•  1024
    Aristotle’s Syllogistic and Core Logic
    History and Philosophy of Logic 35 (2): 120-147. 2014.
    I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristo…Read more
  •  491
    Review of C. S. Jenkins, Grounding Concepts: An Empirical Basis for Arithmetical Knowledge (review)
    Philosophia Mathematica 18 (3): 360-367. 2010.
    This book is written so as to be ‘accessible to philosophers without a mathematical background’. The reviewer can assure the reader that this aim is achieved, even if only by focusing throughout on just one example of an arithmetical truth, namely ‘7+5=12’. This example’s familiarity will be reassuring; but its loneliness in this regard will not. Quantified propositions — even propositions of Goldbach type — are below the author’s radar.The author offers ‘a new kind of arithmetical epistemology’…Read more
  •  331
    Changing the theory of theory change: Reply to my critics
    British Journal for the Philosophy of Science 48 (4): 569-586. 1997.
    Changing the Theory of Theory Change: Towards a Computational Approach’ (Tennant [1994]; henceforth CTTC) claimed that the AGM postulate of recovery is false, and that AGM contractions of theories can be more than minimally mutilating. It also described an alternative, computational method for contracting theories, called the Staining Algorithm. Makinson [1995] and Hansson and Rott [1995] criticized CTTC's arguments against AGM-theory, and its specific proposals for an alternative, computational…Read more
  •  275
    Changing the theory of theory change: Towards a computational approach
    British Journal for the Philosophy of Science 45 (3): 865-897. 1994.
    The Theory of theory change has contraction and revision as its central notions. Of these, contraction is the more fundamental. The best-known theory, due to Alchourrón, Gärdenfors, and Makinson, is based on a few central postulates. The most fundamental of these is the principle of recovery: if one contracts a theory with respect to a sentence, and then adds that sentence back again, one recovers the whole theory. Recovery is demonstrably false. This paper shows why, and investigates how one ca…Read more
  •  274
    Anti-realism and logic: truth as eternal
    Oxford University Press. 1987.
    Anti-realism is a doctrine about logic, language, and meaning that is based on the work of Wittgenstein and Frege. In this book, Professor Tennant clarifies and develops Dummett's arguments for anti-realism and ultimately advocates a radical reform of our logical practices.
  •  270
  •  200
    Carnap, gödel, and the analyticity of arithmetic
    Philosophia Mathematica 16 (1): 100-112. 2008.
    Michael Friedman maintains that Carnap did not fully appreciate the impact of Gödel's first incompleteness theorem on the prospect for a purely syntactic definition of analyticity that would render arithmetic analytically true. This paper argues against this claim. It also challenges a common presumption on the part of defenders of Carnap, in their diagnosis of the force of Gödel's own critique of Carnap in his Gibbs Lecture. The author is grateful to Michael Friedman for valuable comments. Part…Read more
  •  162
    On negation, truth and warranted assertibility
    Analysis 55 (2): 98-104. 1995.
    All parties to the proceedings that follow concur with DS. The question is whether there is anything more to truth than can be gleaned from DS alone. Deflationism holds that there is nothing more to truth than this. Now it would appear that 'warrantedly assertible' can play the role of T in DS. Hence it would appear that the deflationist would be able to identify truth with warranted assertibility
  •  156
    A Defence of Arbitrary Objects
    with Kit Fine
    Aristotelian Society Supplementary Volume 57 (1). 1983.
  •  151
    The Emperor’s New Concepts
    Noûs 36 (s16): 345-377. 2002.
    Christopher Peacocke, in A Study of Concepts, motivates his account of possession conditions for concepts by means of an alleged parallel with the conditions under which numbers are abstracted to give the numerosity of a predicate. There are, however, logical mistakes in Peacocke
  •  146
    I am not a deflationist. I believe that truth and falsity are substantial. The truth of a proposition consists in its having a constructive proof, or truthmaker. The falsity of a proposition consists in its having a constructive disproof, or falsitymaker. Such proofs and disproofs will need to be given modulo acceptable premisses. The choice of these premisses will depend on the discourse in question.
  •  140
    On the necessary existence of numbers
    Noûs 31 (3): 307-336. 1997.
    We examine the arguments on both sides of the recent debate (Hale and Wright v. Field) on the existence, and modal status, of the natural numbers. We formulate precisely, with proper attention to denotational commitments, the analytic conditionals that link talk of numbers with talk of numerosity and with counting. These provide conceptual controls on the concept of number. We argue, against Field, that there is a serious disanalogy between the existence of God and the existence of numbers. We g…Read more
  •  138
    Victor vanquished
    Analysis 62 (2). 2002.
