proceeds to draw some tentative inferences from the threads running through each, and suggest that they illustrate a distinctive flaw in the way in which jus post bellum is addressed by many just war theorists, who not only see the war as the grounds of post bellum duties, but also take it to specify their content: Specifically, they take the rights violations with which wars are imbued to be the basis for post-war action, but take the content of post-war duties to be focused on rectifying those rights violations, rather than the more forward-looking goal of establishing a lasting peace. This backward-looking orientation unduly confines these theorists to making attributions of fault, to a limited palette of normative concepts, and to a focus on the belligerents rather than the international community as a whole. Undoubtedly warfare creates a distinctive normative relationship between belligerent states (though we must question how much of this devolves to the citizens of those states). War does generate grounds for post-war duties – but there are other grounds for those duties too, moreover the grounds should not determine the content. It of course matters that the citizens of two states harmed one another in violation of their rights. But when the war is done, peacebuilding should be the priority, not raking over the wrongs of both sides. Sections 2–4 present the objections, Section 5 offers the tentative analysis and proposes a shift in focus toward an ethics of peacebuilding, and Section 6 concludes. (shrink)

In a recent paper S. McCall adds another link to a chain of attempts to enlist Gödel’s incompleteness result as an argument for the thesis that human reasoning cannot be construed as being carried out by a computer.1 McCall’s paper is undermined by a technical oversight. My concern however is not with the technical point. The argument from Gödel’s result to the no-computer thesis can be made without following McCall’s route; it is then straighter and more forceful. Yet the (...) argument fails in an interesting and revealing way. And it leaves a remainder: if some computer does in fact simulate all our mathematical reasoning, then, in principle, we cannot fully grasp how it works. Gödel’s result also points out a certain essential limitation of self-reflection. The resulting picture parallels, not accidentally, Davidson’s view of psychology, as a science that in principle must remain “imprecise”, not fully spelt out. What is intended here by “fully grasp”, and how all this is related to self-reflection, will become clear at the end of this comment. (shrink)

This paper evaluates a form of dualism, which is referred to here as the dualism of conceptual scheme and undifferentiated reality. According to this dualism, although reality appears to be divided into distinct things from the perspective of our system of concepts, it is actually not. I justify the view that this dualism is incoherent.

I define T-schema deflationism as the thesis that a theory of truth for our language can simply take the form of certain instances of Tarski's schema (T). I show that any effective enumeration of these instances will yield as a dividend an effective enumeration of all truths of our language. But that contradicts Gödel's First Incompleteness Theorem. So the instances of (T) constituting the T-Schema deflationist's theory of truth are not effectively enumerable, which casts doubt on the idea that (...) the T-schema deflationist in any sense has a theory of truth. (The argument in section 2 of "Semantics for Deflationists" supercedes this paper.). (shrink)

We show how second order logic incompleteness follows from incompleteness of arithmetic, as proved by Gödel.

This collection of interviews brings together seven post-continental thinkers to discuss their own personal academic development, their experiences of graduate school and their hopes for post-continental philosophy. Each thinker has been chosen for their importance, popularity and potential. Opening with a short introduction this book offers a rare insight into the world of academic philosophy from the inside. Acting as a handbook to post-continental philosophy this book will prepare students for the unique challenges facing academic philosophy in the coming years. (...) The following thinkers appear in the book: Graham Harman, Jeffrey Malpas, Lee Braver, Stuart Elden, Ian Bogost, Levi R. Byrant, and Adrian Ivakhiv. (shrink)

Le début de l'Isagogè de Porphyre énonce une série de trois questions à propos des genres et des espèces, que l'on tient pour l'origine de la médiévale « Querelle des universaux ». Mais la question s'est posée aux interprètes de savoir si, dans ce texte, Porphyre se référait à certaines thèses historiquement déterminées ou bien s'il construisait ces alternatives de façon théorique, dans une lingua franca non connotée d'un point de vue doctrinal. Cet article, en se concentrant sur la première (...) alternative du questionnaire, tente de montrer que le texte porphyrien prend davantage sens si l'on s'avise que l'époque post-hellénistique (IIe s. av. J.-C. – début du IIIe s. ap. J.-C.) donne déjà à voir une polémique scolaire sur le statut des universaux. Ce n'est ainsi pas seulement le vocabulaire employé par Porphyre qui est doctrinalement connoté, mais l'alternative elle-même, qui fait très probablement référence à un débat entre les thèses platoniciennes, stoïciennes et péripatéticiennes. Alexandre d'Aphrodise constitue une aide précieuse pour reconstruire ce débat, dont l'article esquisse une cartographie. (shrink)

This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere. doi: http://dx.doi.org/ 10.5007 / 1808-1711.2011v15n3p453.

I critically examine the eliminativist theories of race or racism, and the behavioral theory of racism, which provide the theoretical foundation, respectively, for the nominalist and substantive conceptualizations of the idea of a post-racial era. The eliminativist theories seek to eliminate the concepts of “race” or “racism” from our discourse. Such elimination indicates a nominalist sense of the idea of a post-racial era. The behavioral theory of racism argues that racism must be manifested in obviously harmful actions. And because such (...) harmful actions are not prevalent today, this implies that we are in a post-racial era in a substantive sense. I conceptualize some subtle forms of racism that are prevalent today, which cannot be captured by the behavioral theory, but can best be captured by doxastic theories of racism. I conceptualize a substantive idea of a post-racial era, and then argue based on such conceptualization, that we are not in a post-racial era because subtle forms of racism are still prevalent today. (shrink)

This article examines certain motifs from Luis Buñuel's late bourgeois trilogy-- The Discreet Charm of the Bourgoisie ( Le Charme Discret de la Bourgeoisie, 1972), The Phantom of Liberty ( Le Fantôme de la Liberté, 1974), and That Obscure Object of Desire ( Cet Obscur Objet du Désir , 1977)--in order to show how they anticipate key trends in contemporary post-Marxian philosophy. In doing so, it draws upon the work of Slavoj Žižek, whose Lacanian revision of Hegel has provided a (...) model of ideology critique that preserves the structure of dialectical thought while avoiding the impulse to project a closed vision of subjectivity and historical change. In particular, such a model offers a means of reconsidering Buñuel’s concern with the perverse . Rather than having a singular ideological content (i.e., the repressed desire for freedom within bourgeois consciousness), the perverse in Buñuel’s films serves as a more volatile index of ideological conflict: freedom becomes perverse from the perspective of law, and law becomes perverse from the perspective of freedom. To recognize these dialectical reversals not only offers a means of appreciating Buñuel’s sense of humor, but also sheds light on how the late films situate "bourgeois" and "revolutionary" impulses in a much more complex, interdependent, and dynamic relationship with one another.  . (shrink)

This paper shows that some classes of multimodal paraconsistent logics endowed with weak forms of negation are incompletable with respect to Kripke semantics. The reach of such incompleteness is discussed, and we argue that this shortcoming, more than just a logical predicament, may be relevant for attempts to characterize quantum logics and to handle quantum information and quantum computation.

We show that there are denumerably many Post-complete normal modal logics in the language which includes an additional propositional constant. This contrasts with the case when there is no such constant present, for which it is well known that there are only two such logics.

In his 1967 paper Vaught used an ingenious argument to show that every recursively enumerable first order theory that directly interprets the weak system VS of set theory is axiomatizable by a scheme. In this paper we establish a strengthening of Vaught's theorem by weakening the hypothesis of direct interpretability of VS to direct interpretability of the finitely axiomatized fragment VS2 of VS. This improvement significantly increases the scope of the original result, since VS is essentially undecidable, but VS2 (...) has decidable extensions. We also explore the ramifications of our work on finite axiomatizability of schemes in the presence of suitable comprehension principles. (shrink)

... rushing around like the red queen in a world where change is virtuous merely because it is change, we can start by putting up some resistance. ...

