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We examine some of Connes’ criticisms of Robinson’s infinitesimals starting in 1995. Connes sought to exploit the Solovay model S as ammunition against non-standard analysis, but the model tends to boomerang, undercutting Connes’ own earlier work in functional analysis. Connes described the hyperreals as both a “virtual theory” and a “chimera”, yet acknowledged that his argument relies on the transfer principle. We analyze Connes’ “dart-throwing” thought experiment, but reach an opposite conclusion. In S , all definable sets of reals (...) are Lebesgue measurable, suggesting that Connes views a theory as being “virtual” if it is not definable in a suitable model of ZFC. If so, Connes’ claim that a theory of the hyperreals is “virtual” is refuted by the existence of a definable model of the hyperreal field due to Kanovei and Shelah. Free ultrafilters aren’t definable, yet Connes exploited such ultrafilters both in his own earlier work on the classification of factors in the 1970s and 80s, and in Noncommutative Geometry, raising the question whether the latter may not be vulnerable to Connes’ criticism of virtuality. We analyze the philosophical underpinnings of Connes’ argument based on Gödel’s incompleteness theorem, and detect an apparent circularity in Connes’ logic. We document the reliance on non-constructive foundational material, and specifically on the Dixmier trace −∫ (featured on the front cover of Connes’ magnum opus) and the Hahn–Banach theorem, in Connes’ own framework. We also note an inaccuracy in Machover’s critique of infinitesimal-based pedagogy. (shrink)

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In his doctor's thesis [1], Henkin has shown that if a formal logic is consistent, and sufficiently complex, then it must admit a non-standard model. In particular, he showed that there must be a model in which that portion of the model which is supposed to represent the positiveintegers of the formal logic is not in fact isomorphic to the positiveintegers; indeed it is not even well ordered by what is supposed to be the relation (...) of ≦.For the purposes of the present paper, we do not need a precise definition of what is meant by astandard model of a formal logic. The non-standard models which we shall discuss will be flagrantly non-standard, as for instance a model of the sort whose existence is proved by Henkin. It will suffice if we and our readers are in agreement that a model of a formal logic is not astandard model if either: The relation in the model which represents the equality relation in the formal logic is not the equality relation for objects of the model. That portion of the model which is supposed to represent the positiveintegers of the formal logic is not well ordered by the relation ≦. That portion of the model which is supposed to represent the ordinal numbers of the formal logic is not well ordered by the relation ≦. (shrink)

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Non-standard models were introduced by Skolem, first for set theory, then for Peano arithmetic. In the former, Skolem found support for an anti-realist view of absolutely uncountable sets. But in the latter he saw evidence for the impossibility of capturing the intended interpretation by purely deductive methods. In the history of mathematics the concept of a nonstandard model is new. An analysis of some major innovations–the discovery of irrationals, the use of negative and complex numbers, the modern concept of (...) function, and non-Euclidean geometry–reveals them as essentially different from the introduction of non-standard models. Yet, non-Euclidean geometry, which is discussed at some length, is relevant to the present concern; for it raises the issue of intended interpretation. Thestandard model of natural numbers is the best candidate for an intended interpretation that cannot be captured by a deductive system. Next, I suggest, is the concept of a wellordered set, and then, perhaps, the concept of a constructible set. One may have doubts about a realistic conception of thestandard natural numbers, but such doubts cannot gain support from non-standard models. Attempts to utilize non-standard models for an anti-realist position in mathematics, which appeal to meaning-as-use, or to arguments of the kind proposed by Putnam, fail through irrelevance, or lead to incoherence. Robinson’s skepticism, on the other hand, is a coherent position, though one that gives up on providing a detailed philosophical account. The last section enumerates various uses of non-standard models. (shrink)

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If we set ourselves from the point of view of a radical Constructivism, an effective semantic anchorage for an observer system such as the one, for example, represented by the non-trivial machine as imagined by H. von Foerster, can come to be identified only to the extent that the evolving system itself proves able to change the Semantics. This, however, will result in our being able to realize an expression of ourselves as autonomous beings, as subjects, in particular, capable of (...) focusing on the same epistemological conditions relating to our autonomy. A creative autonomy that expresses itself above all in the observer's ability to govern the change taking place. Only the cognitive agent operating in these conditions will actually come to undergo the new embodiment. Here is the passage on one's shoulders to which T. Skolem refers, namely that continuous passage from the first to the second observer that marks the very course of natural evolution. (shrink)

