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30Stochastic Locality and the Bell TheoremsPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1982 601-615. 1982.After some introductory remarks on "experimental metaphysics", a brief survey of the current situation concerning the major types of hidden-variable theories and the inexistence proofs is presented. The category of stochastic, contextual, local theories remains open. Then the main features of a logical analysis of "locality" are sketched. In the deterministic case, a natural "light-cone determination" condition helps bridge the gap that has existed between the physical requirements of the specia…Read more
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39Finitude, infinitude, and isomorphism of interpretations in some nominalistic calculiNoûs 3 (4): 413-425. 1969.
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22Constructivist Mathematics, Quantum Physics and QuantifiersAristotelian Society Supplementary Volume 66 (1). 1992.
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36Randomness and RealityPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978 79-97. 1978.
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152Frege Meets Aristotle: Points as AbstractsPhilosophia Mathematica. 2015.There are a number of regions-based accounts of space/time, due to Whitehead, Roeper, Menger, Tarski, the present authors, and others. They all follow the Aristotelian theme that continua are not composed of points: each region has a proper part. The purpose of this note is to show how to recapture ‘points’ in such frameworks via Scottish neo-logicist abstraction principles. The results recapitulate some Aristotelian themes. A second agenda is to provide a new arena to help decide what is at sta…Read more
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45In a recent paper, while discussing the role of the notion of analyticity in Carnap’s thought, Howard Stein wrote: “The primitive view–surely that of Kant–was that whatever is trivial is obvious. We know that this is wrong; and I would put it that the nature of mathematical knowledge appears more deeply mysterious today than it ever did in earlier centuries – that one of the advances we have made in philosophy has been to come to an understanding of just ∗I am grateful to audiences at the Steinf…Read more
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6Supervenience/Determination a Two-way Street? Yes, But One of the Ways Is the Wrong Way!Journal of Philosophy 89 (1): 42-47. 1992.
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75EPR, bell, and collapse: A route around "stochastic" hidden variablesPhilosophy of Science 54 (4): 558-576. 1987.Two EPR arguments are reviewed, for their own sake, and for the purpose of clarifying the status of "stochastic" hidden variables. The first is a streamlined version of the EPR argument for the incompleteness of quantum mechanics. The role of an anti-instrumentalist ("realist") interpretation of certain probability statements is emphasized. The second traces out one horn of a central foundational dilemma, the collapse dilemma; complex modal reasoning, similar to the original EPR, is used to deri…Read more
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13Review: Stewart Shapiro, Second-Order Languages and Mathematical Practice (review)Journal of Symbolic Logic 54 (1): 291-293. 1989.
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79Quantum Logic and MeaningPSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980. 1980.Quantum logic as genuine non-classical logic provides no solution to the "paradoxes" of quantum mechanics. From the minimal condition that synonyms be substitutable salva veritate, it follows that synonymous sentential connectives be alike in point of truth-functionality. It is a fact of pure mathematics that any assignment Φ of (0, 1) to the subspaces of Hilbert space (dim. ≥ 3) which guarantees truth-preservation of the ordering and truth-functionality of QL negation, violates truth-functional…Read more
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256The new Riddle of radical translationPhilosophy of Science 41 (3): 227-246. 1974.This paper presents parts of a theory of radical translation with applications to the problem of construing reference. First, in sections 1 to 4 the general standpoint, inspired by Goodman's approach to induction, is set forth. Codification of sound translational practice replaces the aim of behavioral reduction of semantic notions. The need for a theory of translational projection (manual construction on the basis of a finite empirical correlation of sentences) is established by showing the ano…Read more
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59Mathematics without Numbers: Towards a Modal-Structural InterpretationPhilosophical Review 101 (4): 919. 1992.
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74Mathematical constructivism in spacetimeBritish Journal for the Philosophy of Science 49 (3): 425-450. 1998.To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As th…Read more
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6Structuralism is a view about the subject matter of mathematics according to which what matters are structural relationships in abstraction from the intrinsic nature of the related objects. Mathematics is seen as the free exploration of structural possibilities, primarily through creative concept formation, postulation, and deduction. The items making up any particular system exemplifying the structure in question are of no importance; all that matters is that they satisfy certain general condit…Read more
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39Responses to Maher, and to Kelly, Schulte, and JuhlPhilosophy of Science 64 (2): 317-322. 1997.None
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68Along with Frege, Russell maintained an absolutist stance regarding the subject matter of mathematics, revealed rather than imposed, or proposed, by logical analysis. The Fregean definition of cardinal number, for example, is viewed as (essentially) correct, not merely adequate for mathematics. And Dedekind’s “structuralist” views come in for criticism in the Principles. But, on reflection, Russell also flirted with views very close to a (different) version of structuralism. Main varieties of modern…Read more
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49Neither categorical nor set-theoretic foundationsReview of Symbolic Logic 6 (1): 16-23. 2013.First we review highlights of the ongoing debate about foundations of category theory, beginning with Fefermantop-down” approach, where particular categories and functors need not be explicitly defined. Possible reasons for resisting the proposal are offered and countered. The upshot is to sustain a pluralism of foundations along lines actually foreseen by Feferman (1977), something that should be welcomed as a way of resolving this long-standing debate
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229The classical continuum without pointsReview of Symbolic Logic 6 (3): 488-512. 2013.We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually ex…Read more
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191995–1996 annual meeting of the association for symbolic logicBulletin of Symbolic Logic 2 (4): 448-472. 1996.
Areas of Specialization
Aesthetics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Philosophy of Physical Science |
Areas of Interest
17th/18th Century Philosophy |