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288More on propositional identityAnalysis 39 (3): 129-132. 1979.We give a semantical account of propositional identity which is stronger than mutual entailment. That is, according to our account: (1) if A = B is true in a model, so are A 'validates' B and B 'validates' A. (2) There exist models m such that A 'validates' B and B 'validates' A are true in m but A = B is not true in m. According to our account the following rule is sound: (3) from (.. A..) = (.. B..) infer A = B. The paper is a response to a paper by James Freeman to an earlier paper by us.
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667Offices and GodSophia 29 (3): 29-34. 1990.Pavel Tichy presents an interpretation of Anselm’s Proslogion III argument. Tichy presents an interpretation of this argument and raises doubts about one of the premises. The authors contend that Tichy’s interpretation of Anselm is wrong. The argument Tichy comes to raise doubts about is not Anselm’s.
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90A Conversation about Numbers and KnowledgeAmerican Philosophical Quarterly 39 (3): 275-287. 2002.This is a dialogue in the philosophy of mathematics. The dialogue descends from the confident assertion that there are infinitely many numbers to an unresolved bewilderment about how we can know there are any numbers at all. At every turn the dialogue brings us only to realize more fully how little is clear to us in our thinking about mathematics.
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128Four views of arithmetical truthPhilosophical Quarterly 40 (159): 155-168. 1990.Four views of arithmetical truth are distinguished: the classical view, the provability view, the extended provability view, the criterial view. The main problem with the first is the ontology it requires one to accept. Two anti-realist views are the two provability views. The first of these is judged to be preferable. However, it requires a non-trivial account of the provability of axioms. The criterial view is gotten from remarks Wittgenstein makes in Tractatus 6.2-6.22 . It is judged to be th…Read more
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Editor's IntroductionPoznan Studies in the Philosophy of the Sciences and the Humanities 90 11-21. 2006.
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242What is a second order theory committed to?Erkenntnis 20 (1). 1983.The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.
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1143Why Substitutional Quantification Does Not Express ExistenceTheory and Decision 50 67-75. 1987.Fundamental to Quine’s philosophy of logic is the thesis that substitutional quantification does not express existence. This paper considers the content of this claim and the reasons for thinking it is true.
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Chapter 4: The Peano AxiomsPoznan Studies in the Philosophy of the Sciences and the Humanities 90 105-128. 2006.
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308True Propositions: A Reply to C.J.F. WilliamsAnalysis 32 (3): 101-106. 1972.This paper replies to points Williams makes to his reply to Sayward’s criticism of Williams’s proposal of ‘for some p ___ states that p & p’ as an analysis of ‘___ is true’.
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1169The Internal/External QuestionGrazier Philosophishe Studien 47 31-41. 1994.For Rudolf Carnap the question ‘Do numbers exist?’ does not have just one sense. Asked from within mathematics, it has a trivial answer that could not possibly divide philosophers of mathematics. Asked from outside of mathematics, it lacks meaning. This paper discusses Carnap ’s distinction and defends much of what he has to say
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160A conversation about numbersPhilosophia 29 (1-4): 191-209. 2002.This is a dialogue in which five characters are involved. Various issues in the philosophy of mathematics are discussed. Among those issues are these: numbers as abstract objects, our knowledge of numbers as abstract objects, a proof as showing a mathematical statement to be true as opposed to the statement being true in virtue of having a proof.
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Chapter 7: Arithmetic and RulesPoznan Studies in the Philosophy of the Sciences and the Humanities 90 183-211. 2006.
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Steiner, M.-The Applicability of Mathematics as a Philosophical ProblemPhilosophical Books 40 284-284. 1999.
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183Relativism and ontologyPhilosophical Quarterly 37 (148): 278-290. 1987.This paper deals with the question of whether there is objectivist truth about set-theoretic matters. The dogmatist and skeptic agree that there is such truth. They disagree about whether this truth is knowable. In contrast, the relativist says there is no objective truth to be known. Two versions of relativism are distinguished in the paper. One of these versions is defended.
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University of Nebraska, LincolnRetired faculty
Lincoln, Nebraska, United States of America