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We give an elementary introduction to non-standard analysis and its applications to the theory of stochastic processes. This is based on a joint book with J. E. Fenstad, R. Høegh-Krohn and T. Lindstrøm. In particular we give a discussion of an hyperfinite theory of Dirichlet forms with applications to the study of the Hamiltonian for a quantum mechanical particle in the potential created by a polymer. We also discuss new results on the existence of attractive polymer measures in dimension (...) d ≤ 5, with applications to the (φ 1 2 φ 2 2 )d-mode1 of interacting quantum fields. (shrink)

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Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for (...) anyone interested in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

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Galileo's paradox of infinity involves comparing the set of natural numbers, N, and the set of squares, {n2 : n ∈ N}. Galileo sets up a one-to-one correspondence between these sets; on this basis, the number of the elements of N is considered to be equal to the number of the elements of {n2 : n ∈ N}. It also characterizes the set of squares as smaller than the set of natural numbers, since ``there are many more numbers than squares". (...) As a result, it concludes that infinities cannot be compared in terms of greater--lesser and the law of trichotomy does not apply to them. Cantor's cardinal numbers provide a measure for sets. Cantor gives a definition of the relation greater–lesser between cardinal numbers and establishes the law of trichotomy for these numbers. Yet, when Cantor's theory is applied to subsets of N, it gives that any set can be either finite or of the power ℵ0. Thus, although the set of squares is the subset of N, they are of the same cardinality. Benci, Di Nasso introduces specific numbers to measure sets called numerosities. With numerosities, the following claim is true: numerosity of A< numerosity of B, whenever A ⊈ B. In this paper, we present a simplified version of the theory of numerosities that applies to subsets of N. This theory complies with Galileo's presupposition that when A ⊈ B, then the number of elements in A is smaller than the number of elements in B. Specifically, we show that as the numerosity of N is the number α, the numerosity of the set of squares is the integer part of the number √α, that is ⌊√α⌋, and the inequality ⌊√α⌋< α holds. (shrink)

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We propose a set theory, called NRFST, in which the Cantorian axiom of infinity is negated, and a new notion of infinity is introduced via nonstandard methods, i. e. via adequate notions ofstandard and internal, two unary predicates added to the language of ZF. After some initial results on NRFST, we investigate its relative consistency with respect to ZF and Kawai's WNST.

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Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 58 Heft: 4 Seiten: 473-488.

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In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10].

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We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible bystandard methods, undermining Halmos’ criticisms. (shrink)

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Twenty years after cultivating a new orientation for aesthetics via the concept of non-photography, François Laruelle returns, having further developed his notion of a non-standard aesthetics. Published for the first time in a bilingual edition, _Photo-Fiction, a Non-Standard Aesthetics_ expounds on Laruelle’s current explorations into a photographic thinking as an alternative to the worn-out notions of aesthetics based on an assumed domination of philosophy over art. He proposes a new philosophical photo-fictional apparatus, or philo-fiction, that strives for a (...) discursive mimesis of the photographic apparatus and the flash of the Real entailed in its process of image making. “A bit like if an artisan, to use a Socratic example, instead of making a camera based off of diagrams found in manuals, on the contrary had as his or her project the designing of a completely new apparatus of philo-fiction, thus capable of producing not simply photos, but photo-fictions.” One must enter into a space for seeing the vectorial and the imaginary number. Laruelle’s philo-fictions become not art installations, but “theoretical installations” calling for the consideration of the possibility of a non-standard aesthetics being of an equal or superior power to art and philosophy, an aesthetics in-the-last-instance that is itself an inventive and creative act of the most contemporary kind. (shrink)

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We propose an intuitive understanding of the statement: ‘an axiom (or: an axiomatic basis) determines the meaning of the only specific constant occurring in it.’ We introduce some basic semantics for functors of the category s/n,n of Lesniewski’s Ontology. Using these results we prove that the popular claim that the axioms of Ontology determine the meaning of the primitive constants is false.

