• Vintage Enthusiasms: Essays in Honour of J L Bell (edited book)
    with P. Clark and M. Hallet
    . 2008.
  •  2
    Truth and the liar
    with Michael Hallet and Peter Clark
    In David DeVidi, Michael Hallett & Peter Clark (eds.), Logic, Mathematics, Philosophy, Vintage Enthusiasms: Essays in Honour of John L. Bell, Springer. 2011.
    Frege famously claimed that logic is the science of truth: “To discover truths is the task of all science; it falls to logic to discern the laws of truth” (Frege, 1956, p. 289). But just like the other foundational concept of set, truth at that time was intimately associated with paradox; in the case of truth, the Liar paradox. The set-theoretical paradoxes had their teeth drawn by being recognised as reductio proofs of assumptions that had seemed too obvious to warrant stating explicitly, but w…Read more
  •  39
    No Mere Difference
    Dialogue 56 (2): 357-379. 2017.
  •  9
    A Logical Approach to Philosophy: Essays in Memory of Graham Solomon (edited book)
    with Tim Kenyon
    Springer. 2006.
    Graham Solomon, to whom this collection is dedicated, went into hospital for antibiotic treatment of pneumonia in Oc- ber, 2001. Three days later, on Nov. 1, he died of a massive stroke, at the age of 44. Solomon was well liked by those who got the chance to know him—it was a revelation to?nd out, when helping to sort out his a?airs after his death, how many “friends” he had whom he had actually never met, as his email included correspondence with philosophers around the world running sometimes …Read more
  •  12
    The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic ; analytical philosophy, philosophy of science, philosophy of mathematic…Read more
  •  344
    We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a…Read more
  • Term-Forming Operators in First Order Logic
    Dissertation, The University of Western Ontario (Canada). 1994.
    The two main accomplishments of this thesis are that it provides the first adequate semantics for Hilbert's epsilon-operator and that it describes a general semantics for term forming operators more flexible than any in the literature. ;The epsilon-operator was introduced by David Hilbert in the 1920s as a term forming operator in first order logic. The semantics so far available for epsilon has been designed for classical two-valued logic, and has required that additional extensionality assumpt…Read more
  •  85
    Tolerance and metalanguages in carnap'slogical syntax of language
    with Graham Solomon
    Synthese 103 (1). 1995.
    Michael Friedman has recently argued that Carnap'sLogical Syntax of Language is fundamentally flawed in a way that reveals the ultimate failure of logical positivism. Friedman's argument depends crucially on two claims: (1) that Carnap was committed to the view that there is a universal metalanguage and (2) that given what Carnap wanted from a metalanguage, in particular given that he wanted a definition of analytic for an object language, he was in fact committed to a hierarchy of stronger and …Read more
  • ¸ Itedevidikenyon2006 (edited book)
    Springer Verlag. 2006.
  •  1
    Naturalizing Natural Deduction
    In David DeVidi & Herbert Korté (eds.), , De Gruyter. 2014.
  •  4
    □ In intuitionistic modal logic1
    with Graham Solomon
    Australasian Journal of Philosophy 75 (2): 201-213. 1997.
  •  68
    Tarski on “essentially richer” metalanguages
    with Graham Solomon
    Journal of Philosophical Logic 28 (1): 1-28. 1999.
    It is well known that Tarski proved a result which can be stated roughly as: no sufficiently rich, consistent, classical language can contain its own truth definition. Tarski's way around this problem is to deal with two languages at a time, an object language for which we are defining truth and a metalanguage in which the definition occurs. An obvious question then is: under what conditions can we construct a definition of truth for a given object language. Tarski claims that it is necessary an…Read more
  •  24
    Intuitionistic ε- and τ-calculi
    Mathematical Logic Quarterly 41 (4): 523-546. 1995.
    There are several open problems in the study of the calculi which result from adding either of Hilbert's ϵ- or τ-operators to the first order intuitionistic predicate calculus. This paper provides answers to several of them. In particular, the first complete and sound semantics for these calculi are presented, in both a “quasi-extensional” version which uses choice functions in a straightforward way to interpret the ϵ- or τ-terms, and in a form which does not require extensionality assumptions. …Read more
  •  83
    On Confusions About Bivalence and Excluded Middle
    with Graham Solomon
    Dialogue 38 (4): 785-. 1999.
    RésuméCet article discute diverses confusions, actueles ou potentielles, liées á la bivalence et au tiers exclu. Il s'agit, en particulier, 1) d'examiner divers cas illustrant les rapports entre la bivalence et le tiers exclu ; 2) de discuter la thése selon laquelle le tiers exclu et le schéma-T de Tarskipour la vérité entraînent la bivalence; 3) de proposer quelques remarques sur les rapports entre la bivalence, le tiers exclu et la preuve par l'absurde; 4) de scruter un argument répandu selon …Read more
  •  10
    Free logic: Selected essays (review)
    Bulletin of Symbolic Logic 9 (4): 521-523. 2003.
  •  59
    Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic. Each logic is introduced with a brief description of some aspect of its philosophical significance, and wherever possible semantic and proof methods are employed to facilitate comparison of the various systems. The book is designed to be us…Read more
  •  17
    16. Vagueness and Intuitionistic Logic: On the Wright Track
    In Kent A. Peacock & Andrew D. Irvine (eds.), Mistakes of reason: essays in honour of John Woods, University of Toronto Press. pp. 279-295. 2005.
  •  33
    □ In intuitionistic modal logic1
    with Graham Solomon
    Australasian Journal of Philosophy 75 (2). 1997.
    This Article does not have an abstract
  •  68
    Analogues of knowability
    with Tim Kenyon
    Australasian Journal of Philosophy 81 (4). 2003.
    An interesting recent reply to the Paradox of Knowability is Neil Tennant's proposal: to restrict the anti-realist's knowability thesis to truths the knowing of which is logically consistent. However, this proposal is egregiously ad hoc unless motivated by something other than the wish to save anti-realism from embarrassment. We examine Tennant's argument that his restriction is motivated by parallel considerations in cases that are neutral with respect to debates about realism. We conclude that…Read more
  • De Gruyter. 2014.
  •  2
    REVIEWS-Free logic: Selected essays
    with K. Lambert
    Bulletin of Symbolic Logic 9 (4): 521-523. 2003.
  • Intuitionistic varepsilon - and τ -calculi
    Mathematical Logic Quarterly 41 (4): 523--546. 1995.