The epistemological and sociological consequences of post-modernity include the inability to show moral strangers, in terms they can see as binding, the moral wrongness of activities such as abortion. Such activities can be perceived as morally disordered within a content-full moral narrative, but not outside of the context it brings. Though one can salvage something of the Enlightenment project of justifying a morality that can bind moral strangers, one is left with moral and metaphysical views that can be recognized as (...) impoverished and incomplete by those who live their lives within the embrace of a content-full moral narrative. The cardinal dualism of post-modemity is not that which separates mind from body, but the gulf between the morality binding moral strangers and that binding moral friends. Keywords: dualism, human embryo, personhood, post-modernity CiteULike Connotea Del.icio.us What's this? (shrink)

The author argues that the decline of philosophical thought and research in Russia is over. He describes the state of present-day philosophy in Russia, its background, and prospects for development citing concrete examples and little known facts.Any survey of the state of the philosophy in post-Communist Russia is a complicated task requiring accuracy and completness. Whether I succeed in this task remains to be seen, although I shall be content if I manage to present a clear picture. It will of (...) course be subjective and reflect my interests and preferences, remaining in this sense quite incomplete. But I aim to present a concise survey, identifying the most important trends, personalities, and topics of discussion. (shrink)

Social Justice and Political Change, involves the collaboration of thirty social scientists in twelve countries, and represents broad-ranging comparative ...

The paper studies two formal schemes related to -completeness.LetS be a suitable formal theory containing primitive recursive arithmetic and letT be a formal extension ofS. Denoted by (a), (b) and (c), respectively, are the following three propositions (where (x) is a formula with the only free variable x): (a) (for anyn) ( T (n)), (b) T x Pr T (–(x)–) and (c) T x(x) (the notational conventions are those of Smoryski [3]). The aim of this paper is to examine the (...) meaning of the schemes which result from the formalizations, over the base theoryS, of the implications (b) (c) and (a) (b), where ranges over all formulae. The analysis yields two results overS : 1. the schema corresponding to (b) (c) is equivalent to ¬Cons T and 2. the schema corresponding to (a) (b) is not consistent with 1-CON T. The former result follows from a simple adaptation of the -incompleteness proof; the second is new and is based on a particular application of the diagonalization lemma. (shrink)

Gödel began his 1951 Gibbs Lecture by stating: “Research in the foundations of mathematics during the past few decades has produced some results which seem to me of interest, not only in themselves, but also with regard to their implications for the traditional philosophical problems about the nature of mathematics.” (Gödel 1951) Gödel is referring here especially to his own incompleteness theorems (Gödel 1931). Gödel’s first incompleteness theorem (as improved by Rosser (1936)) says that for any consistent formalized (...) system F, which contains elementary arithmetic, there exists a sentence GF of the language of the system which is true but unprovable in that system. Gödel’s second incompleteness theorem states that no consistent formal system can prove its own consistency. (shrink)

This article offers a new scheme of the relation between positive and negative freedom that is based on a retrieval of T. H. Green's theory of freedom and on further reconstructions of his theory. Some of the distinctions in the literature have proven difficult to sustain, and this has resulted in a weakening of the dichotomy in principle, and of the concepts of positive and negative freedom independently of each other. The main distinction between negative and positive freedom offered (...) here is based on the relation of freedom to the will. We have two kinds of freedom, in both our private and social spheres, because there are two types of goods that we, as human beings, pursue: ordinary and moral. This distinction proves to be sustainable, manages to explain the antagonistic nature of the two concepts, and provides grounds for the support of the two kinds of freedom in their own right. (shrink)

Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even in the (...) above wider sense. More systematically, we investigate the interplay of truth definitions and model conditions, proving a preservation theorem characterizing those types of truth definition which generate the minimal modal logic. (shrink)

Abstract Recently, strong arguments have been offered for the inclusion of jus post bellum in just war theory. If this addition is indeed justified, it is plain that, due to the variety in types of post-conflict situation, the content of jus post bellum will necessarily vary. One instance when it looks as if it should become "extended" in its scope, ranging well beyond (for example) issues of "just peace terms," is when occupation of a defeated enemy is necessary. In this (...) situation, this article argues that an engagement by jus post bellum with the morality of post-conflict reconstruction is unavoidable. However, the resulting extension of jus post bellum 's stipulations threatens to generate conflict with another tenet that it would surely wish to endorse with respect to "just occupation," namely, that sovereignty or self-determination should be restored to the occupied people as soon as is reasonably possible. Hence, the action-guiding objective of the theory could become significantly problematized. The article concludes by considering whether this problem supports the claim that the addition of jus post bellum to just war theory is actually more problematic than its supporters have realized. (shrink)

Theorem 1 of Ketland 1999 is not quite correct as stated. The theorem would imply that the disquotational T-scheme – suitably restricted to avoid the liar paradox – is conservative over pure logic. But it has been pointed out (e.g. Halbach 2001, “How Innocent is Deflationism?”, Synthese 126, pp. 179-181) that this is not the case, for one can prove ∃x∃y(x ≠ y) from the T-scheme (lemma 2 below).

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness (...) theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists. (shrink)

This article shows that in two respects, Gödel's incompleteness theorem strongly supports the arguments of Edgar Morin's complexity paradigm. First, from the viewpoint of the content of Gödel's theorem, the latter justifies the basic view of complexity paradigm according to which knowledge is a dynamic, unfinished process, and develops by way of self-criticism and self-transcendence. Second, from the viewpoint of the proof procedure of Gödel's theorem, the latter confirms the complexity paradigm's circular line of inference through which is formed (...) the all-round knowledge of a concrete object. (shrink)

Richard Rorty has argued that Donald Davidson can be classified as a neopragmatist. To this end, Rorty has tried to show that Davidson's views share important similarities with those of Peirce, James, and Dewey. Davidson, for his part, has tended to resist Rorty's attempts to classify his views in this way. Interestingly, the reasons for Rorty's classification and the reasons for Davidson's resistance share a common trait: an appeal to the elimination of the dualism of conceptual scheme and experiential (...) content on the basis of an assumed background of shared beliefs. According to Rorty, Davidson's background of shared beliefs is closely related to the notion of funded experience found in those thinkers often .. (shrink)

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, (...) within the constraints of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the (...) standard readings, for example by adopting sequent rules with multiple conclusions. Another is to explore what readings the natural deduction rules do enforce. When the notion of a model of a rule is generalized, it is found that natural deduction rules express “intuitionistic” readings of their connectives. A third approach is presented here. The intuitionistic readings emerge when models of rules are defined globally, but the notion of a local model of a rule is also natural. Using this benchmark, natural deduction rules enforce exactly the classical readings of the connectives, while this is not true of axiomatic systems. This vindicates the historical motivation for natural deduction rules. One odd consequence of using the local model benchmark is that some systems of propositional logic are not complete for the semantics that their rules express. Parallels are drawn with incompleteness results in modal logic to help make sense of this. (shrink)

Introduction: Archaeology and Post-Structuralism Ian Bapty and Tim Yates i If it recedes one day, leaving behind its works and signs on the shores of our ...

This book offers an exciting re-interpretation of Auguste Comte, the founder of French sociology. Following the development of his philosophy of positivism, Comte later focused on the importance of the emotions in his philosophy resulting in the creation of a new religious system, the Religion of Humanity. Andrew Wernick provides the first in-depth critique of Comte's concept of religion and its place in his thinking on politics, sociology and philosophy of science. He places Comte's ideas in the context of post-1789 (...) French political and intellectual history, and of modern philosophy, especially postmodernism. Wernick relates Comte to Marx and Nietzsche as seminal figures of modernity and examines key features of modern and postmodern French social theory, tracing the inherent flaws and disintegration of Comte's system. Wernick offers original and fascinating insights in this rich study which will attract a wide audience from sociologists and philosophers to cultural theorists and historians. (shrink)