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The kilogram prototype is an object manufactured in late nineteenth century to serve as thestandard unit of mass worldwide. Since then, the kilogram definition has been determined by this unique object, making it a peculiar case in metrological studies. However, after realizing that the prototype’s mass was unexpectedly changing, scientists are seeking a new way to define the kilogram in pure mathematical terms.

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Skolem studied the germs at infinity of the smallest class of real valued functions on the positive real line containing the constant $1$, the identity function ${\mathbf {x}}$, and such that whenever f and g are in the set, $f+g,fg$ and $f^g$ are in the set. This set of germs is well ordered and Skolem conjectured that its order type is epsilon-zero. Van den Dries and Levitz computed the order type of the fragment below $2^{2^{\mathbf {x}}}$. Here we prove that (...) the set of asymptotic classes within any Archimedean class of Skolem functions has order type $\omega $. As a consequence we obtain, for each positive integer n, an upper bound for the fragment below $2^{n^{\mathbf {x}}}$. We deduce an epsilon-zero upper bound for the fragment below $2^{{\mathbf {x}}^{\mathbf {x}}}$, improving the previous epsilon-omega bound by Levitz. A novel feature of our approach is the use of Conway’s surreal number for asymptotic calculations. (shrink)

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"Stains" can serve as a metaphor for the role allotted to meaninglessness not only by partisans of the deterritorializing force of "brute matter", but also by diagnosers of symbolic incompleteness. For both, the blindspot that will lead to the disturbance of a given regime of meaning must be determined through a smear or glitch which that regime cannot sublate: the mark of a Real stripped of systematising mediation. However, we argue that it is all too easy to allow the stringency (...) of this Real to be undermined by the inflation in its name of merely contingent empirical instances. Such blockages to theoretical and artistic practice can be removed with the aid of the articulation of incompleteness and inconsistency implied by François Laruelle's conception of the Real as non-consistent but hypercomplete "radical immanence". À rebours of Laruelle himself, different types of meaninglessness can then be distinguished, de-metaphorized, and conceptualized as "noise". (shrink)

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Forthcoming in S. Artemov and R. Parikh, Proceedings of the ESSLLI 2006 Workshop on Rationality and Knowledge.

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Bibliography of A. A. Fraenkel (p. ix-x)--Axiomatic set theory. Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre, von P. Bernays.--On some problems involving inaccessible cardinals, by P. Erdös and A. Tarski.--Comparing the axioms of local and universal choice, by A. Lévy.--Frankel's addition to the axioms of Zermelo, by R. Mantague.--More on the axiom of extensionality, by D. Scott.--The problem of predicativity, by J. R. Shoenfield.--Mathematical logic. Grundgedanken einer typenfreien Logik, von W. Ackermann.--On the use of Hilbert's [epsilon]-operator in scientific theories, (...) by R. Carnap.--Basic verifiability in the combinatory theory of restricted generality, by H. B. Curry.--Uniqueness ordinals in constructive number classes, by H. Putnam.--On the construction of models, by A. Robinson.--Interpretation of mathematical theories in the first order predicate calculus, by T. Skolem.--The elementary character of two notions from general algebra, by R. Vaught.--Foundations of arithmetic and analysis. Axiomatic method and intuitionism, by A. Heyting.--On rank-decreasing functions, by G. Kurepa.--On non-standard models for number theory, by E. Mendelson.--Concerning the problem of axiomatizability of the field of real numbers in the weak second order logic, by A. Mostowski.--Non-standard models and independence of the induction axiom, by M. O. Rabin.--Sur les ensembles raréfiés de nombres naturels, par W. Sierpinski.--Philosophy of logic and mathematics. Remarks on the paradoxes of logic and set theory, by E. W. Beth.--Logique formalisée et raisonnement juridique, par R. Feys.--Im Umkreis der sogenannten Raumprobleme, von H. Freudenthal.--Process and existence in mathematics, by H. Wang. (shrink)

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Teachers of children of all ages are enjoined by the National Curriculum for English to develop their pupils’ ability to write instandard English. This study explores the implications of these injunctions by examining the use of non-standard dialect grammar in the writing of 362 texts written by pupils of 11 an 15 years of age. It is established that most of the forms used are found in all four of the geographical regions sampled. The grammatical features of (...) these non-standard dialects and the frequency with which they occur are itemised and compared with a study of spoken English based on the same corpus. There is found to be considerable overlap between these and other recent studies of non-standard dialects in schools, although non-standard dialects are used more widely in speech than in writing. (shrink)

