-
31Peter Schroeder-Heister on Proof-Theoretic Semantics (edited book)Springer. 2024.This open access book is a superb collection of some fifteen chapters inspired by Schroeder-Heister's groundbreaking work, written by leading experts in the field, plus an extensive autobiography and comments on the various contributions by Schroeder-Heister himself. For several decades, Peter Schroeder-Heister has been a central figure in proof-theoretic semantics, a field of study situated at the interface of logic, theoretical computer science, natural-language semantics, and the philosophy o…Read more
-
160Critical Remarks on Frege’s Conception of Logic by Patricia Blanchette (review)Journal 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.
-
109Tractarian First-Order Logic: Identity and the N-OperatorReview of Symbolic Logic 5 (4): 538-573. 2012.In theTractatus, Wittgenstein advocates two major notational innovations in logic. First, identity is to be expressed by identity of the sign only, not by a sign for identity. Secondly, only one logical operator, called “N” by Wittgenstein, should be employed in the construction of compound formulas. We show that, despite claims to the contrary in the literature, both of these proposals can be realized, severally and jointly, in expressively complete systems of first-order logic. Building on ear…Read more
-
34On Equivalence Relations Between Interpreted Languages, with an Application to Modal and First-Order LanguageErkenntnis 88 (1): 193-213. 2021.I examine notions of equivalence between logics (understood as languages interpreted model-theoretically) and develop two new ones that invoke not only the algebraic but also the string-theoretic structure of the underlying language. As an application, I show how to construe modal operator languages as what might be called typographical notational variants of _bona fide_ first-order languages.
-
24The Quest for Frege's NachlassIn Michael Beaney & Erich Reck (eds.), Gottlob Frege: Critical Assessments of Leading Philosophers, Vol. I, Routledge. pp. 54-67. 2005.
-
Auf der Suche nach Freges NachlaßIn Gottfried Gabriel & Uwe Dathe (eds.), Gottlob Frege - Werk und Wirkung, Mentis. pp. 267-282. 2000.
-
73Are quantifiers intensional operators?Inquiry: An Interdisciplinary Journal of Philosophy 64 (5-6): 511-532. 2021.ABSTRACT In this paper, I ask whether quantifiers are intensional operators, with variable assignments playing the role of indices. Certain formulations of extensional type theory suggest an affirmative answer, but the most satisfactory among them suffer from a contamination of their semantic ontology with syntactic material. I lay out ‘Fregean’ versions of extensional type theory that are free from syntactic contamination and suggest a negative answer to our question.
-
137The proper treatment of variables in predicate logicLinguistics and Philosophy 41 (2): 209-249. 2018.In §93 of The Principles of Mathematics, Bertrand Russell observes that “the variable is a very complicated logical entity, by no means easy to analyze correctly”. This assessment is borne out by the fact that even now we have no fully satisfactory understanding of the role of variables in a compositional semantics for first-order logic. In standard Tarskian semantics, variables are treated as meaning-bearing entities; moreover, they serve as the basic building blocks of all meanings, which are …Read more
-
88Identity and quantificationPhilosophical Studies 174 (3): 759-770. 2017.It is a philosophical commonplace that quantification involves, invokes, or presupposes, the relation of identity. There seem to be two major sources for this belief: the conviction that identity is implicated in the phenomenon of bound variable recurrence within the scope of a quantifier; memories of Quine’s insistence that quantification requires absolute identity for the values of variables. With respect to, I show that the only extant argument for a dependence of variable recurrence on ident…Read more
-
34On the relations between Heinrich Scholz and Jan ŁukasiewiczHistory and Philosophy of Logic 28 (1): 67-81. 2007.The aim of the present study is (1) to show, on the basis of a number of unpublished documents, how Heinrich Scholz supported his Warsaw colleague Jan ?ukasiewicz, the Polish logician, during World War II, and (2) to discuss the efforts he made in order to enable Jan ?ukasiewicz and his wife Regina to move from Warsaw to Münster under life-threatening circumstances. In the first section, we explain how Scholz provided financial help to ?ukasiewicz, and we also adduce evidence of the risks incurr…Read more
-
43World travelling and mood swingsIn Benedikt Löwe, Thoralf Räsch & Wolfgang Malzkorn (eds.), Foundations of the Formal Sciences II, Kluwer Academic Publishers. 2003.It is not quite as easy to see that there is in fact no formula of this modal language having the same truth conditions (in terms of S5 Kripke semantics) as (1). This was rst conjectured by Allen Hazen2 and later proved by Harold Hodes3. We present a simple direct proof of this result and discuss some consequences for the logical analysis of ordinary modal discourse.
-
43Fragments of $HA$ based on $\Sigma_1$ -inductionArchive for Mathematical Logic 37 (1): 37-49. 1997.In the first part of this paper we investigate the intuitionistic version $iI\!\Sigma_1$ of $I\!\Sigma_1$ (in the language of $PRA$ ), using Kleene's recursive realizability techniques. Our treatment closely parallels the usual one for $HA$ and establishes a number of nice properties for $iI\!\Sigma_1$ , e.g. existence of primitive recursive choice functions (this is established by different means also in [D94]). We then sharpen an unpublished theorem of Visser's to the effect that quantifier al…Read more
-
60On Ramsey's 'Silly Delusion' Regarding Tractatus 5.53In Giuseppe Primiero & Shahid Rahman (eds.), Acts of Knowledge: History, Philosophy and Logic, College Publications. 2009.We investigate a variant of the variable convention proposed at Tractatus 5.53ff for the purpose of eliminating the identity sign from logical notation. The variant in question is what Hintikka has called the strongly exclusive interpretation of the variables, and turns out to be what Ramsey initially (and erroneously) took to be Wittgenstein's intended method. We provide a tableau calculus for this identity-free logic, together with soundness and completeness proofs, as well as a proof of mutua…Read more
-
132Frege’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
-
76Gingerbread 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
-
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.
-
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.
-
129In 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
-
125Actuality 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
-
132Wittgensteinian 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
-
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.
-
68Aspekte 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
-
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
-
232011 spring meeting of the association for symbolic logicBulletin of Symbolic Logic 18 (1): 135-141. 2012.
-
51Modality, mood, and descriptionsIn Reinhard Kahle (ed.), Intensionality: An Interdisciplinary Discussion, Ak Peters. 2005.§1. Introduction. By means of what semantic features is a proper name tied to its bearer? This is a puzzling question indeed: proper names — like “Aristotle” or “Paris” — are syntactically simple, and it therefore does not seem possible to reduce their meanings, by means of a principle of compositionality, to the meanings of more basic, and hence perhaps more tractable, linguistic elements.
Irvine, California, United States of America
Areas of Specialization
23 more
Areas of Interest
27 more