    The naive anti-realist holds the following principle: (◊K) All truths are knowable. This unrestricted generalization (◊K), as is now well known, falls prey to Fitch’s Paradox (Fitch 1963: 38, Theorem 1). It can be used as the only suspect principle, alongside others that cannot be impugned, to prove quite generally, and constructively, that the set {p, ¬Kp} is inconsistent (Tennant 1997: 261). From this it would follow, intuitionistically, that any proposition that is never actually known to be …Read more
  •  119
    Deflationism and the gödel phenomena
    Mind 111 (443): 551-582. 2002.
    consistent and sufficiently strong system of first-order formal arithmetic fails to decide some independent Gödel sentence. We examine consistent first-order extensions of such systems. Our purpose is to discover what is minimally required by way of such extension in order to be able to prove the Gödel sentence in a non-trivial fashion. The extended methods of formal proof must capture the essentials of the so-called ‘semantical argument’ for the truth of the Gödel sentence. We are concerned to …Read more
  •  116
    What is a Rule of Inference?
    Review of Symbolic Logic 14 (2): 307-346. 2021.
    We explore the problems that confront any attempt to explain or explicate exactly what a primitive logical rule of inferenceis, orconsists in. We arrive at a proposed solution that places a surprisingly heavy load on the prospect of being able to understand and deal with specifications of rules that are essentiallyself-referring. That is, any rule$\rho $is to be understood via a specification that involves, embedded within it, reference to rule$\rho $itself. Just how we arrive at this position i…Read more
  •  115
    The full price of truth
    Analysis 58 (3). 1998.
    Some ideas gain currency as soon as there is a linguistic medium of exchange. Truth is one such. Its role in our intellectual economy is much like that of money in the real one. Canonical warrants to make assertions are like gold bars. Truth-claims are like paper money: promises to produce gold bars on demand.
  •  110
    Mind, Mathematics and the I gnorabimusstreit
    British Journal for the History of Philosophy 15 (4). 2007.
    1Certain developments in recent philosophy of mind that contemporary philosophers would regard as both novel and important were fully anticipated by writers in (or reacting to) the tradition of Nat...
  •  109
    Peter G¨ ardenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM -postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So G¨
  •  107
    Is This a Proof I See before Me?
    Analysis 41 (3). 1980.
  •  101
    Cut for core logic
    Review of Symbolic Logic 5 (3): 450-479. 2012.
    The motivation for Core Logic is explained. Its system of proof is set out. It is then shown that, although the system has no Cut rule, its relation of deducibility obeys Cut with epistemic gain.
  •  100
    This study is in two parts. In the first part, various important principles of classical extensional mereology are derived on the basis of a nice axiomatization involving ‘part of’ and fusion. All results are proved here with full Fregean rigor. They are chosen because they are needed for the second part. In the second part, this natural-deduction framework is used in order to regiment David Lewis’s justification of his Division Thesis, which features prominently in his combination of mereology …Read more
  •  98
    Rule-Circularity and the Justification of Deduction
    Philosophical Quarterly 55 (221). 2005.
    I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown tha…Read more
  •  98
    Review of PENELOPE MADDY. Naturalism in Mathematics. Oxford: Clarendon Press, 1997
  •  95
    We present a logically detailed case-study of explanation and prediction in Newtonian mechanics. The case in question is that of a planet's elliptical orbit in the Sun's gravitational field. Care is taken to distinguish the respective contributions of the mathematics that is being applied, and of the empirical hypotheses that receive a mathematical formulation. This enables one to appreciate how in this case the overall logical structure of scientific explanation and prediction is exactly in acc…Read more
  •  94
    Williamson’s Woes
    Synthese 173 (1): 9-23. 2010.
    This is a reply to Timothy Williamson ’s paper ‘Tennant’s Troubles’. It defends against Williamson ’s objections the anti-realist’s knowability principle based on the author’s ‘local’ restriction strategy involving Cartesian propositions, set out in The Taming of the True. Williamson ’s purported Fitchian reductio, involving the unknown number of books on his table, is analyzed in detail and shown to be fallacious. Williamson ’s attempt to cause problems for the anti-realist by means of a suppos…Read more
  •  93
    The taming of the true
    Oxford University Press. 1997.
    The Taming of the True poses a broad challenge to realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant argues compellingly that every truth is knowable, and that an effective logical system can be based on this principle. He lays the foundations for global semantic anti-realism and extends its consequences from the philosophy of mathematics and logic to the theory of meaning, metaphysics, and epistemology.
  •  90
    Inferentialism is explained as an attempt to provide an account of meaning that is more sensitive (than the tradition of truth-conditional theorizing deriving from Tarski and Davidson) to what is learned when one masters meanings.
  •  89
    Paradoxes of pure curiosity
    Theory and Decision 38 (3): 321-330. 1995.
    We consider how a rational decision theorist would justify committing resources to an investigation designed to satisfy pure curiosity. We derive a strange result about the need to be completely open-minded about the outcome