
154Frege on Consistency and Conceptual AnalysisPhilosophia Mathematica 15 (3): 321346. 2007.Gottlob Frege famously rejects the methodology for consistency and independence proofs offered by David Hilbert in the latter's Foundations of Geometry. The present essay defends against recent criticism the view that this rejection turns on Frege's understanding of logical entailment, on which the entailment relation is sensitive to the contents of nonlogical terminology. The goals are (a) to clarify further Frege's understanding of logic and of the role of conceptual analysis in logical inves…Read more

137Models and modalitySynthese 124 (12): 4572. 2000.This paper examines the connection between modeltheoretic truth and necessary truth. It is argued that though the modeltheoretic truths of some standard languages are demonstrably ''''necessary'''' (in a precise sense), the widespread view of modeltheoretic truth as providing a general guarantee of necessity is mistaken. Several arguments to the contrary are criticized.

105Relative Identity and CardinalityCanadian Journal of Philosophy 29 (2). 1999.Peter Geach famously holds that there is no such thing as absolute identity. There are rather, as Geach sees it, a variety of relative identity relations, each essentially connected with a particular monadic predicate. Though we can strictly and meaningfully say that an individual a is the same man as the individual b, or that a is the same statue as b, we cannot, on this view, strictly and meaningfully say that the individual a simply is b. It is difficult to find anything like a persuasive arg…Read more

95Logical consequenceIn Lou Goble (ed.), The Blackwell Guide to Philosophical Logic, Blackwell. pp. 2001115. 2001.

69Review of A. George and D. J. Velleman, Philosophies of MathematicsPhilosophia Mathematica 11 (3): 358362. 2003.

49Frege's reductionHistory and Philosophy of Logic 15 (1): 85103. 1994.This paper defends the view that Frege’s reduction of arithmetic to logic would, if successful, have shown that arithmetical knowledge is analytic in essentially Kant’s sense. It is argued, as against Paul Benacerraf, that Frege’s apparent acceptance of multiple reductions is compatible with this epistemological thesis. The importance of this defense is that (a) it clarifies the role of proof, definition, and analysis in Frege’s logicist works; and (b) it demonstrates that the Fregean style of r…Read more

45The Breadth of the ParadoxPhilosophia Mathematica 24 (1): 3049. 2016.This essay examines Frege's reaction to Russell's Paradox and his views about the grounding of existence claims in mathematics. It is argued that Frege's strict requirements on existential proofs would rule out the attempt to ground arithmetic in. It is hoped that this discussion will help to clarify the ways in which Frege's position is both coherent and significantly different from the neologicist position on the issues of: what's required for proofs of existence; the connection between model…Read more

45The FregeHilbert ControversyThe Stanford Encyclopedia of Philosophy. 2007.In the early years of the twentieth century, Gottlob Frege and David Hilbert, two titans of mathematical logic, engaged in a controversy regarding the correct understanding of the role of axioms in mathematical theories, and the correct way to demonstrate consistency and independence results for such axioms. The controversy touches on a number of difficult questions in logic and the philosophy of logic, and marks an important turningpoint in the development of modern logic. This entry gives an …Read more

36Review of Colin McGinn, Logical Properties (review)Notre Dame Philosophical Reviews 2002 (3). 2002.

36Frege's Conception of LogicOup Usa. 2012.In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic

32Hourya BenisSinaceur, Marco Panza, and Gabriel Sandu.Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms (review)Philosophia Mathematica. forthcoming.Hourya BenisSinaceur, Marco Panza, and Gabriel Sandu. Functions and Generality of Logic: Reflections on Dedekind’s and Frege’s Logicisms. Logic, Epistemology, and the Unity of Science; 37. Springer, 2015. ISBN: 9783319171081 ; 9783319367828, 9783319171098.. Pp. xxi + 125.

26Frege on Formality and the 1906 IndependenceTestIn Godehard Link (ed.), Formalism and Beyond: On the Nature of Mathematical Discourse, De Gruyter. pp. 97118. 2014.

26Realism and ParadoxNotre Dame Journal of Formal Logic 41 (3): 227241. 2000.This essay addresses the question of the effect of Russell's paradox on Frege's distinctive brand of arithmetical realism. It is argued that the effect is not just to undermine Frege's specific account of numbers as extensions (courses of value) but more importantly to undermine his general means of explaining the objectdirectedness of arithmetical discourse. It is argued that contemporary neoFregean attempts to revive that explanation do not successfully avoid the central problem brought to l…Read more

7Reply to Cook, Rossberg and WehmeierJournal for the History of Analytical Philosophy 3 (7). 2015.All contributions included in the present issue were originally presented at an ‘Author Meets Critics’ session organised by Richard Zach at the Pacific Meeting of the American Philosophical Association in San Diego in the Spring of 2014.

2Frege on Mathematical ProgressIn Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition, Springer. 2016.Frege claims that mathematical theories are collections of thoughts, and that scientific continuity turns on thoughtidentity. This essay explores the difficulties posed for this conception of mathematics by the conceptual development canonically involved in mathematical progress. The central difficulties are that mathematical development often involves sufficient conceptual progress that mature versions of theories do not involve easilyrecognizable synonyms of their earlier versions, and that …Read more

2Models in Geometry and Logic: 18701920In Sober Seppälä Niniiluoto (ed.), Logic, Methodology and Philosophy of Science  Proceedings of the 15th International Congress, College Publications. pp. 4161. 2017.

13 Mathematical Objects and IdentityIn Michael O'Rourke Corey Washington (ed.), Situating Semantics: Essays on the Philosophy of John Perry, . pp. 73. 2007.

Logicism ReconsideredDissertation, Stanford University. 1990.This thesis is an examination of Frege's logicism, and of a number of objections which are widely viewed as refutations of the logicist thesis. In the view offered here, logicism is designed to provide answers to two questions: that of the nature of arithmetical truth, and that of the source of arithmetical knowledge. ;The first objection dealt with here is the view that logicism is not an epistemologically significant thesis, due to the fact that the epistemological status of logic itself is no…Read more
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