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This study explores the phenomenon of the so-called “third reading” of propositional attitude reports. This reading, which was originally explored in the dissertation of J. Fodor (1973) and has since become one of the significant problems in the formal semantics of natural languages, differs from the more well-known de re and de dicto readings by being an intermediate case. If the de re interpretation can be referred to as transparent specific, and the de dicto interpretation as opaque non-specific, then the (...) third reading is transparent non-specific. Fodor'sstandard solution has been the subject of much discussion in the literature and has given rise to a series of widely accepted counterexamples that are thought to demonstrate the limitations of Fodor's solution. At the same time, alternative approaches to the explication of these readings also suffer from formal shortcomings (for example, some of them did not satisfy the requirement of meaning compositionality, which is a basic requirement in formal semantic literature). This study points out that the analysis of all complex cases of the third reading did not fully take into account their syntactic structure. This remained unnoticed due to the ellipsis in many of these cases. It is shown that a restoration of the ellided syntactic structure makes it possible to analyze all hard cases as basic ones using the classicalstandard analysis proposed by Fodor supplemented by the principles of admissibility of substitution of L-equivalent expressions in intensional contexts (known since G. Frege and R. Carnap). In the final part of the work, it is demonstrated how exactly the main complex cases of the “third reading” are explicated in terms of thestandard approach. (shrink)

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In [4] the authors studied the residue field of a model M of IΔ0 + Ω1 for the principal ideal generated by a prime p. One of the main results is that M/ has a unique extension of each finite degree. In this paper we are interested in understanding the structure of any quotient field of M, i.e. we will study the quotient M/I for I a maximal ideal of M. We prove that any quotient field of M satisfies the (...) property of having a unique extension of each finite degree. We will use some of Cherlin's ideas from [3], where he studies the ideal theory of nonstandard algebraicintegers. (shrink)

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In his Mathesis rationis Leibniz discounted out of hand four categorical propositions that would have considerably broadened the resultant syllogistic logic. He did this despite the facts both that he had devised a suitable manner for expressing the latent quantification over terms, and that he had reasoned adequately to determine which of the syllogisms in the resulting broadened logic were valid. Leibniz's reasons for discounting these non-standard propositions are shown to be inadequate, and the resultant syllogistic logic is outlined.

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In the context of life sciences, we are constantly confronted with information that possesses precise semantic values and appears essentially immersed in a specific evolutionary trend. In such a framework, Nature appears, in Monod’s words, as a tinkerer characterized by the presence of precise principles of self-organization. However, while Monod was obliged to incorporate his brilliant intuitions into the framework of first-order cybernetics and a theory of information with an exclusively syntactic character such as that defined by Shannon, research advances (...) in recent decades have led not only to the definition of a second-order cybernetics but also to an exploration of the boundaries of semantic information. As H. Atlan states, on a biological level "the function self-organizes together with its meaning". Hence the need to refer to a conceptual theory of complexity and to a theory of self-organization characterized in an intentional sense. There is also a need to introduce, at the genetic level, a distinction between coder and ruler as well as the opportunity to define a real software space for natural evolution. The recourse to non-standard model theory, the opening to a new general semantics, and the innovative definition of the relationship between coder and ruler can be considered, today, among the most powerful theoretical tools at our disposal in order to correctly define the contours of that new conceptual revolution increasingly referred to as metabiology. This book focuses on identifying and investigating the role played by these particular theoretical tools in the development of this new scientific paradigm. Nature "speaks" by means of mathematical forms: we can observe these forms, but they are, at the same time, inside us as they populate our organs of cognition. In this context, the volume highlights how metabiology appears primarily to refer to the growth itself of our instruments of participatory knowledge of the world. (shrink)