A common objection to Russell's theory of descriptions concerns incomplete definite descriptions: uses of (for example) ‘the book is overdue’ in contexts where there is clearly more than one book. Many contemporary Russellians hold that such utterances will invariably convey a contextually determined complete proposition, for example, that the book in your briefcase is overdue. But according to the objection this gets things wrong: typically, when a speaker utters such a sentence, no facts about the context or the speaker's communicative (...) intentions single out a particular description-theoretic proposition as the proposition expressed. However, this is an objection only if it is assumed that successful linguistic communication requires the hearer to identify a proposition uniquely intended by the speaker. We argue that this assumption is mistaken. On our view, no proposition, descriptive or referential, is uniquely intended in such a context; thus, no proposition can nor need be identified as the proposition expressed. One significant upshot is that, once the aforementioned assumption is rejected, incompleteness no longer poses a threat to Russell's theory of descriptions. (shrink)

Contemporary philosophers of mind tend to assume that the world of nature can be reduced to basic physics. Yet there are features of the mind consciousness, intentionality, normativity that do not seem to be reducible to physics or neuroscience. This explanatory gap between mind and brain has thus been a major cause of concern in recent philosophy of mind. Reductionists hold that, despite all appearances, the mind can be reduced to the brain. Eliminativists hold that it cannot, and that this (...) implies that there is something illegitimate about the mentalistic vocabulary. Dualists hold that the mental is irreducible, and that this implies either a substance or a property dualism. Mysterian non-reductive physicalists hold that the mind is uniquely irreducible, perhaps due to some limitation of our self-understanding. In this book, Steven Horst argues that this whole conversation is based on assumptions left over from an outdated philosophy of science. While reductionism was part of the philosophical orthodoxy fifty years ago, it has been decisively rejected by philosophers of science over the past thirty years, and for good reason. True reductions are in fact exceedingly rare in the sciences, and the conviction that they were there to be found was an artifact of armchair assumptions of 17th century Rationalists and 20th century Logical Empiricists. The explanatory gaps between mind and brain are far from unique. In fact, in the sciences it is gaps all the way down.And if reductions are rare in even the physical sciences, there is little reason to expect them in the case of psychology. Horst argues that this calls for a complete re-thinking of the contemporary problematic in philosophy of mind. Reductionism, dualism, eliminativism and non-reductive materialism are each severely compromised by post-reductionist philosophy of science, and philosophy of mind is in need of a new paradigm. Horst suggests that such a paradigm might be found in Cognitive Pluralism: the view that human cognitive architecture constrains us to understand the world through a plurality of partial, idealized, and pragmatically-constrained models, each employing a particular representational system optimized for its own problem domain. Such an architecture can explain the disunities of knowledge, and is plausible on evolutionary grounds. (shrink)

This paper explores the meaning of social justice and development in post-apartheid South Africa. It begins with social justice as a process of equalisation, presenting some evidence of the challenge and explaining the difficulty of achieving racial equality. Recognition of changes in national development strategy in the post-apartheid era, and their implications for inequality, leads to discussion of alternative development ethics, which involves reconsideration of what stands for the good life. The possibility of a combination of traditional African (...) communitarianism and the ethic of care is explored, as a basis for an alternative conception of the good. Some impediments to the realisation of such a vision are identified. (shrink)

From the historical roots of second-wave feminism to current debates about feminist theory and politics. This introduction to Anglo-American feminist thought provides a critical and panoramic survey of dominant trends in feminism since 1968. Feminism is too often considered a monolithic movement, consisting of an enormous range of women and ideologies, with both similar and different perspectives and approaches. The book is divided into two parts, the first of which takes a close look at the most influential strands of feminism: (...) liberal feminism, Marxist/socialist feminism, radical feminism, lesbian feminism, and black feminism. In later chapters, Whelehan ties these complexities of, and conflicts within, feminism. The role and relationship of men to feminism, and feminism's often thorny relationship to postmodernism, are also the subject of chapter length treatment. Concluding with a provocative discussion of the much-heralded advent of post-feminism and the rise of the new feminist superstars such as Camille Paglia, Naomi Wolf, Susan Faludi, and Katie Roiphe, Modern Feminist thought is an ideal text for students and a book no feminist teacher or activist should be without. (shrink)

All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give arguments against Priest’s (...) use of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox. (shrink)

The modal fictionalist faces a problem due to the fact that her chosen story seems to be incomplete—certain things are neither fictionally true nor fictionally false. The significance of this problem is not localized to modal fictionalism, however, since many fictionalists will face it too. By examining how the fictionalist should analyze the notion of truth according to her story, and, in particular, the role that conditionals play for the fictionalist, I develop a novel and elegant solution to the (...) class='Hi'>incompleteness problem. (shrink)

He argues that the intuitively provable arithmetic sentences constitute a recursively enumerable set, which has a Gödel sentence which is itself intuitively provable. The incompleteness theorem does not apply, since the set of provable arithmetic sentences is not consistent. The purpose of this article is to sharpen Priest's argument, avoiding reference to informal notions, consensus, or Church's thesis. We add Priest's dialetheic semantics to ordinary Peano arithmetic PA, to produce a recursively axiomatized formal system PA that contains its own (...) truth predicate. Whether one is a dialetheist or not, PA is a legitimate, rigorously defined formal system, and one can explore its proof-theoretic properties. The system is inconsistent (but presumably non-trivial), and it proves its own Gödel sentence as well as its own soundness. Although this much is perhaps welcome to the dialetheist, it has some untoward consequences. There are purely arithmetic (indeed, 0) sentences that are both provable and refutable in PA. So if the dialetheist maintains that PA is sound, then he must hold that there are true contradictions in the most elementary language of arithmetic. Moreover, the thorough dialetheist must hold that there is a number g which both is and is not the code of a derivation of the indicated Gödel sentence of PA. For the thorough dialetheist, it follows ordinary PA and even Robinson arithmetic are themselves inconsistent theories. I argue that this is a bitter pill for the dialetheist to swallow. (shrink)

A detailed examination of post-Marxist political theory, focusing especially on the work of Laclau, Habermas, and Derrida. Devenney identifies common concerns between these theorists and demostrates how the respective strenghts of each compliment the weaknesses of the other.

The Kimberley Process Certification Scheme is an innovation in global governance that combines a voluntary industry-led certification system with an inter-state import/export control regime. States, industry, and activists speedily negotiated it in large part due to the concentrated structure of the industry, and the complementary nature of emerging norms regarding both corporate behavior and international intervention in civil conflicts. The potential strength of the Kimberley Process lies in its state-led border controls, but these are being undermined by weak national (...) governments. This effort may not provide an effective model for regulating other “conflict commodities” because of the unique character of the diamond market. (shrink)

Informal statements of Gödel's Second Incompleteness Theorem, referred to here as Informal Second Incompleteness, are simple and dramatic. However, current versions of Formal Second Incompleteness are complicated and awkward. We present new versions of Formal Second Incompleteness that are simple, and informally imply Informal Second Incompleteness. These results rest on the isolation of simple formal properties shared by consistency statements. Here we do not address any issues concerning proofs of Second Incompleteness.

It is well understood and appreciated that Gödel’s Incompleteness Theorems apply to sufficiently strong, formal deductive systems. In particular, the theorems apply to systems which are adequate for conventional number theory. Less well known is that there exist algorithms which can be applied to such a system to generate a gödel-sentence for that system. Although the generation of a sentence is not equivalent to proving its truth, the present paper argues that the existence of these algorithms, when conjoined with (...) Gödel’s results and accepted theorems of recursion theory, does provide the basis for an apparent paradox. The difficulty arises when such an algorithm is embedded within a computer program of sufficient arithmetic power. The required computer program (an AI system) is described herein, and the paradox is derived. A solution to the paradox is proposed, which, it is argued, illuminates the truth status of axioms in formal models of programs and Turing machines. (shrink)

What were the earliest reactions to Gödel's incompleteness theorems? After a brief summary of previous work in this area I analyse, by means of unpublished archival material, the first reactions in Vienna and Berlin to Gödel's groundbreaking results. In particular, I look at how Carnap, Hempel, von Neumann, Kaufmann, and Chwistek, among others, dealt with the new results.

