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80Frege's RecipeJournal of Philosophy 113 (7): 309-345. 2016.In this paper, we present a formal recipe that Frege followed in his magnum opus “Grundgesetze der Arithmetik” when formulating his definitions. This recipe is not explicitly mentioned as such by Frege, but we will offer strong reasons to believe that Frege applied it in developing the formal material of Grundgesetze. We then show that a version of Basic Law V plays a fundamental role in Frege’s recipe and, in what follows, we will explicate what exactly this role is and explain how it differs f…Read more
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177Ed Zalta's Version of Neo-Logicism: a friendly letter of complaintIn Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis, Ontos. pp. 11--305. 2009.In this short letter to Ed Zalta we raise a number of issues with regards to his version of Neo-Logicism. The letter is, in parts, based on a longer manuscript entitled “What Neo-Logicism could not be” which is in preparation. A response by Ed Zalta to our letter can be found on his website: http://mally.stanford.edu/publications.html (entry C3).
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97Frege on Sense Identity, Basic Law V, and AnalysisPhilosophia Mathematica 24 (1): 9-29. 2016.The paper challenges a widely held interpretation of Frege's conception of logic on which the constituent clauses of basic law V have the same sense. I argue against this interpretation by first carefully looking at the development of Frege's thoughts in Grundlagen with respect to the status of abstraction principles. In doing so, I put forth a new interpretation of Grundlagen §64 and Frege's idea of ‘recarving of content’. I then argue that there is strong evidence in Grundgesetze that Frege di…Read more
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70What is the purpose of neo-logicism?Traveaux de Logique 18 33-61. 2007.This paper introduces and evaluates two contemporary approaches of neo-logicism. Our aim is to highlight the differences between these two neo-logicist programmes and clarify what each projects attempts to achieve. To this end, we first introduce the programme of the Scottish school – as defended by Bob Hale and Crispin Wright1 which we believe to be a..
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70Richard G. Heck Jr. Reading Frege's Grundgesetze. Oxford: Oxford University Press, 2012. ISBN: 978-0-19-923370-0 ; 978-0-19-874437-5 ; 978-0-19-165535-7 . Pp. xvii + 296 (review)Philosophia Mathematica 23 (2): 289-293. 2015.
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1A Framework for Implicit Definitions and the A prioriIn Philip A. Ebert & Marcus Rossberg (eds.), Abstractionism: Essays in Philosophy of Mathematics, Oxford University Press Uk. pp. 133--160. 2016.
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119A Puzzle About Ontological CommitmentsPhilosophia Mathematica 16 (2): 209-226. 2008.This paper raises and then discusses a puzzle concerning the ontological commitments of mathematical principles. The main focus here is Hume's Principle—a statement that, embedded in second-order logic, allows for a deduction of the second-order Peano axioms. The puzzle aims to put pressure on so-called epistemic rejectionism, a position that rejects the analytic status of Hume's Principle. The upshot will be to elicit a new and very basic disagreement between epistemic rejectionism and the neo-…Read more
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777The good, the bad and the uglySynthese 170 (3): 415-441. 2009.This paper discusses the neo-logicist approach to the foundations of mathematics by highlighting an issue that arises from looking at the Bad Company objection from an epistemological perspective. For the most part, our issue is independent of the details of any resolution of the Bad Company objection and, as we will show, it concerns other foundational approaches in the philosophy of mathematics. In the first two sections, we give a brief overview of the "Scottish" neo-logicist school, present …Read more
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489Abstraction and identityDialectica 59 (2). 2005.A co-authored article with Roy T. Cook forthcoming in a special edition on the Caesar Problem of the journal Dialectica. We argue against the appeal to equivalence classes in resolving the Caesar Problem.
University of St. Andrews
PhD, 2006
Stirling, United Kingdom of Great Britain and Northern Ireland
Areas of Specialization
Epistemology |
Philosophy of Mathematics |
20th Century Analytic Philosophy |