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Profile: Neil Tennant (Ohio State University)
  1.  32
    Neil Tennant (1997). The Taming of the True. Oxford University Press.
    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.
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  2.  94
    Neil Tennant (1987). Anti-Realism and Logic: Truth as Eternal. Oxford University Press.
    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.
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  3.  11
    Neil Tennant (forthcoming). Normalizability, Cut Eliminability and Paradox. Synthese:1-20.
    This is a reply to the considerations advanced by Schroeder-Heister and Tranchini as prima facie problematic for the proof-theoretic criterion of paradoxicality, as originally presented in Tennant and subsequently amended in Tennant. Countering these considerations lends new importance to the parallelized forms of elimination rules in natural deduction.
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  4.  48
    Neil Tennant (2012). Cut for Core Logic. Review of Symbolic Logic 5 (3):450-479.
    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.
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  5.  46
    Neil Tennant (2002). Deflationism and the Gödel Phenomena. Mind 111 (443):551-582.
    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 show that the (...)
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  6.  18
    Neil Tennant (2014). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica 22 (3):321-344.
    We examine the sense in which logic is a priori, and explain how mathematical theories can be dichotomized non-trivially into analytic and synthetic portions. We argue that Core Logic contains exactly the a-priori-because-analytically-valid deductive principles. We introduce the reader to Core Logic by explaining its relationship to other logical systems, and stating its rules of inference. Important metatheorems about Core Logic are reported, and its important features noted. Core Logic can serve as the basis for a foundational program that could (...)
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  7.  93
    Neil Tennant (2005). Deflationism and the Gödel Phenomena: Reply to Ketland. Mind 114 (453):89-96.
    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.
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  8.  89
    Neil Tennant (2002). Victor Vanquished. Analysis 62 (2):135–142.
    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 true (by anyone, (...)
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  9. Neil Tennant (2009). Revamping the Restriction Strategy. In Joe Salerno (ed.), New Essays on the Knowability Paradox. Oxford University Press
    This study continues the anti-realist’s quest for a principled way to avoid Fitch’s paradox. It is proposed that the Cartesian restriction on the anti-realist’s knowability principle ‘ϕ, therefore 3Kϕ’ should be formulated as a consistency requirement not on the premise ϕ of an application of the rule, but rather on the set of assumptions on which the relevant occurrence of ϕ depends. It is stressed, by reference to illustrative proofs, how important it is to have proofs in normal form before (...)
     
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  10. Neil Tennant (1997). The Taming of the True. Oxford University Press Uk.
    The Taming of the True poses a broad challenge to the realist views of meaning and truth that have been prominent in recent philosophy. Neil Tennant starts with a careful critical survey of the realism debate, guiding the reader through its complexities; he then presents a sustained defence of the anti-realist view that every truth is knowable in principle, and that grasp of meaning must be able to be made manifest. Sceptical arguments for the indeterminacy or non-factuality of meaning are (...)
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  11.  90
    Neil Tennant (2014). Aristotle's Syllogistic and Core Logic. History and Philosophy of Logic 35 (2):120-147.
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  12.  9
    Neil Tennant (2012). Changes of Mind: An Essay on Rational Belief Revision. Oxford University Press.
    An account of how a rational agent should revise beliefs in the light of new evidence.
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  13.  7
    H. A. Lewis & Neil Tennant (1981). Natural Logic. Philosophical Quarterly 31 (125):376.
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  14.  30
    Neil Tennant (2001). Is Every Truth Knowable? Reply to Williamson. Ratio 14 (3):263–280.
    This paper addresses an objection raised by Timothy Williamson to the ‘restriction strategy’ that I proposed, in The Taming of The True, in order to deal with the Fitch paradox. Williamson provides a new version of a Fitch-style argument that purports to show that even the restricted principle of knowability suffers the same fate as the unrestricted one. I show here that the new argument is fallacious. The source of the fallacy is a misunderstanding of the condition used in stating (...)
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  15.  40
    Neil Tennant (1985). Weir and Those 'Disproofs' I Saw Before Me. Analysis 45 (4):208 - 212.
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  16. Neil Tennant (1997). Changing the Theory of Theory Change: Reply to My Critics. British Journal for the Philosophy of Science 48 (4):569-586.
    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 approach. This paper replies as comprehensively as space allows.
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  17. Neil Tennant (1985). Minimal Logic is Adequate for Popperian Science. British Journal for the Philosophy of Science 36 (3):325-329.