The evidence today is practically uncontested: about thirty years ago we left Fordism behind and entered a new phase of capitalism. That the structures of the post-Fordist social order call for new modes of social critique is also a prevalent idea. The category of alienation continues, however, to be discredited. Nevertheless it is not clear that the categories of democracy (as apparatuses of non-domination), justice and the good life are capable of bringing about the political effects that may be expected (...) today from the concept of alienation. For these reasons, not only the historical diagnostic that appears to have authorized jettisoning the problematic of alienation but also the model of critique used to replace it demand critical scrutiny. (shrink)

This short sketch of Gödel’s incompleteness proof shows how it arises naturally from Cantor’s diagonalization method [1891]. It renders Gödel’s proof and its relation to the semantic paradoxes transparent. Some historical details, which are often ignored, are pointed out. We also make some observations on circularity and draw brief comparisons with natural language. The sketch does not include the messy details of the arithmetization of the language, but the motives for it are made obvious. We suggest this as a (...) more efficient way to teach the topic than what is found in the standard textbooks. For the sake of self–containment Cantor’s original diagonalization is included. A broader and more technical perspective on diagonalization is given in [Gaifman 2005]. In [1891] Cantor presented a new type of argument that shows that the set of all binary sequences (sequences of the form a0, a1,…,an,…, where each ai is either 0 or 1) is not denumerable ─ that is, cannot be arranged in a sequence, where the index ranges over the natural numbers. Let A0, A2,…An, … be a sequence of binary sequences. Say An = an,0, an,1, …, an,i, … . Define a new sequence A* = b0, b1,…,bn,… , by putting. (shrink)

How do we prove true but unprovable propositions? Gödel produced a statement whose undecidability derives from its ad hoc construction. Concrete or mathematical incompleteness results are interesting unprovable statements of formal arithmetic. We point out where exactly the unprovability lies in the ordinary ‘mathematical’ proofs of two interesting formally unprovable propositions, the Kruskal-Friedman theorem on trees and Girard's normalization theorem in type theory. Their validity is based on robust cognitive performances, which ground mathematics in our relation to space and (...) time, such as symmetries and order, or on the generality of Herbrand's notion of ‘prototype proof’. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as ?the class of all individuals?. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes (...) multiple universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

The volumes of G¨ odel’s collected papers under review consist almost entirely of a rich selection of his philosophical/scientific correspondence, including English translations face-to-face with the originals when the latter are in German. The residue consists of correspondence with editors (more amusing than of any scientific value) and five letters from G¨ odel to his mother, in which explains to her his religious views. The term “selection” is strongly operative here: The editors state the total number of items of personal (...) and scientific correspondence in G¨ odel’s Nachlass to be around thirty-five hundred. The correspondence selected involves fifty correspondents, and the editors list the most prominent of these: Paul Bernays, William Boone, Rudolph Carnap. Paul Cohen, Burton Dreben, Jacques Herbrand, Arend Heyting, Karl Menger, Ernest Nagel, Emil Post, Abraham Robinson, Alfred Tarski, Stanislaw Ulam, John von Neumann, Hao Wang, and Ernest Zermelo. The correspondence is arranged alphebetically, with A-G in Volume IV. The imbalance results from the disproportionate size of the Bernays correrspondence: 85 letters are included (almost all of them), spanning 234 pages) including the face-to-face originals and translations). Each volume contains a calendar of all the items included in the volume together with separate calendars listing all known correspondence (whether included or not) with the major correspondents (seven in Volume IV and ten in Volume V). Let me recommend to the reader the review of these same volumes by Paolo Mancosu in the Notre Dame Journal of Formal Logic 45 (2004):109- 125. This essay very nicely describes much of the correspondence in terms of broad themes relating, especially, to the incompleteness theorems—their origins in G¨ odel’s thought, their reception, their impact on Hilbert’s program. (shrink)

This study examines the similarities and differences in pre- and post-Sarbanes-Oxley corporate ethics codes and codes of conduct using the framework of structuration theory. Following the passage of the Sarbanes-Oxley (SOX) legislation in 2002 in the United States, publicly traded companies there undertook development and revision of their codes of ethics in response to new regulatory requirements as well as incentives under the U.S. Corporate Sentencing Guidelines, which were also revised as part of the SOX mandates. Questions that remain are (...) whether these new or revised codes are effective means of communicating changed ethical foci and attitudes in organizations. Centering resonance analysis (CRA) is used to identify differences and similarities across time and industries by analyzing word networks of 46 pre- and post-SOX corporate codes of ethics. Analyses focus on content and structure of generated word networks as well as resulting factors that emerged from the texts. Results are interpreted from the structuration perspective that content and structure of codes are constrained and enabled by system structures while they function to produce and reproduce those structures. Results indicate that corporate codes of ethics are formal discourses of ethics, laws, and control. Code structure has changed across time, with an increased emphasis on compliance in post-SOX codes. Implications for research and practice are discussed in light of findings. (shrink)

In this paper I argue that it is more difficult to see how Godel's incompleteness theorems and related consistency proofs for formal systems are consistent with the views of formalists, mechanists and traditional intuitionists than it is to see how they are consistent with a particular form of mathematical realism. If the incompleteness theorems and consistency proofs are better explained by this form of realism then we can also see how there is room for skepticism about Church's Thesis (...) and the claim that minds are machines. (shrink)

This essay offers a critique of environmental ethics and argues that a post-environmental ethics may be unavoidable. It does so by exposing and questioning the ontological assumptions common to otherwise different modalities of environmental ethics. These modalities, it is argued, rest upon an implicit or explicit 'material essentialism'. Such essentialism entails the belief that putatively 'environmental' entities have discrete and relatively enduring properties. These properties 'anchor' ethical claims and permit the objects of ethical considerability to be named. Against this, it (...) is argued that a non-essentialist ontology is preferable. This ontology presumes neither that environmental phenomena are simply environmental nor that their properties can be 'fixed' under some determinate description. Drawing on recent 'hybrid' research in human geography and elsewhere, it is suggested that the motility and mutability of ostensibly environmental entities be recognised. This recognition, I conclude, desta bilises conventional environmental ethics and calls for a more supple mode of ethical reasoning. (shrink)

Elizabeth Prior claims that dispositional predicates are incomplete in the sense that they have more than one argument place. To back up this claim, she offers a number of arguments that involve such ordinary dispositional predicates as ‘fragile’, ‘soluble’, and so on. In this paper, I will first demonstrate that one of Prior’s arguments that ‘is fragile’ is an incomplete predicate is mistaken. This, however, does not immediately mean that Prior is wrong that ‘fragile’ is an incomplete predicate. On the (...) contrary, I maintain that she has offered another valid argument that does indeed establish the claim that ‘fragile’ is an incomplete predicate. I will argue further that Prior is right that ‘soluble’ is an incomplete predicate. Then does this mean that all dispositional predicates are incomplete? I don’t think so. I will suggest that there are complete dispositional predicates that have no more than one argument place. Finally, by relying on my discussion of the incompleteness of dispositional predicates, I will attempt to provide a better understanding of the context-dependence and intrinsic nature of dispositional ascriptions. (shrink)

Descartes developed a compelling characterization of mental and physical phenomena which has remained more or less canonical for Western philosophy ever since. The greatest testament to the power of Cartesian thinking is its ubiquity. Even philosophers who are critical of post-Cartesian anthropology (philosophers,for instance, who are self-professed exponents of one or another form of hylomorphism) nevertheless tacitly endorse Cartesian assumptions. Part of what leads to this strange inconsistency is that by and large philosophers no longer know what a non-Cartesian anthropology (...) looks like. I discuss some commitments characteristic of post-Cartesian philosophy of mind, and present an alternative conception of psychological phenomena more consistent with a hylomorphic framework. (shrink)

This essay explores how the doctrine of the Resurrection informs theological reflection on reconciliation in post-Apartheid South Africa. It begins by establishing the fragile and liminal state of reconciliation, despite the efforts of the Truth and Reconciliation Commission. It then argues that the Resurrection offers an ecstatic and relational understanding of the human, which in turn provides a basis for advancing claims regarding human dignity and well-being. In conversation with the work of Oliver O'Donovan and James Alison on the Resurrection, (...) this view is further contextualized by incorporating insights from ubuntu and from the work of Judith Butler on grieving. The essay closes with proposals for how the church in post-Apartheid South Africa can give witness to the Resurrection in its immediate life and work through advocacy and carrying on the politics of grieving. (shrink)

