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134Frege’s permutation argument revisitedSynthese 147 (1): 43-61. 2005.In Section 10 of Grundgesetze, Volume I, Frege advances a mathematical argument (known as the permutation argument), by means of which he intends to show that an arbitrary value-range may be identified with the True, and any other one with the False, without contradicting any stipulations previously introduced (we shall call this claim the identifiability thesis, following Schroeder-Heister (1987)). As far as we are aware, there is no consensus in the literature as to (i) the proper inte…Read more
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77Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians–Two Recently Discovered DocumentsBritish Journal for the History of Philosophy 21 (3). 2013.(2012). Gingerbread Nuts and Pebbles: Frege and the Neo-Kantians – Two Recently Discovered Documents. British Journal for the History of Philosophy. ???aop.label???. doi: 10.1080/09608788.2012.692665
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24College, 124 Raymond avenue, poughkeepsie, ny 12604, usa. In a review, a reference “jsl xliii 148,” for example, refers either to the publication reviewed on page 148 of volume 43 of the journal, or to the review itself (which contains full bibliographical information for the reviewed publication). Analogously, a reference “bsl VII 376” refers to the review beginning on page 376 in volume 7 of this bulletin, or (review)Bulletin of Symbolic Logic 17 (1). 2011.
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70Still Living Without Identity: Reply to TruemanAustralasian Journal of Philosophy 92 (1): 173-175. 2014.In ‘Eliminating Identity: A Reply to Wehmeier’, Robert Trueman attacks my claim that a commitment to a binary relation of identity is logically unnecessary and philosophically undesirable. I show that his two most serious objections are unconvincing.
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130In the moodJournal of Philosophical Logic 33 (6): 607-630. 2004.The purpose of the present paper is to challenge some received assumptions about the logical analysis of modal English, and to show that these assumptions are crucial to certain debates in current philosophy of language. Specifically, I will argue that the standard analysis in terms of quantified modal logic mistakenly fudges important grammatical distinctions, and that the validity of Kripke's modal argument against description theories of proper names crucially depends on ensuing equivocations
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129Actuality in Propositional Modal LogicStudia Logica 101 (3): 487-503. 2013.We show that the actuality operator A is redundant in any propositional modal logic characterized by a class of Kripke models (respectively, neighborhood models). Specifically, we prove that for every formula ${\phi}$ in the propositional modal language with A, there is a formula ${\psi}$ not containing A such that ${\phi}$ and ${\psi}$ are materially equivalent at the actual world in every Kripke model (respectively, neighborhood model). Inspection of the proofs leads to corresponding proof-the…Read more
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133Wittgensteinian Tableaux, Identity, and Co-DenotationErkenntnis 69 (3): 363-376. 2008.Wittgensteinian predicate logic (W-logic) is characterized by the requirement that the objects mentioned within the scope of a quantifier be excluded from the range of the associated bound variable. I present a sound and complete tableaux calculus for this logic and discuss issues of translatability between Wittgensteinian and standard predicate logic in languages with and without individual constants. A metalinguistic co-denotation predicate, akin to Frege’s triple bar of the Begriffsschrift, i…Read more
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33Russell's paradox in consistent fragments of Frege's grundgesetze der arithmetikIn Godehard Link (ed.), One Hundred Years of Russell’s Paradox, De Gruyter. 2004.We provide an overview of consistent fragments of the theory of Frege’s Grundgesetze der Arithmetik that arise by restricting the second-order comprehension schema. We discuss how such theories avoid inconsistency and show how the reasoning underlying Russell’s paradox can be put to use in an investigation of these fragments.
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69Aspekte der frege–hilbert-korrespondenzHistory and Philosophy of Logic 18 (4): 201-209. 1997.In a letter to Frege of 29 December 1899, Hilbert advances his formalist doctrine, according to which consistency of an arbitrary set of mathematical sentences is a sufficient condition for its truth and for the existence of the concepts described by it. This paper discusses Frege's analysis, as carried out in the context of the Frege-Hilbert correspondence, of the formalist approach in particular and the axiomatic method in general. We close with a speculation about Frege's influence on Hilbert…Read more
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130On the consistency of the Δ11-CA fragment of Frege's grundgesetzeJournal of Philosophical Logic 31 (4): 301-311. 2002.It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicat…Read more
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232011 spring meeting of the association for symbolic logicBulletin of Symbolic Logic 18 (1): 135-141. 2012.
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