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230Does category theory provide a framework for mathematical structuralism?Philosophia Mathematica 11 (2): 129-157. 2003.Category theory and topos theory have been seen as providing a structuralist framework for mathematics autonomous vis-a-vis set theory. It is argued here that these theories require a background logic of relations and substantive assumptions addressing mathematical existence of categories themselves. We propose a synthesis of Bell's many-topoi view and modal-structuralism. Surprisingly, a combination of mereology and plural quantification suffices to describe hypothetical large domains, recoveri…Read more
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60Real analysis without classesPhilosophia Mathematica 2 (3): 228-250. 1994.This paper explores strengths and limitations of both predicativism and nominalism, especially in connection with the problem of characterizing the continuum. Although the natural number structure can be recovered predicatively (despite appearances), no predicative system can characterize even the full predicative continuum which the classicist can recognize. It is shown, however, that the classical second-order theory of continua (third-order number theory) can be recovered nominalistically, by…Read more
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90Bayes and beyondPhilosophy of Science 64 (2): 191-221. 1997.Several leading topics outstanding after John Earman's Bayes or Bust? are investigated further, with emphasis on the relevance of Bayesian explication in epistemology of science, despite certain limitations. (1) Dutch Book arguments are reformulated so that their independence from utility and preference in epistemic contexts is evident. (2) The Bayesian analysis of the Quine-Duhem problem is pursued; the phenomenon of a "protective belt" of auxiliary statements around reasonably successful theor…Read more
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49Pluralism and the Foundations of MathematicsIn ¸ Itekellersetal:Sp, . pp. 65--79. 2006.A plurality of approaches to foundational aspects of mathematics is a fact of life. Two loci of this are discussed here, the classicism/constructivism controversy over standards of proof, and the plurality of universes of discourse for mathematics arising in set theory and in category theory, whose problematic relationship is discussed. The first case illustrates the hypothesis that a sufficiently rich subject matter may require a multiplicity of approaches. The second case, while in some respects …Read more
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140Dualling: A critique of an argument of Popper and MillerBritish Journal for the Philosophy of Science 37 (2): 220-223. 1986.
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40The Classical Continuum without Points – CORRIGENDUMReview of Symbolic Logic 6 (3): 571-571. 2013.
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54Interpretations of Probability in Quantum Mechanics: A Case of “Experimental Metaphysics”In Wayne C. Myrvold & Joy Christian (eds.), Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle, Springer. pp. 211--227. 2009.
Areas of Specialization
Aesthetics |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Philosophy of Physical Science |
Areas of Interest
17th/18th Century Philosophy |