This book is the first comprehensive guide and introduction to the central theorists in the post-marxist intellectual tradition. In jargon free language it seeks to unpack, explain, and review many of the key figures behind the rethinking of the legacy of Marx and Marxism in theory and practice. Key thinkers covered include Cornelius Castoriadis, Jean-Francois Lyotard, Deleuze and Guattari, Laclau and Mouffe, Agnes Heller, Jacques Derrida, Jurgen Habermas and post-Marxist feminism. Underlying the whole text is the central question: What is (...) Post-Marxism? Each chapter covers a key thinker or contribution and thus can be read as a stand alone introduction to the principal aspects of their approach. Each chapter is also followed by a summary of key points with a guide to further reading. Key Thinkers from Critical Theory to Post-Marxism provides an ideal introduction to a hitherto complex subject and will be essential reading for all students of contemporary social and political inquiry today. (shrink)

The study draws attention to the transfer of management theories and practices from traditional capitalist countries such as the USA and UK to post-socialist countries that are currently experiencing radical change as they seek to introduce market reforms. It is highlighted that the efficacy of this transfer of management theories and practices is, in part, dependent upon the extent to which work-related attitudes and values vary between traditional capitalist and former socialist contexts. We highlight that practices such as Human Resource (...) Management (HRM) and Organization Development (OD) are inextricably associated with conceptions surrounding culture and society, as well as to variables such as job satisfaction and organisational commitment. The main aim of this study is to compare various attitudes and values of employees in traditional capitalist countries and post-socialist countries. On the basis of the findings of an attitudinal survey of (N = 5914) workers in 15 countries we conclude that certain aspects of the attitudes and values of workers in post-socialist countries and traditional capitalist countries differ significantly. Specifically, these differences were found in respect of context-related and job-related attitudes, and also in relation to the importance that the respondents attached to the subject of ethics more generally. The implications of the study are discussed particularly in relation to the transfer of management theory and practices between traditional capitalist and post-socialist contexts. (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)

In recent years a number of criticisms have been raised against the formal systems of mathematical logic. The latter, qualified as closed systems, have been contrasted with systems of a new kind, called open systems, whose main feature is that they are always subject to unanticipated outcomes in their operation and can receive new information from outside at any time [cf. Hewitt 1991]. While Gödel's incompleteness theorem has been widely used to refute the main contentions of Hilbert's program, it (...) does not seem to have been generally used to point out the inadequacy of a basic ingredient of that program - the concept of formal system as a closed system - and to stress the need to replace it by the concept of formal system as an open system. (shrink)

What Gödel accomplished in the decade of the 1930s before joining the Institute changed the face of mathematical logic and continues to influence its development. As you gather from my title, I’ll be talking about the most famous of his results in that period, but first I want to indulge in some personal reminiscences. In many ways this is a sentimental journey for me. I was a member of the Institute in 1959-60, a couple of years after receiving my PhD (...) at the University of California in Berkeley, where I had worked with Alfred Tarski, another great logician. The subject of my dissertation was directly concerned with the method of arithmetization that Gödel had used to prove his theorems, and my main concern after that was to study systematic ways of overcoming incompleteness. Mathematical logic was going through a period of prodigious development in the 1950s and 1960s, and Berkeley and Princeton were two meccas for researchers in that field. For me, the prospect of meeting with Gödel and drawing on him for guidance and inspiration was particularly exciting. I didn’t know at the time what it took to get invited. Hassler Whitney commented for an obituary notice in 1978 that “it was hard to appoint a new member in logic at the Institute because Gödel could not prove to himself that a number of candidates shouldn’t be members, with the evidence at hand.” That makes it sound like the problem for Gödel was deciding who not to invite. Anyhow, I ended up being one of the lucky few. (shrink)

This paper explores the relationships between Davidson's indeterminacy of interpretation thesis and two semantic properties of sentences that have come to be recognized recently, namely semantic incompleteness and semantic indecision.1 More specifically, I will examine what the indeterminacy thesis entails for sentences of the form 'By sentence S (or word w), agent A means that m' and 'Agent A believes that p.' My primary goal is to shed light on the indeterminacy thesis and its consequences. I will distinguish two (...) kinds of indeterminacy that have very different sources and very different consequences. But this does not purport to be an exhaustive study: there may well be other forms of indeterminacy that this .. (shrink)

We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.

Full proofs of the Gödel incompleteness theorems are highly intricate affairs. Much of the intricacy lies in the details of setting up and checking the properties of a coding system representing the syntax of an object language (typically, that of arithmetic) within that same language. These details are seldom illuminating and tend to obscure the core of the argument. For this reason a number of efforts have been made to present the essentials of the proofs of Gödel’s theorems without (...) getting mired in syntactic or computational details. One of the most important of these efforts was made by Löb [8] in connection with his analysis of sentences asserting their own provability. Löb formulated three conditions (now known as the Hilbert-Bernays-Löb derivability conditions), on the provability predicate in a formal system which are jointly sufficient to yield the Gödel’s second incompleteness theorem for it. A key role in Löb’s analysis is played by (a special case of) what later became known as the diagonalization or fixed point property of formal systems, a property which had already, in essence, been exploited by Gödel in his original proofs of the incompleteness theorems. The fixed point property plays a central role in Lawvere’s [7] category-theoretic account of incompleteness phenomena (see also [10]). Incompleteness theorems have also been subjected to intensive investigation within the framework of modal logic (see, e.g.[4], [5]). In this formulation the modal operator takes up the role previously played by the provability predicate, and the derivability conditions on the latter are translated into algebraic conditions (the so-called GL, i.e., Gödel–Löb, conditions) on the former. My purpose here is to present a framework for incompleteness phenomena, fully compatible with intuitionistic or constructive principles, in which the idea of a coding system is retained, only in a 2 simple, but very general form, a form wholly free of syntactical notions. As codes we shall take the elements of an arbitrary given nonempty set, possibly, but not necessarily, the set of natural numbers.. (shrink)

The contention that abortion harms women constitutes a new strategy employed by the pro-life movement to supplement arguments about fetal rights. David C. Reardon is a prominent promoter of this strategy. Post-abortion syndrome purports to establish that abortion psychologically harms women and, indeed, can harm persons associated with women who have abortions. Thus, harms that abortion is alleged to produce are multiplied. Claims of repression are employed to complicate efforts to disprove the existence of psychological harm and causal antecedents of (...) trauma are only selectively investigated. We argue that there is no such thing as post-abortion syndrome and that the psychological harms Reardon and others claim abortion inflicts on women can usually be ascribed to different causes. We question the evidence accumulated by Reardon and his analysis of data accumulated by others. Most importantly, we question whether the conclusions Reardon has drawn follow from the evidence he cites. (shrink)

This article considers Derrida's reading of Walter Benjamin's ‘Critique of Violence’ in ‘Force of Law’ with particular reference to the claims Derrida makes in his controversial ‘Post-Scriptum’. The article focuses in particular on Derrida's claim – a claim situated within the context of a discourse on the ‘final solution’ – that the ‘Critique of Violence’ is too Heideggerian. This claim is explored in the article mainly through reading Heidegger's ‘Anaximander's Saying’ with the purpose of showing some affinities between his and (...) Benjamin's notions of justice and also with respect to the importance both thinkers bestow on the purity of the name. Particular attention is paid to the notion of ‘divine violence’ and its ‘complicity’ with the ‘worst’ also in relation to the questions of the witness and the animal in Benjamin and Heidegger. The article insists on the importance of the theme of the singular witness in the thinking of justice and divine violence and opens up possible avenues for exploring Derrida's relation to Benjamin. (shrink)

After Enlightenment: The Post-Secular Vision of J. G. Hamann is a comprehensive introduction to the life and works of 18th-century German philosopher, J. G. ...