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Introductory collection of writings by a creative and subversive thinker, ranging from the origins of “non-philosophy” to its evolution into what Laruelle now calls “non-standard philosophy.” The question “What is non-philosophy?” must be replaced by the question about what it can and cannot do. To ask what it can do is already to acknowledge that its capacities are not unlimited. This question is partly Spinozist: no-one knows what a body can do. It is partly Kantian: circumscribe philosophy's illusory power, (...) the power of reason or the faculties, and do not extend its sufficiency in the shape of by way of another philosophy. It is also partly Marxist: how much of philosophy can be transformed through practice, how much of it can be withdrawn from its “ideological” use? And finally, it is also partly Wittgensteinian: how can one limit philosophical language through its proper use? This introductory collection of writings by creative and subversive thinker François Laruelle opens with an introduction based upon an in-depth interview that traces the abiding concerns of his prolific output. The eleven newly translated essays that follow, dating from 1985 to the present, range from the origins of “non-philosophy” to its evolution into what Laruelle now calls “non-standard philosophy.” Two appendices present a number of Laruelle's experimental texts, which have not previously appeared in English translation, and a transcript of an early intervention and discussion on his “transvaluation” of Kant's transcendental method. (shrink)

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This essay will strive to provide the reader with various entry points into the project of François Laruelle's non-standard philosophy and its relation to non-aesthetics, via its relation to philosophy as rigorous fiction. It is a new genre, what Laruelle also calls a philo-fiction. Via Laruelle's preoccupation with photography as a new kind of thought, we will follow his trajectory of applying non-philosophy to photography. From his concept of non-photography and continued in Photo-Fiction, a Non-Standard Aesthetics, Laruelle's practice (...) of striving to create a genre of thinking that would be akin to science fiction and use philosophy as material shows itself in the form of experimental, theoretical applications of his philo-fiction to the photo. In their performative thrust, one can begin to see the components or what he calls aspects of philosophy and quantum physics, including the use of superposition and the imaginary number, as well as conceptual personae and generic humanity. Laruelle's work has at its base a highly poetic, fictional strain that in striving to superpose philosophy and art (fiction) also has at its core a place for reducing the violence of decision and actions attempting to work within a space of radical immanence and radical passivity. A performation-withoutperformance. Laruelle will call the photo a ?weak insurrection.? This particle of Laruelle strives merely for such a poetic attempt. (shrink)

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This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.

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In ${\mathbf{H}}$ , a set theory with the comprehension principle within Łukasiewicz infinite-valued predicate logic, we prove that a statement which can be interpreted as “there is an infinite descending sequence of initial segments of ω” is truth value 1 in any model of ${\mathbf{H}}$ , and we prove an analogy of Hájek’s theorem with a very simple procedure.

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In his preface, Hunter explains that this volume is intended to provide for non-mathematicians an introduction to the most important results of modern mathematical logic. The reader will find here the work of Post, Skolem, Gödel, Church, Henkin, and others, presented in a terse and closely-knit style. Though acknowledging the trend toward natural deduction systems, Hunter sticks to more classical axiomatic systems on the grounds that the proofs of metatheorems are simplified by that choice. He begins with a formal system (...) of propositional logic, for which he develops proofs of completeness, consistency, and decidability. Systems of first order predicate logic are then dealt with, and Church's and Gödel's results on undecidability and incompleteness are presented. There is a brief, useful discussion indicating what parts of first order predicate logic are decidable. It is assumed that the reader has some familiarity with elementary formal logic: Hunter develops the set-theoretical results he requires. The compactness of the presentation is facilitated by the use of earlier results for propositional logic to obtain certain results for predicate logic. Especially helpful is Hunter's technique of prefacing each of the longer and more difficult proofs with a section explaining the key ideas and the general method of proof; summaries are also often provided in conclusion. Because of the orientation of the book, a more extensive discussion of the significance of the results obtained and the philosophical issues which have been raised concerning some of them, would have been welcome. Nonetheless, this is a good, concise introduction for those who are not yet prepared to tackle the more technical literature. A bibliography is provided for those interested in pursuing the subject in greater detail.--E. M. F. (shrink)

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A theoretical development is carried to establish fundamental results about rank-initial embeddings and automorphisms of countable non-standard models of set theory, with a keen eye for their sets of fixed points. These results are then combined into a “geometric technique” used to prove several results about countable non-standard models of set theory. In particular, back-and-forth constructions are carried out to establish various generalizations and refinements of Friedman’s theorem on the existence of rank-initial embeddings between countable non-standard models (...) of the fragment \ + \-Separation of \; and Gaifman’s technique of iterated ultrapowers is employed to show that any countable model of \ can be elementarily rank-end-extended to models with well-behaved automorphisms whose sets of fixed points equal the original model. These theoretical developments are then utilized to prove various results relating self-embeddings, automorphisms, their sets of fixed points, strong rank-cuts, and set theories of different strengths. Two examples: The notion of “strong rank-cut” is characterized in terms of the theory \, and in terms of fixed-point sets of self-embeddings. (shrink)

