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53Mathematical methods in philosophy: Editors' introductionReview of Symbolic Logic 1 (2): 143-145. 2008.Mathematics and philosophy have historically enjoyed a mutually beneficial and productive relationship, as a brief review of the work of mathematician–philosophers such as Descartes, Leibniz, Bolzano, Dedekind, Frege, Brouwer, Hilbert, Gödel, and Weyl easily confirms. In the last century, it was especially mathematical logic and research in the foundations of mathematics which, to a significant extent, have been driven by philosophical motivations and carried out by technically minded philosophe…Read more
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10Semantic Nominalism: How I Learned to Stop Worrying and Love UniversalsIn Francesca Boccuni & Andrea Sereni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics, Springer International Publishing. 2016.Aldo Antonelli offers a novel view on abstraction principles in order to solve a traditional tension between different requirements: that the claims of science be taken at face value, even when involving putative reference to mathematical entities; and that referents of mathematical terms are identified and their possible relations to other objects specified. In his view, abstraction principles provide representatives for equivalence classes of second-order entities that are available provided t…Read more
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111Game-theoretic axioms for local rationality and bounded knowledgeJournal of Logic, Language and Information 4 (2): 145-167. 1995.We present an axiomatic approach for a class of finite, extensive form games of perfect information that makes use of notions like “rationality at a node” and “knowledge at a node.” We distinguish between the game theorist's and the players' own “theory of the game.” The latter is a theory that is sufficient for each player to infer a certain sequence of moves, whereas the former is intended as a justification of such a sequence of moves. While in general the game theorist's theory of the game i…Read more
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42Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3, Nonmonotonic Reasoning and Uncertain ReasoningBulletin of Symbolic Logic 6 (4): 480-484. 2000.
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Non-monotonic LogicIn Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, The Metaphysics Research Lab. 2014.
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20In the light of logic, by Solomon Feferman, Logic and computation in philosophy, Oxford University Press, New York, Oxford, etc., 1998, xii + 340 pp (review)Bulletin of Symbolic Logic 7 (2): 270-277. 2001.
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18Patricia A. Blanchette. Frege's conception of logic. Oxford University Press, 2012. xv + 190 pp (review)Bulletin of Symbolic Logic 19 (2): 219-222. 2013.
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36Completeness and Decidability of General First-Order LogicJournal of Philosophical Logic 46 (3): 233-257. 2017.This paper investigates the “general” semantics for first-order logic introduced to Antonelli, 637–58, 2013): a sound and complete axiom system is given, and the satisfiability problem for the general semantics is reduced to the satisfiability of formulas in the Guarded Fragment of Andréka et al. :217–274, 1998), thereby showing the former decidable. A truth-tree method is presented in the Appendix.
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2Extensional Quotients for Type Theory and the Consistency Problem for NFJournal of Symbolic Logic 63 (1): 247-261. 1998.
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984Frege's Other ProgramNotre Dame Journal of Formal Logic 46 (1): 1-17. 2005.Frege's logicist program requires that arithmetic be reduced to logic. Such a program has recently been revamped by the "neologicist" approach of Hale and Wright. Less attention has been given to Frege's extensionalist program, according to which arithmetic is to be reconstructed in terms of a theory of extensions of concepts. This paper deals just with such a theory. We present a system of second-order logic augmented with a predicate representing the fact that an object x is the extension of a…Read more
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256Life on the RangeIn A. Torza (ed.), Quantifiers, Quantifiers, and Quantifiers, Synthese Library. pp. 171-189. 2015.
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64A Note on Induction, Abstraction, and Dedekind-FinitenessNotre Dame Journal of Formal Logic 53 (2): 187-192. 2012.The purpose of this note is to present a simplification of the system of arithmetical axioms given in previous work; specifically, it is shown how the induction principle can in fact be obtained from the remaining axioms, without the need of explicit postulation. The argument might be of more general interest, beyond the specifics of the proposed axiomatization, as it highlights the interaction of the notion of Dedekind-finiteness and the induction principle
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128Numerical Abstraction via the Frege QuantifierNotre Dame Journal of Formal Logic 51 (2): 161-179. 2010.This paper presents a formalization of first-order arithmetic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interaction of a nonstandard cardinality quantifier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a nonreductionist conception of logicism, a deflationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the…Read more
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1Virtuous circles: From fixed points to revision rulesIn Anil Gupta & Andre Chapuis (eds.), Circularity, Definition, and Truth, Indian Council of Philosophical Research. pp. 1--27. 2000.
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20University of California at Berkeley Berkeley, CA, USA March 24–27, 2011Bulletin of Symbolic Logic 18 (2). 2012.
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32Review: Dov M. Gabbay, C. J. Hogger, J. A. Robinson, D. Nute, Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 3, Nonmonotonic Reasoning and Uncertain Reasoning (review)Bulletin of Symbolic Logic 6 (4): 480-484. 2000.
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47The Complexity of Revision, RevisedNotre Dame Journal of Formal Logic 43 (2): 75-78. 2002.The purpose of this note is to acknowledge a gap in a previous paper, "The complexity of revision," and to provide a corrected version of the argument.
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126On the general interpretation of first-order quantifiersReview of Symbolic Logic 6 (4): 637-658. 2013.While second-order quantifiers have long been known to admit nonstandard, or interpretations, first-order quantifiers (when properly viewed as predicates of predicates) also allow a kind of interpretation that does not presuppose the full power-set of that interpretationgeneral” interpretations for (unary) first-order quantifiers in a general setting, emphasizing the effects of imposing various further constraints that the interpretation is to satisfy
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56Review of Frege's Theorem (review)International Studies in the Philosophy of Science 26 (2): 219-222. 2012.No abstract
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41Paradoxes of Belief and Strategic Rationality, Koons Robert. Cambridge: Cambridge University Press, 1992, xii + 174 pages (review)Economics and Philosophy 9 (2): 305. 1993.
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56Book Review: Keith Simmons. Universality and the Liar: An Essay on Truth and the Diagonal Argument (review)Notre Dame Journal of Formal Logic 37 (1): 152-159. 1996.
Davis, California, United States of America
Areas of Specialization
Philosophy of Language |
Logic and Philosophy of Logic |
Philosophy of Mathematics |
Areas of Interest
Philosophy of Cognitive Science |
General Philosophy of Science |