In addition to this being the centenary of Kurt Gödel’s birth, January marked 75 years since the publication (1931) of his stunning incompleteness theorems. Though widely known in one form or another by practicing mathematicians, and generally thought to say something fundamental about the limits and potentialities of mathematical knowledge, the actual importance of these results for mathematics is little understood. Nor is this an isolated example among famous results. For example, not long ago, Philip Davis wrote me about (...) what he calls The Paradox of Irrelevance: “There are many math problems that have achieved the cachet of tremendous significance, e.g. Fermat, 4 color, Kepler’s packing, Gödel, etc. Of Fermat, I have read: ‘the most famous math problem of all time.’ Of Gödel, I have read: ‘the most mathematically significant achievement of the 20th century.’ … Yet, these problems have engaged the attention of relatively few research mathematicians—even in pure math.” What accounts for this disconnect between fame and relevance? Before going into the question for Gödel’s theorems, it should be distinguished in one respect from the other examples mentioned, which in any case form quite a mixed bag. Namely, each of the Fermat, 4 color, and Kepler’s packing problems posed a stand-out challenge following extended efforts to settle them; meeting the challenge in each case required new ideas or approaches and intense work, obviously of different degrees. By contrast, Gödel’s theorems were simply unexpected, and their proofs, though requiring novel techniques, were not difficult on the scale of things. Setting that aside, my view of Gödel’s incompleteness theorems is that their relevance to mathematical logic (and its offspring in the theory of computation) is paramount; further, their philosophical relevance is significant, but in just what way is far from settled; and finally, their mathematical relevance outside of logic is very much unsubstantiated but is the object of ongoing, tantalizing efforts.. (shrink)

In the paper some applications of Gödel's incompleteness theorems to discussions of problems of computer science are presented. In particular the problem of relations between the mind and machine (arguments by J.J.C. Smart and J.R. Lucas) is discussed. Next Gödel's opinion on this issue is studied. Finally some interpretations of Gödel's incompleteness theorems from the point of view of the information theory are presented.

The article points to similarities between Radical Orthodoxy and the Post-Structuralist critique of rationalistic secularism together with a shared appraisal of aesthecism. However, although the people of Radical Orthodoxy are sympathetic to the modern experience of immanence, they criticize the flattened immanence which seems to result from a post-structuralist perspective, and claim instead that immanence has to be appreciated as creational (and therefore participating in the divine) in order to withstand the threat of nihilism. Thus, Post-Structuralism is only an ally (...) up until the point where it tends to undermine the foot-hold in pre-modern tradition and the commitment to revealed truth. Yet, the way in which Radical Orthodoxy appeals to the better myth (contrary to the ontology of difference pertaining to Post-Structuralism) still carries with it traits of postmodernism and thereby risks the relativism it strives to avoid. (shrink)

Like Heisenberg’s uncertainty principle, Gödel’s incompleteness theorem has captured the public imagination, supposedly demonstrating that there are absolute limits to what can be known. More specifically, it is thought to tell us that there are mathematical truths which can never be proved. These are among the many misconceptions and misuses of Gödel’s theorem and its consequences. Incompleteness has been held to show, for example, that there cannot be a Theory of Everything, the so-called holy grail of modern physics. (...) Some philosophers and mathematicians say it proves that minds can’t be modelled by machines, while others argue that they can be modelled but that Gödel’s theorem shows we can’t know it. Postmodernists have claimed to find support in it for the view that objective truth is chimerical. And in the Bibliography of Christianity and Mathematics (yes, there is such a publication) it is asserted that ‘theologians can be comforted in their failure to systematize revealed truth because mathematicians cannot grasp all mathematical truths in their systems either.’ Not only that, the incompleteness theorem is held to imply the existence of God, since only He can decide all truths. Even Rebecca Goldstein’s book, whose laudable aim is to provide non-technical expositions of the incompleteness theorems (there are two) for a general audience and place them in their historical and biographical context, makes extravagant claims and distorts their significance. As Goldstein sees it, Gödel’s theorems are ‘the most prolix theorems in the history of mathematics’ and address themselves ‘to the central question of the humanities – ‘what is it to be human?’ – since they involve ‘such vast and messy areas as the nature of truth and knowledge and certainty’. Unfortunately, these weighty claims disintegrate under closer examination, while the book as a whole is marred by a number of disturbing conceptual and historical errors. On the face of it, Goldstein would appear to have been an ideal choice to present Gödel’s work: she received a PhD in Philosophy from Princeton University in 1977 and since then has taught philosophy of science and philosophy of mind at several.... (shrink)

This dissertation is an analysis of the development of dialectic and argumentation theory in post-classical Islamic intellectual history. The central concerns of the thesis are; treatises on the theoretical understanding of the concept of dialectic and argumentation theory, and how, in practice, the concept of dialectic, as expressed in the Greek classical tradition, was received and used by five communities in the Islamic intellectual camp. It shows how dialectic as an argumentative discourse diffused into five communities (theologicians, poets, grammarians, philosophers (...) and jurists) and how these local dialectics that the individual communities developed fused into a single system to form a general argumentation theory (adab al-bahth) applicable to all fields. I evaluate a treatise by Shams al-Din Samarqandi (d.702/1302), the founder of this general theory, and the treatises that were written after him as a result of his work. I concentrate specifically on work by 'Ad}ud al-Din al-Iji (d.756/1355), Sayyid Sharif al-Jurjani (d.816/1413), Taşköprüzâde (d.968/1561), Saçaklızâde (d.1150/1737) and Gelenbevî (d.1205/1791) and analyze how each writer (from Samarqandi to Gelenbevî) altered the shape of argumentative discourse and how later intellectuals in the post-classical Islamic world responded to that discourse bequeathed by their predecessors. What is striking about the period that this dissertation investigates (from 1300-1800) is the persistence of what could be called the linguistic turn in argumentation theory. After a centuries-long run, the jadal-based dialectic of the classical period was displaced by a new argumentation theory, which was dominantly linguistic in character. This linguistic turn in argumentation dates from the final quarter of the fourteenth century in Iji's impressively prescient work on 'ilm al-wad'. This idea, which finally surfaced in the post-classical period, that argumentation is about definition and that, therefore, defining is the business of language—even perhaps, that language is the only available medium for understanding and being understood—affected the way that argumentation theory was processed throughout most of the period in question.The argumentative discourse that started with Ibn al-Rawandi in the third/ninth century left a permanent imprint on Islamic intellectual history, which was then full of concepts, terminology and objectives from this discourse up until the late nineteenth century. From this perspective, Islamic intellectual history can be read as the tension between two languages: the "language of dialectic" (jadal) and the "language of demonstration" (burhan), each of which refer not only to a significant feature of that history, but also to a feature that could dramatically alter the interpretation of that history. (shrink)

This article explores the relation between the government and the media in post-apartheid South Africa. An overview is given of key developments and tensions between the government and the media in the first 10 years of democracy and the ethical frameworks underlying the respective positions. An overview of the debate between the so-called "national interest" and the "public interest" is given, and linked to normative ethical frameworks of libertarianism vis-a-vis communitarianism. A mean between the 2 is suggested in the form (...) of mutualism, whereas the necessity for conceptual clarification in debating the relation between the government and the media is emphasized. (shrink)

Weber's discussion of bureaucracy is generally taken as descriptive of organized social structure within a rational-legal society. This is understandable; yet elsewhere in Weber's sociology he cautions against precisely this kind of analysis. His counsel against reification, his emphasis upon subjective ideas standing behind social action, his characterization of "society" as subjective orientation to legitimacy, his discussion of organization and social relationships as probabilities of behavior in accordance with subjective belief in their existence, and his tendency to describe the wide (...) range of world views within the vocabularies of those who subscribe to them-all mitigate against viewing his description of bureaucratic standardization as Weber's own world view, much less as his sociology. Rather the discussion can be understood as a description of bureaucracy from within the bureaucratic setting and as a set of ideas subjectively held to as a basis of legitimacy, ideas whose truth value are largely irrelevant for Weberian analysis. This qualification of bureaucracy as a mentality supplements the more widely acknowledged ideal-type qualification and provides a basis for increased Weberian insight. Such insight dovetails with post-functionalist sociological theory, explains the origins and consequences of functionalist theory, and provides new understandings of recent findings in empirically based research. Moreover, it helps to focus current research away from bureaucracy as an existent entity and toward a phenomenon Weber identifies as the central process of Western civilization: the rationalization (bureaucratization) of human behavior, a process both unfulfillable and unstoppable. (shrink)