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The paper proposes (1.) a non-standard interpretation of the proverbial expression “deuteros plous” by giving a fresh look to Phaedo, 99c9-d1. Then (2.) it proceeds to the philosophical problem raised in this passage according to this interpretation, that is, the problem of the “hypothesis” or the “unproved principle”. It indicates finally (3.) the kernel of truth contained in thestandard Interpretation and it concludes with some remarks on the “weakness of the logoi”.

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In response to Bhupinder Singh Anand''s article CAN WE REALLY FALSIFY TRUTH BY DICTAT? in THE REASONER II, 1, January 2008,that denies the existence of nonstandard models of Peano Arithmetic, we prove from Compactness the existence of such models.

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Examples involving common causes — most prominently, examples involving genetically influenced choices — are analytically equivalent not tostandard Newcomb Problems — in which the Predictor genuinely predicts the agent's decision — but to non-standard Newcomb Problems — in which the Predictor guarantees the truth of her predictions by interfering with the agent's decision to make the agent choose as it was predicted she would. When properly qualified, causal and epistemic decision theories diverge only onstandard — (...) not on non-standard — Newcomb Problems, and thus not on examples involving common causes. (shrink)

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The aim of the paper is to present some non-standard modalities (such as non-contingency, contingency, essence and accident) based on S5-models in a framework of cut-free hypersequent calculi. We also study negated modalities, i.e. negated necessity and negated possibility, which produce paraconsistent and paracomplete negations respectively. As a basis for our calculi, we use Restall's cut-free hypersequent calculus for S5. We modify its rules for the above-mentioned modalities and prove strong soundness and completeness theorems by a Hintikka-style argument. As (...) a consequence, we obtain a cut admissibility theorem. Finally, we present a constructive syntactic proof of cut elimination theorem. (shrink)

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In lieu of an abstract, here is a brief excerpt of the content:HUME'S BUNDLES, SELF-CONSCIOUSNESS AND KANT Even if we are inclined to view Hume's attempt to explain ascriptions of personal identity as an abysmal failure, we might still be sympathetic toward his proposal to replace the going substance theory of the nature of mind with his bundle account. Thus we might fault Hume for erecting an unachievably highstandard for personal identity, or round on him for excluding bodily (...) criteria 2... from his solution, but nonetheless applaud his spiriting away of the Cartesian soul substance leaving his "true idea of the human mind" (261) as a collection of perceptions in its stead. However, Hume's concern to give an account of the idea of the unity of a human mind in terms of related perceptions has run into notoriously rough sledding, not the least of which is the fact that Hume himself in his Appendix to "Of Personal Identity" seems to abandon his bundle theory in despair. In this paper I shall first be concerned to examine the criticism of his bundle theory which Hume brings forth in the Appendix and explain why I think the core difficulty remains insoluble for Hume. I shall then go on to suggest that the unworkability of Húmete bundle theory is directly tied to his failure to appreciate certain features of the peculiarly first person nature of his question about the make-up of minds. In thus emphasizing the place of the first person voice in my interpretation I am stealing a leaf, if not a chapter, from Kant. But this is as it should be since one of the aims of this essay is to provide an interpretation of Hume's difficulties with his account of the nature of mind which explains part of the reason why 'self-consciousness' (or 'apperception') looms so very large in the Critique of Pure Reason attack upon Hume's type of bundle theory. 60. 1. Hume's Second Thoughts In a burst of self criticism at the Appendix to the section on personal identity, Hume brings forth this objection to his own efforts:...Having thus loosen' d all our particular perceptions, when I proceed to explain the principle of connexion, which binds them together, and makes us attribute to them a real simplicity and identity; I am sensible, that my account is very defective, and that nothing but the seeming evidence of the precedent reasonings cou'd have indue' d me to receive it (635). After additional reflections Hume encapsulates his objection thus:...All my hopes vanish, when I come to explain the principles, that unite our successive perceptions in our thought or consciousness (6SS-6). What is the defect Hume calls to our attention? Notice first that the footnote on page 635 explicitly refers us back to that part of his account Hume considers defective; and when we look back to the text of the Treatise in question, page 260, we find it is precisely there that Hume uses the analogy of a republic to sketch his bundle theory of the unity of mind in terms of the two associative principles, resemblance and causation. So it must somehow be that this account in terms of the associative principles is mistaken. But what then is the mistake? According to Hume it is that he cannot 'explain' the principles which unite the discrete percepts. Now it seems to me there are only two possible things Hume could mean in saying this. He could mean either (1) that the principles which connect the percepts of one mind are instances of the associative principles, but he cannot explain them; or (2) there must be other, non-associative, principles which connect the percepts of a single mind and these he cannot explain. 61. I think we can safely conclude (1) cannot represent Hume's misgivings when he says he is unable to explain the uniting principles of the mental bundles. There is first the fact that he does not call into question his general programme of accounting for the nature of the unity of complex things by the principles of causation, resemblance and contiguity — for example, ships, plants, animals, houses and rivers (e.g. 257f) — but only his... (shrink)

