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Profile: Neil Tennant (Ohio State University)
  1. Aw Moore, John Allen Paulos, Ad Irvine, Brian Rotman, Mark Steiner & Neil Tennant (unknown). 320 Index. Philosophical Papers 1896 (99).
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  2. Neil Tennant, On Negation, Truth and U Arranted Assertibility.
    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.
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  3. Neil Tennant, Contents.
    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 Argu- ment’ 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 (...)
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  4. Neil Tennant, §1. Exposition.
    Peacocke argues for a ‘generalized rationalism’, holding that ‘all entitlement has a fundamentally a priori component.’ (2) But his rationalism ‘differs from those of Frege and Gödel, just as theirs differ from that of Leibniz.’ He requires both substantive theories of intentional content and of understanding, and systematic formal theories of referential semantics and truth. We need an externalist theory of content: ‘Only mental states with externally individuated contents can make judgements about the external, mind-independent world rational.’ (123) Purely evidential (...)
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  5. Neil Tennant, Inferentialism, Logicism, Harmony, and a Counterpoint.
    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.
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  6. 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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  7. Neil Tennant, Theory-Contraction is NP-Complete.
    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 dependencynetworks 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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  8. Neil Tennant, Ultimate Normal Forms for Parallelized Natural Deductions.
    The system of natural deduction that originated with Gentzen (1934–5), and for which Prawitz (1965) 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 (...)
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  9. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part I: A Problem for Realism. Philosophia Mathematica:nku006.
    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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  10. Neil Tennant (forthcoming). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica:nku009.
    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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  11. Neil Tennant (2014). Aristotle's Syllogistic and Core Logic. History and Philosophy of Logic 35 (2):120-147.
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  12. Neil Tennant (2014). Introducing Philosophy: Its Importance in an Age of Science and Religion. Routledge.
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  13. Neil Tennant (2014). The Logical Structure of Evolutionary Explanation and Prediction: Darwinism's Fundamental Schema. Biology and Philosophy 29 (5):611-655.
    We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), implies (...)
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  14. Neil Tennant, Logicism and Neologicism. Stanford Encyclopedia of Philosophy.
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  15. Neil Tennant (2013). Parts, Classes and ≪em Class="a-Plus-Plus"≫Parts of Classes≪/Em≫: An Anti-Realist Reading of Lewisian Mereology. Synthese 190 (4):709-742.
    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 (and Gentzenian) 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 (...)
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  16. 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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  17. 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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  18. Neil Tennant (2010). Review of C. S. Jenkins, Grounding Concepts: An Empirical Basis for Arithmetical Knowledge. [REVIEW] Philosophia Mathematica 18 (3):360-367.
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  19. Neil Tennant (2010). Harmony in a Sequent Setting. Analysis 70 (3):462 - 468.
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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. 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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  22. 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 (...)
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  23. 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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  24. 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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  25. Neil Tennant (2008). Belief-Revision, the Ramsey Test, Monotonicity, and the so-Called Impossibility Results. Review of Symbolic Logic 1 (4):402-423.
    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¨.
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  26. Neil Tennant (2008). Introduction to Special Issue: Carnap and Some Contemporaries. Philosophia Mathematica 16 (1):1-3.
  27. Neil Tennant (2008). Introduction. Philosophia Mathematica 16 (1):1-3.
    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 abshacted to give the numerosity of a predicate. There are, however, logical mistakes in Peacocke's treatment of numbers, which undermine his intended analogy. Nevertheless Peacocke's account of possession conditions for concepts is not rendered inadequate simply by virtue of being deprived of the intended analogy and the motivation it was supposed to afford. (...)
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  28. Neil Tennant (2007). Existence and Identity in Free Logic: A Problem for Inferentialism? Mind 116 (464):1055-1078.
    Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.
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  29. Neil Tennant (2007). Mind, Mathematics and the Ignorabimusstreit. British Journal for the History of Philosophy 15 (4):745 – 773.
  30. 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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  31. 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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  32. 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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  33. Neil Tennant (2006). Editor's Page: Editorial. American Philosophical Quarterly 43 (4):281 - 282.
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  34. 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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  35. Neil Tennant (2005). Contracting Intuitionistic Theories. Studia Logica 80 (2-3):369 - 391.
    I reformulate the AGM-account of contraction (which would yield an account also of revision). The reformulation involves using introduction and elimination rules for relational notions. Then I investigate the extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence.
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  36. 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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  37. 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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  38. Neil Tennant (2005). The Realm of Reason. Journal of Philosophy 102 (3):155-162.
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  39. Neil Tennant (2004). An Anti-Realist Critique of Dialetheism. In Graham Priest, J. C. Beall & Bradley Armour-Garb (eds.), The Law of Non-Contradiction. Clarendon Press.
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  40. 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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  41. Neil Tennant (2003). Review of B. Hale and C. Wright, The Reason's Proper Study. [REVIEW] Philosophia Mathematica 11 (2):226-241.
    The over-arching theme is that we can redeem Frege's key philosophical insights concerning (natural and real) numbers and our knowledge of them, despite Russell's famous discovery of paradox in Frege's own theory of classes. That paradox notwithstanding, numbers are still logical objects, in some sense created or generated by methods or principles of abstraction— which of course cannot be as ambitious as Frege's Basic Law U. These principles not only bring numbers into existence, as it were, but also afford a (...)
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  42. Neil Tennant (2003). Bob Hale and Crispin Wright. The Reason's Proper Study: Essays Towards a Neo-Fregean Philosophy of Mathematics. Philosophia Mathematica 11 (2):226-240.
     
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  43. Neil Tennant (2003). Frege's Content-Principle and Relevant Deducibility. Journal of Philosophical Logic 32 (3):245-258.
    Given the harmony principle for logical operators, compositionality ought to ensure that harmony should obtain at the level of whole contents. That is, the role of a content qua premise ought to be balanced exactly by its role as a conclusion. Frege's contextual definition of propositional content happens to exploit this balance, and one appeals to the Cut rule to show that the definition is adequate. We show here that Frege's definition remains adequate even when one relevantizes logic by abandoning (...)
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  44. Neil Tennant (2003). Naturalism in Mathematics. International Studies in Philosophy 35 (4):351-352.
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  45. 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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  46. Neil Tennant (2002). The Emperor's New Concepts. Noûs 36 (16):345-377.
    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.
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  47. Neil Tennant (2002). The Future with Cloning. In James H. Fetzer (ed.), Consciousness Evolving. John Benjamins. 34--223.
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  48. 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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  49. Neil Tennant (2002). ``Victor Vanquished&Quot. Analysis 62:135-142.
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  50. Neil Tennant (2001). 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 (i) the role of the axiom of choice in proving the equivalence of the game-theoretic account with the standard truth-theoretic account; (ii) the alleged need for quantification over strategies when providing a game-theoretic semantics; and (iii) 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 (...)
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