Recently criticism and theory have maintained that Kant's aesthetic theory is central to modernism, and have used Foucault's archaeology to interrogate that modernism. This paper suggests that archaeology ultimately cannot escape Kant's hold because it depends on Kantian theses. The first section will consider how a recent exponent of an 'archaeological' viewpoint characterizes Kant's theory and will set out the critical role Kant ascribes to art. The second section compares Kant and Foucault to argue that despite appearances their projects turn (...) out to be substantially coterminal. My interest in comparing these critics is not only to be provocative but also to show that post-modernist thinking, at least in the guise of Foucault, needs and uses standards that Kant proposes. (shrink)

Gödel’s incompleteness applies to any system with recursively enumerable axioms and rules of inference. Chaitin’s approach to Gödel’s incompleteness relates the incompleteness to the amount of information contained in the axioms. Zurek’s quantum Darwinism attempts the physical description of the universe using information as one of its major components. The capacity of quantum Darwinism to describe quantum measurement in great detail without requiring ad-hoc non-unitary evolution makes it a good candidate for describing the transition from quantum to (...) classical. A baby-universe diffusion model of cosmic inflation is analyzed using quantum Darwinism. In this model cosmic inflation can be approximated as Brownian motion of a quantum field, and quantum Darwinism implies that molecular interaction during Brownian motion will make the quantum field decohere. The quantum Darwinism approach to decoherence in the baby-universe cosmic-inflation model yields the decoherence times of the baby-universes. The result is the equation relating the baby-universe’s decoherence time with the Hubble parameter, and that the decoherence time is considerably shorter than the cosmic inflation period. (shrink)

This paper reconsiders the relation between Kantian transcendental reflection (including transcendental idealism) and 20th century philosophy of science. As has been pointed out by Michael Friedman and others, the notion of a "relativized a priori" played a central role in Rudolf Carnap's, Hans Reichenbach's and other logical empiricists' thought. Thus, even though the logical empiricists dispensed with Kantian synthetic a priori judgments, they did maintain a crucial Kantian doctrine, viz., a distinction between the (transcendental) level of establishing norms for empirical (...) inquiry and the (empirical) level of norm-governed inquiry itself. Even though Thomas Kuhn's theory of scientific revolutions is often taken to be diametrically opposed to the received view of science inherited from logical empiricism, a version of this basically Kantian distinction is preserved in Kuhn's thought. In this respect, as Friedman has argued, Kuhn is closer to Carnap's theory of linguistic frameworks than, say, W.V. Quine's holistic naturalism. Kuhn, indeed, might be described as a "new Kant" in post-empiricist philosophy of science. This article examines, first, the relativization of the Kantian a priori in Reichenbach's work, arguing that while Reichenbach (after having given up his original Kantianism) criticized "transcendentalism", he nevertheless retained, in a reinterpreted form, a Kantian-like transcendental method, claiming that the task of philosophy (of science) is to discover and analyze the presuppositions underlying the applicability of conceptual systems. Then, some reflections on Kuhn's views on realism are offered, and it is suggested that Kuhn (as well as some other influential contributors to the realism debate, such as Hilary Putnam) can be reinterpreted as a (relativized, naturalized) Kantian transcendental idealist. Given the central importance of Kuhnian themes in contemporary philosophy of science, it is no exaggeration to claim that Kantian transcendental inquiry into the constitutive principles of empirical knowledge, and even transcendental idealism (as the framework for such inquiry), still have a crucial role to play in this field and deserve further scrutiny. (shrink)

In this post-9/11 era marked by religious and ethnic conflicts and the rise of cultural intolerance, ambiguities arising from the conflation of multiculturalism, sexism, and religious fundamentalism jeopardize the delivery of culturally safe nursing care to non-Western populations. This new social reality requires nurses to develop a heightened awareness of health issues pertaining to racism and ethnocentrism to provide culturally safe care to non-Western immigrants or refugees. Through the lens of post-colonial feminism, this paper explores the challenge of providing culturally (...) safe nursing care in the context of the post-9/11 in Canadian healthcare settings. A critical appraisal of the literature demonstrates that post-colonial feminism, despite some limitations, remains a valuable theoretical perspective to apply in cultural nursing research and develop culturally safe nursing practice. Post-colonial feminism offers the analytical lens to understand how health, social and cultural context, race and gender intersect to impact on non-Western populations' health. However, an uncritical application of post-colonial feminism may not serve racialized men's and women's interests because of its essentialist risk. Post-colonial feminism must expand its epistemological assumptions to integrate Taylor's concept of identity and recognition and Bakhtin's concepts of dialogism and unfinalizability to explore non-Western populations' health issues and the context of nursing practice. This would strengthen the theoretical adequacy of post-colonial feminist approaches in unveiling the process of racialization that arises from the conflation of multiculturalism, sexism, and religious fundamentalism in Western healthcare settings. (shrink)

• How to construct a ‘canonical’ Gödel sentence • If PA is sound, it is negation imcomplete • Generalizing that result to sound p.r. axiomatized theories whose language extends LA • ω-incompleteness, ω-inconsistency • If PA is ω-consistent, it is negation imcomplete • Generalizing that result to ω-consistent p.r. axiomatized theories which extend Q..

Karl Ameriks has recently devoted an entire volume to defending what he calls "orthodox" Kantianism against what he judges to be the "errors" of such post-Kantian idealists as K. L. Reinhold and J. G. Fichte and to exposing what he claims is the frequently unnoticed but always deleterious influence of post-Kantianism upon certain prominent strands of contemporary philosophy. In response, this paper challenges Ameriks' interpretation of Kantianism itself and of the "post-Kantian project", as well as his construal of transcendental idealism. (...) This is followed by some remarks concerning Reinhold's and Fichte's actual "arguments" for transcendental idealism and a rejection of Ameriks' characterizations of the same. Ameriks' interpretation of "the primacy of the practical" within Fichte's philosophy is also analyzed and criticized, as are his unsubstantiated claims concerning the powerful "indirect" influence of the writings of Reinhold and Fichte upon contemporary philosophy. (shrink)

Sayer argues that Popper defended a logicist philosophy of science. The problem with such logicism is that it creates what is termed here as a `truncated foundationalism', which restricts epistemic certainty to the logical form of scientific theories whilst having nothing to say about their substantive contents. Against this it is argued that critical realism, which Sayer advocates, produces a linguistic version of truncated foundationalism and that Popper's problem-solving philosophy, with its emphasis on developing knowledge through criticism, eschews all forms (...) of foundationalism and is better able to account for the development of substantive knowledge claims. Key Words: critical realism • fallibilism • logicism • post-positivism • truncated foundationalism. (shrink)

Many recent articles argue that participants who seroconvert during HIV prevention trials deserve treatment when they develop AIDS, and there is a general consensus that the participants in HIV/AIDS treatment trials should have continuing post-trial access. As a result, the primary concern of many ethicists and activists has shifted from justifying an obligation to treat trial participants, to working out mechanisms through which treatment could be provided. In this paper I argue that this shift frequently conceals an important assumption: that (...) if there is an obligation to supply treatment, then any party who could provide it may be prevailed upon to discharge the obligation. This assumption is false. The reasons why trial participants should get ART affect who has the duty to provide it. We should not burden governments with the obligations of sponsors, nor researchers with the obligations of the international community. And we should not deprive a group of treatment because their need is less salient than that of research participants. Insisting otherwise may lead to people being wrongfully deprived of access to antiretrovirals. (shrink)

It is frequently said that biology is emerging from a long phase of reductionism. It would be certainly more correct to say that biologists are abandoning a certain form of reductionism. We describe this past form, and the experiments which challenged the previous vision. To face the difficulties which were met, biologists use a series of concepts and metaphors - pleiotropy, tinkering, epigenetics - the ambiguity of which masks the difficulties, instead of solving them. In a similar way, the word (...) “post-genomics” has different meanings, depending upon who uses it. Which of these meanings will become dominant in the future is an open question. (shrink)