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As political and economic systems of the world become increasingly globalized, education systems in developed nations have established standardized curriculum. Meanwhile, opposing interpretations of globalization, neoliberalism and progressivism, have inspired the growth of different paradigmatic models for global education. Grounded in neoliberalism, the human capital model views education as a means for preparing a skilled workforce; derived from progressivism, the world systems model focuses on educating individuals for global citizenship and civic participation. The purpose of this document analysis is two-fold: (...) (1) to examine the social studies content standards of the U.S. and other developed countries to determine how globalization is presented in state-mandated curricula, and (2) to evaluate whether the depiction of globalization in each set of standards reflects a human capital or world systems model. Our findings indicate that U.S. state content standards heavily emphasize the economics of globalization; non-U.S. standards present a more holistic picture of globalization. Consequently, U.S. standards are more aligned with a human capital model of education whereas non-U.S. standards reflect a world systems interpretation. These findings suggest that students in the U.S. are prepared differently than their counterparts in other developed countries, which has implications for international relations. (shrink)

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Gideon Rosen has recently sketched an argument which aims to establish that the notion of metaphysical modality is systematically ambiguous. His argument contains a crucial sub-argument which has been used to argue for Metaphysical Contingentism, the view that some claims of fundamental metaphysics are metaphysically contingent rather than necessary. In this paper, Rosen’s argument is explicated in detail and it is argued that the most straight-forward reconstruction fails to support its intended conclusion. Two possible ways to save the argument are (...) rebutted and it is furthermore argued that the crucial sub-argument only supports a rather particular variant of Metaphysical Contingentism. (shrink)

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We construct an algebra of generalized functions endowed with a canonical embedding of the space of Schwartz distributions.We offer a solution to the problem of multiplication of Schwartz distributions similar to but different from Colombeau’s solution.We show that the set of scalars of our algebra is an algebraically closed field unlike its counterpart in Colombeau theory, which is a ring with zero divisors. We prove a Hahn–Banach extension principle which does not hold in Colombeau theory. We establish a connection between (...) our theory with non-standard analysis and thus answer, although indirectly, a question raised by Colombeau. This article provides a bridge between Colombeau theory of generalized functions and non-standard analysis. (shrink)

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The outline of modern macroeconomics took shape in Britain in the early nineteenth century thanks, in part, to David Ricardo, one of the most influential economists of the time. Britain was challenged by monetary inflation, industrial unemployment and the loss of jobs abroad. Ricardo pointed the way forward. As a financier and Member of Parliament, he was well versed in politics and commercial affairs. His expertise is shown by the practicality of his proposals, including the resumption of the gold (...) class='Hi'>standard, which was essential given the destabilizing policy of the Bank of England. Ricardo's expertise appears also in his debate with T. R. Malthus about whether an industrial economy can suffer a prolonged depression. Say's Law of Markets and the Quantity Theory of Money figure prominently in his works, but not in an extreme form. He was instead a subtle theorist, recognizing the non-neutrality of money, trade depressions and unemployment. (shrink)