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  18. Neil Tennant (1994). Changing the Theory of Theory Change: Towards a Computational Approach. British Journal for the Philosophy of Science 45 (3):865-897.
    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 can (...)
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  19.  15
    Neil Tennant (2016). Rule-Irredundancy and the Sequent Calculus for Core Logic. Notre Dame Journal of Formal Logic 57 (1):105-125.
    We explore the consequences, for logical system-building, of taking seriously the aim of having irredundant rules of inference, and a preference for proofs of stronger results over proofs of weaker ones. This leads one to reconsider the structural rules of REFLEXIVITY, THINNING, and CUT. REFLEXIVITY survives in the minimally necessary form $\varphi:\varphi$. Proofs have to get started. CUT is subject to a CUT-elimination theorem, to the effect that one can always make do without applications of CUT. So CUT is redundant, (...)
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  20. Neil Tennant (2010). Inferential Semantics for First-Order Logic : Motivating Rules of Inference From Rules of Evaluation. In T. J. Smiley, Jonathan Lear & Alex Oliver (eds.), The Force of Argument: Essays in Honor of Timothy Smiley. Routledge 223--257.
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  21.  58
    Neil Tennant (1995). On Paradox Without Self-Reference. Analysis 55 (3):199 - 207.
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  22. Neil Tennant (1987). Natural Deduction and Sequent Calculus for Intuitionistic Relevant Logic. Journal of Symbolic Logic 52 (3):665-680.
  23.  66
    Neil Tennant (1997). On the Necessary Existence of Numbers. Noûs 31 (3):307-336.
    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 give (...)
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  24. Neil Tennant, Natural Logicism Via the Logic of Orderly Pairing.
    The aim here is to describe how to complete the constructive logicist program, in the author’s book Anti-Realism and Logic, of deriving all the Peano-Dedekind postulates for arithmetic within a theory of natural numbers that also accounts for their applicability in counting finite collections of objects. The axioms still to be derived are those for addition and multiplication. Frege did not derive them in a fully explicit, conceptually illuminating way. Nor has any neo-Fregean done so.
     
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  25.  50
    Neil Tennant (2010). Williamson's Woes. Synthese 173 (1):9-23.
    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 supposed rigid designator generates a contradiction (...)
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  26.  19
    Neil Tennant, Logicism and Neologicism. Stanford Encyclopedia of Philosophy.
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  27.  97
    Neil Tennant (1981). Is This a Proof I See Before Me? Analysis 41 (3):115 - 119.
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  28.  41
    Neil Tennant (2004). A General Theory of Abstraction Operators. Philosophical Quarterly 54 (214):105-133.
    I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers as answering (...)
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  29.  14
    Neil Tennant (2003). Theory-Contraction is NP-Complete. Logic Journal of the IGPL 11 (6):675-693.
    I investigate the problem of contracting a dependency-network with respect to any of its nodes. The resulting contraction must not contain the node in question, but must also be a minimal mutilation of the original network. Identifying successful and minimally mutilating contractions of dependency-networks is non-trivial, especially when non-well-founded networks are to be taken into account. I prove that the contraction problem is NP-complete.1.
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  30.  64
    Neil Tennant (2010). Review of C. S. Jenkins, Grounding Concepts: An Empirical Basis for Arithmetical Knowledge. [REVIEW] Philosophia Mathematica 18 (3):360-367.
    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’, one which ‘respects (...)
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  31.  14
    Neil Tennant (1982). Proof and Paradox. Dialectica 36 (2‐3):265-296.
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  32.  12
    Neil Tennant (2006). On the Degeneracy of the Full AGM-Theory of Theory-Revision. Journal of Symbolic Logic 71 (2):661 - 676.
    A general method is provided whereby bizarre revisions of consistent theories with respect to contingent sentences that they refute can be delivered by revision-functions satisfying both the basic and the supplementary postulates of the AGM-theory of theory-revision.
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  33.  66
    Neil Tennant (2010). The Logical Structure of Scientific Explanation and Prediction: Planetary Orbits in a Sun's Gravitational Field. Studia Logica 95 (1/2):207 - 232.
    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 accordance with the hypotheticodeductive model.
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  34.  39
    Neil Tennant (2005). Rule-Circularity and the Justification of Deduction. Philosophical Quarterly 55 (221):625 - 648.
    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 that the rules of Disquotation and (...)