Social scientists increasingly claim that work structures based on the mass production or "Fordist" paradigm have grown obsolete, giving way to a more flexible, "post-Fordist" structure of work. These claims have been much disputed, however, giving rise to a sharply polarized debate over the outcome of workplace restructuring. I seek to reorient the debate by subjecting the post-Fordist approach to theoretical and empirical critique. Several theoretical weaknesses internal to the post-Fordist approach are identified, including its uncertain handling of "power" and (...) "efficiency" as factors that shape work organizations; its failure to acknowledge multiple responses to the crisis of Fordism, several of which seem at odds with the post-Fordist paradigm; and its tendency to neglect the resurgence of economic dualism and disparity within organizations and industries. Review of the empirical literature suggests that, despite scattered support for the post-Fordist approach, important anomalies exist (such as the growing authority of "mental" over manual labor) that post-Fordism seems powerless to explain. In spite of its ample contributions, post-Fordist theory provides a seriously distorted guide to the nature of workplace change in the United States. Two alternative perspectives toward the restructuring of work organizations are sketched-neoinstitutionalist and "flexible accumulation" models-which seem likely to inspire more fruitful lines of research on the disparate patterns currently unfolding within American work organizations. (shrink)

For quite some time there has been a collective perception of a moral crisis in post- Mao China. This perception is informed by standards held by members of Chinese society rather than by standards outside of it. In this article, the author attempts to lay the groundwork for a philosophical analysis of this moral crisis. He first explains why it is appropriate to speak of a moral crisis and then examines the structure of the crisis. This examination is partly conceptual (...) and partly causal. The conceptual section of the article discusses terms frequently used in connection with the crisis and introduces some terms and distinctions of the author’s own for further clarity. The causal section traces the moral crisis to a crisis of identification with moral authority or exemplars, the latter crisis in turn containing important clues to the structure of self and agency in Chinese moral culture. (shrink)

For some years now, Jürgen Habermas, possibly the most influential European philosopher of today, has been producing a growing number of publications on world politics. In the historical context of the collapse of bipolarity and the advent of the triad, along with the punitive wars in the Gulf and Yugoslavia, he is very far from being alone: Jacques Derrida and Noberto Bobbio,Michael Walzer and John Rawls, to name only the most forceful, have also been thinking out loud about the new (...) political configurations beyond the nation-state. The characteristic feature of Habermas’s thought is to perceive a radically new historical configuration, which he calls a‘post-national constellation’ and which would justify the development of a new political project, as a transition to a new cosmopolitan law. In what follows, I examine the precise modalities that are supposed to transform his philosophical design into political and legal arrangements, attempting to dissect the Habermasian vision of a post-Cold War politics better adapted to the challenges of the new century, and to throw light on the ideology behind it, as a prolegomenon to the larger project Habermas invites us to undertake. (shrink)

The post-modern, post-enlightenment debate on the nature of being begins with Heidegger’s assertion that the “ancient interpretation of the being of beings” is informed by “the determination of the sense of being as ... ‘presence.’”[i] This understanding, which reduces being to temporal presence, is supposed to have set all subsequent philosophical reflection. At its origin is “Aristotle’s essay on time.” In Heidegger’s reading, Aristotle interprets entities with regard to the present, equating their being with temporal presence. He also takes time (...) itself as a present entity--i.e., “as just one being among others.”[ii] In an interpretation that is essentially “oriented to the world,” Aristotle thus collapses being and temporal presence to the point that the countable nows are, in their presence, taken as entities. Aristotle’s essay, Heidegger claims, “has essentially determined every subsequent account of time--Bergson’s included.” Even “the Kantian interpretation of time” remains under its sway.[iii] Given this, the “destruction” of the tradition that Heidegger proposes[iv] is a destruction of this account.[v] Only through such a destruction can we uncover what the Aristotelian account conceals. In making time objective, it hides Dasein’s (or human being’s) role in temporalization. The project of Being and Time is to uncover this through “the repeated interpretation of the structures of Dasein ... as modes of temporalization.”[vi]. (shrink)

The author examines, historically and theoretically, issues related to the state and current tendencies of post-Soviet Russian philosophy. The accent falls on the meta-philosophical question, what is philosophy?, or as the Russians often say, what is philosophizing?. In the Russian case, this question has presently to be handled in a cultural context ridden with a sense of discontinuity following the Soviet collapse. The author sketches some concepts intended to shed light on the nature of the relation between a philosophical culture (...) and the wider socio-cultural context in which it is embedded. The model is applied to the case of post-Soviet philosophy in order to see if and to what extent the logic of Soviet philosophizing and its place in the Soviet socio-cultural order has affected current philosophical tendencies in Russia, above all at the meta-philosophical level. The author concludes with a summary and commentary of the views of A.S. Akhiezer. (shrink)

This book puts forward a revisionist view of Japanese wartime thinking. It seeks to explore why Japanese intellectuals, historians and philosophers of the time insisted that Japan had to turn its back on the West and attack the United States and the British Empire. Based on a close reading of the texts written by members of the highly influential Kyoto School, and revisiting the dialogue between the Kyoto School and the German philosopher Heidegger, it argues that the work of Kyoto (...) thinkers cannot be dismissed as mere fascist propaganda, and that this work, in which race is a key theme, constitutes a reasoned case for a post-White world. The author also argues that this theme is increasingly relevant at present, as demographic changes are set to transform the political and social landscape of North America and Western Europe over the next fifty years. (shrink)

Presumed long-since dead by Nietzsche, God has made a remarkable comeback in the recent work of Derrida and Levinas who have made people think about theology and what it has to offer in light of the nihilism of postmodern thinking. Post-Secular Philosophy explores the relationship between theology, the major thinkers of the philosophical tradition, and the broader debates about God within modern philosophy and the role of God in postmodern thought. Beginning with Descartes, Kant and Hegel and ending with Derrida, (...) Levinas and Baudrillard, this book provides a thorough discussion of the philosophical and cultural importance of theology within postmodernism. Fifteen chapters consider each of these philosophers in turn: Descartes, Kant, Hegel, Kierkegaard, Nietzsche, Heidegger, Freud, Wittgenstein, Lacan, Levinas, Derrida, Marion, Kristeva, Irigaray and Baudrillard. (shrink)

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin''s famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure (...) of the strength of the theory.I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental. (shrink)

In a quartet of books, Neil MacCormick develops in great detail his institutional theory of law. According to this theory, law is an institutional normative order. As we shall see, save for one key difference, MacCormick's institutional theory of a legal system closely parallels Hart's positivist theory. Though his theory of a legal system looks very much like Hart's positivist theory, he concludes that a central positivist tenet is false. He argues that, contra positivism, moral considerations are necessarily determinants of (...) a legal system's laws; for, on his account, radically unjust norms necessarily are not law. Thus, MacCormick theory presents us with a surprising juxtaposition - in his words, a post-positivist synthesis of positivism and natural law theory. In this essay, I examine whether it is possible to reach a natural law conclusion on the basis of what is traditionally taken to be a positivist foundation. I argue that MacCormick's and Julie Dickson's attempts (on MacCormick's behalf) to do this are not promising. However, I also argue that MacCormick's theory of law has resources for a more promising approach to this argument, and I attempt to mine these resources. (shrink)

In Episode 1, we introduced the very idea of a negation-incomplete formalized theory T . We noted that if we aim to construct a theory of basic arithmetic, we’ll ideally like the theory to be able to prove all the truths expressible in the language of basic arithmetic, and hence to be negation complete. But Gödel’s First Incompleteness Theorem says, very roughly, that a nice theory T containing enough arithmetic will always be negation incomplete. Now, the Theorem comes in (...) two flavours, depending on whether we cash out the idea of being ‘nice enough’ in terms of (i) the semantic idea of T ’s being a sound theory, or (ii) the idea of odel’s own T ’s being a consistent theory which proves enough arithmetic. And we noted that G¨. (shrink)