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POSTURES ET PRATIQUES DE L'HOMME Libéralisme, philosophie non-standard et pensée japonaise Jordanco SEKULOVSKI Nous, les sans-philosophie ASIE Japon -/- La philosophie véhicule des distinctions dualistes dont la conflictualité affaiblit gravement notre sentiment de solidarité humaine ; affronter la philosophie sur son propre terrain mène à une impasse, toute objection à son règne métaphysique devant, pour être reçue, se formuler dans les termes mêmes de la métaphysique... Il s'agit donc de changer de terrain, ou de chemin... L'auteur s'appuie sur le (...) kâta japonais qui forme la base des techniques de soi et façonne la pensée et les pratiques sociétales : une alternative crédible à la pensée-monde occidentale aujourd'hui dans l'impasse. -/- - format : 135 x 215 cm ISBN : 978-2-343-00792-2 • septembre 2013 • 222 pages EAN13 : 9782343007922 EAN PDF : 9782336322865. (shrink)

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In this article I intend to show that the inference problem, one of the main objections raised against the anti-Humean theory of natural laws defended by Dretske, Tooley and Armstrong (?DTA theory? for short), can be successfully answered. First, I argue that a proper solution should meet two essential requirements that the proposals made by the DTA theorists do not satisfy. Then I state a solution to the inference problem that assumes a local immanentistic view of universals, a partial definition (...) of the nomic necessitation relation as a relation of existential dependence, and a principle constraining multiple occupancy. I also argue that my solution meets the two requirements. Finally, I deal with non-standard laws such as exclusion laws, causal laws and laws involving spatiotemporal parameters. (shrink)

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This study investigates the impact of fraud/lawsuit revelation on U.S. top executive turnover and compensation. It also examines potential explanatory variables affecting the executive turnover and compensation among U.S. fraud/lawsuit firms. Four important findings are documented. First, there was significantly higher executive turnover among U.S. firms with fraud/lawsuit revelation in the Wall Street Journal than matched firms without such revelation. Second, although on average, U.S. top executives received an increase in cash compensation after fraud/lawsuit revelation, this increase is smaller than (...) that of matched non-fraud/lawsuit firms. Third, fraud/lawsuit firms were more likely to change top executive when chief executive officer (CEO) was not the board chairman and CEO had been on the board for a short time. Fourth, fraud/lawsuit firms were more likely to reduce their executive cash compensation when profitability was low, firms were involved in fraud, the compensation committee size was small, and the board met more often. These findings indicate that although, in general, U.S. fraud/lawsuits firms did not reduce their executive cash compensation, those involved in fraud were more likely to reduce their executive cash compensation than to change their top executives. The finding, that ethical standards is not a significant factor for U.S. executive turnover nor compensation reduction, suggests that ethics appears to play no part in the board’s decisions, and that U.S. firms may have ethical standards in writing but they do not implement nor enforce the standards. (shrink)

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A structure ${\mathbb Y}$ of a relational language L is called almost chainable iff there are a finite set $F \subset Y$ and a linear order $\,<$ on the set $Y\setminus F$ such that for each partial automorphism $\varphi $ of the linear order $\langle Y\setminus F,<\rangle $ the mapping $\mathop {\mathrm {id}}\nolimits _F \cup \varphi $ is a partial automorphism of ${\mathbb Y}$. By theorems of Fraïssé and Pouzet, an infinite structure ${\mathbb Y}$ is almost chainable iff the (...) profile of ${\mathbb Y}$ is bounded; namely, iff there is a positive integer m such that ${\mathbb Y}$ has $\leq m$ non-isomorphic substructures of size n, for each positive integer n. A complete first order L-theory ${\mathcal T}$ having infinite models is called almost chainable iff all models of ${\mathcal T}$ are almost chainable and it is shown that the last condition is equivalent to the existence of one countable almost chainable model of ${\mathcal T}$. In addition, it is proved that an almost chainable theory has either one or continuum many non-isomorphic countable models and, thus, the Vaught conjecture is confirmed for almost chainable theories. (shrink)

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This paper presents an axiomatization of the principle of maximizing expected utility that does not rely on the independence axiom or sure-thing principle. Perhaps more importantly the new axiomatization is based on an ex ante approach, instead of thestandard ex post approach. An ex post approach utilizes the decision maker's preferences among risky acts for generating a utility and a probability function, whereas in the ex ante approach a set of preferences among potential outcomes are on the input (...) side of the theory and the decision maker's preferences among risky acts on the output side. (shrink)

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