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  35.  27
    Neil Tennant (2007). What Might Logic and Methodology Have Offered the Dover School Board, Had They Been Willing to Listen? Public Affairs Quarterly 21 (2):149-167.
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  36. Neil Tennant (1992). Autologic. Edinburgh University Press.
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  37.  63
    Kit Fine & Neil Tennant (1983). A Defence of Arbitrary Objects. Aristotelian Society Supplementary Volume 57:55 - 89.
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  38. Neil Tennant (1977). Truth, Meaning and Decidability. Mind 86 (343):368-387.
  39.  70
    Neil Tennant (1995). ``On Negation, Truth, and Warranted Assertibility". Analysis 54 (2):98-104.
    Wright's argument in Chapter 1 of "Truth and Objectivity" for the claim that truth and warranted assertibility are not the same is shown to make unwarranted use of non-constructive negation.
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  40.  34
    Neil Tennant (2014). Logic, Mathematics, and the A Priori, Part I: A Problem for Realism. Philosophia Mathematica 22 (3):308-320.
    This is Part I of a two-part study of the foundations of mathematics through the lenses of (i) apriority and analyticity, and (ii) the resources supplied by Core Logic. Here we explain what is meant by apriority, as the notion applies to knowledge and possibly also to truths in general. We distinguish grounds for knowledge from grounds of truth, in light of our recent work on truthmakers. We then examine the role of apriority in the realism/anti-realism debate. We raise a (...)
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  41.  16
    Neil Tennant (2006). New Foundations for a Relational Theory of Theory-Revision. Journal of Philosophical Logic 35 (5):489 - 528.
    AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions 'J is a contraction of K with respect to A' and 'J is a revision of K with respect to A'. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and (...)
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  42.  19
    Neil Tennant (1984). Perfect Validity, Entailment and Paraconsistency. Studia Logica 43 (1-2):181 - 200.
    This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is (...)
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  43.  65
    Neil Tennant (2006). A Note on the Irrelevance of Probabilistic Irrelevance. Analysis 66 (289):32–35.
    In his book Bayes or Bust?, John Earman (1992: 63–65) seeks to set out the Bayesian reasoning that would vindicate the pre-theoretic intuition that a theory receives confirmation from having its observational predictions borne out by experience.
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  44.  94
    Neil Tennant (1998). The Full Price of Truth. Analysis 58 (3):221–228.
    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.
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  45.  3
    Neil Tennant (2010). Game Theory and Conventiont. Nordic Journal of Philosophical Logic 6 (1):3-19.
    This paper rebuts criticisms by Hintikka of the author's account of game-theoretic semantics for classical logic. At issue are the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; the alleged need for quantification over strategies when providing a game-theoretic semantics; and the role of Tarski's Convention T. As a result of the ideas marshalled in response to Hintikka, the author puts forward a new conjecture concerning the relationship among truth, (...)
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  46. Neil Tennant (2008). Carnap, Gödel, and the Analyticity of Arithmetic. Philosophia Mathematica 16 (1):100-112.
    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 of the research (...)
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  47.  17
    Neil Tennant (1981). Formal Games and Forms for Games. Linguistics and Philosophy 4 (2):311 - 320.
  48.  11
    Neil Tennant (1986). The Withering Away of Formal Semantics? Mind and Language 1 (4):302-318.
  49.  28
    Neil Tennant (2002). Ultimate Normal Forms for Parallelized Natural Deductions. Logic Journal of the IGPL 10 (3):299-337.
    The system of natural deduction that originated with Gentzen , and for which Prawitz proved a normalization theorem, is re-cast so that all elimination rules are in parallel form. This enables one to prove a very exigent normalization theorem. The normal forms that it provides have all disjunction-eliminations as low as possible, and have no major premisses for eliminations standing as conclusions of any rules. Normal natural deductions are isomorphic to cut-free, weakening-free sequent proofs. This form of normalization theorem renders (...)
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  50.  21
    Diana Raffman Deutsch, George Schumm & Neil Tennant (1998). Clusions From Gödel's Incompleteness Theorems, and Related Results From Mathematical Logic. Languages, Minds, and Machines Figure Prominently in the Discussion. Gödel's Theorems Surely Tell Us Something About These Important Matters. But What? A Descriptive Title for This Paper Would Be “Gödel, Lucas, Penrose, Tur”. [REVIEW] Bulletin of Symbolic Logic 4 (3).
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