-
53Mathematical RelativismHistory and Philosophy of Logic 10 (1): 53-65. 1989.We set out a doctrine about truth for the statements of mathematics?a doctrine which we think is a worthy competitor to realist views in the philosophy of mathematics?and argue that this doctrine, which we shall call ?mathematical relativism?, withstands objections better than do other non-realist accounts
-
Chapter 9: Thesis TwoPoznan Studies in the Philosophy of the Sciences and the Humanities 90 241-253. 2006.
-
425Strawson on CategoriesJournal of Critical Analysis 7 (3): 83-88. 1978.A type theory constructed with reference to a particular language will associate with each monadic predicate P of that language a class of individuals C(P) of which it is categorically significant to predicate P (or which P spans, for short). The extension of P is a subset of C(P), which is a subset of the language’s universe of discourse. The set C(P) is a category discriminated by the language. The relation 'is spanned by the same predicates as' divides the language’s universe of discourse int…Read more
-
168There Is A Problem with Substitutional QuantificationTheoria 68 (1): 4-12. 2002.Whereas arithmetical quantification is substitutional in the sense that a some-quantification is true only if some instance of it is true, it does not follow (and, in fact, is not true) that an account of the truth-conditions of the sentences of the language of arithmetic can be given by a substitutional semantics. A substitutional semantics fails in a most fundamental fashion: it fails to articulate the truth-conditions of the quantifications with which it is concerned. This is what is defended…Read more
-
323A Wittgensteinian Philosophy of MathematicsLogic and Logical Philosophy 15 (2): 55-69. 2005.Three theses are gleaned from Wittgenstein’s writing. First, extra-mathematical uses of mathematical expressions are not referential uses. Second, the senses of the expressions of pure mathematics are to be found in their uses outside of mathematics. Third, mathematical truth is fixed by mathematical proof. These theses are defended. The philosophy of mathematics defined by the three theses is compared with realism, nominalism, and formalism.
-
Chapter 5: Existence, Number, and RealismPoznan Studies in the Philosophy of the Sciences and the Humanities 90 129-155. 2006.
-
238Propositions and eternal sentencesMind 77 (308): 537-542. 1968.Two different uses of ‘proposition’ are distinguished: the meaning of an eternal sentence is distinguished from that which can be asserted, believed, conjectured, and so on. It is argued that, in the second sense of ‘proposition’, it is not the case that every proposition can be expressed by an eternal sentence.
-
51Absurdity and spanningPhilosophia 2 (3): 227-238. 1972.On the basis of observations J. J. C. Smart once made concerning the absurdity of sentences like 'The seat of the bed is hard', a plausible case can be made that there is little point to developing a theory of types, particularly one of the sort envisaged by Fred Sommers. The authors defend such theories against this objection by a partial elucidation of the distinctions between the concepts of spanning and predicability and between category mistakenness and absurdity in general. The argument su…Read more
-
64More 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 respondes to a criticism of an earlier paper by James Freeman
-
125W.d. Ross on acting from motivesJournal of Value Inquiry 22 (4): 299-306. 1988.This paper defends a position held by W, D, Ross that it is no part of one’s duty to have a certain motive since one cannot by choice have it here and now.
-
80Indenumerability and substitutional quantificationNotre Dame Journal of Formal Logic 23 (4): 358-366. 1982.We here establish two theorems which refute a pair of what we believe to be plausible assumptions about differences between objectual and substitutional quantification. The assumptions (roughly stated) are as follows: (1) there is at least one set d and denumerable first order language L such that d is the domain set of no interpretation of L in which objectual and substitutional quantification coincide. (2) There exist interpreted, denumerable, first order languages K with indenumerable domains…Read more
-
504Are All Tautologies True?Logique Et Analyse 125 (125-126): 3-14. 1989.The paper asks: are all tautologies true in a language with truth-value gaps? It answers that they are not. No tautology is false, of course, but not all are true. It also contends that not all contradictions are false in a language with truth-value gaps, though none are true.
-
43God and empty termsInternational Journal for Philosophy of Religion 18 (3). 1985.This paper is a criticism of Plantinga’s analysis of a version of the ontological argument. He thinks it is obvious that his version is valid and that the only question of interest is whether a key premise is true. The paper lays out two relevant semantical accounts of modal logic. It contends that Plantinga needs to show that one is preferable to the other.
-
56More 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.
-
10The received distinction between pragmatics, semantics and syntaxFoundations of Language 11 (1): 97-104. 1974.
-
31A semantical account of the vicious circle principleNotre Dame Journal of Formal Logic 20 (3): 595-598. 1979.Here we give a semantical account of propositional quantification that is intended to formally represent Russell’s view that one cannot express a proposition about "all" propositions. According to the account the authors give, Russell’s view bears an interesting relation to the view that there are no sets which are members of themselves.
-
28Is English infinite?Philosophical Papers 17 (2): 141-151. 1988.It is argued that English is finite. By this is meant that it contains only finitely many expressions. The conclusion is reached by arguing: (1) only finitely many expressions of English are tokenable; (2) if E is an expression of English, then E is tokenable.
-
102Did the greeks discover the irrationals?Philosophy 74 (2): 169-176. 1999.A popular view is that the great discovery of Pythagoras was that there are irrational numbers, e.g., the positive square root of two. Against this it is argued that mathematics and geometry, together with their applications, do not show that there are irrational numbers or compel assent to that proposition.
-
124Steiner versus Wittgenstein: Remarks on Differing Views of Mathematical TruthTheoria 20 (3): 347-352. 2005.Mark Steiner criticizes some remarks Wittgenstein makes about Gödel. Steiner takes Wittgenstein to be disputing a mathematical result. The paper argues that Wittgenstein does no such thing. The contrast between the realist and the demonstrativist concerning mathematical truth is examined. Wittgenstein is held to side with neither camp. Rather, his point is that a realist argument is inconclusive
-
94The Lessons of the LiarTheory and Decision 11 (1): 55-70. 1979.The paper argues that the liar paradox teaches us these lessons about English. First, the paradox-yielding sentence is a sentence of English that is neither true nor false in English. Second, there is no English name for any such thing as a set of all and only true sentences of English. Third, ‘is true in English’ does not satisfy the axiom of comprehension.
-
Chapter 10: Thesis ThreePoznan Studies in the Philosophy of the Sciences and the Humanities 90 254-283. 2006.
-
20Remarks on Peano ArithmeticRussell: The Journal of Bertrand Russell Studies 20 (1): 27-32. 2000.Russell held that the theory of natural numbers could be derived from three primitive concepts: number, successor and zero. This leaves out multiplication and addition. Russell introduces these concepts by recursive definition. It is argued that this does not render addition or multiplication any less primitive than the other three. To this it might be replied that any recursive definition can be transformed into a complete or explicit definition with the help of a little set theory. But that is…Read more
-
163Tarski and Proper ClassesAnalysis 40 (4): 6-11. 1980.In this paper the authors argue that if Tarski’s definition of truth for the calculus of classes is correct, then set theories which assert the existence of proper classes (classes which are not the member of anything) are incorrect.
-
410Bound Variables and Schematic LettersLogique Et Analyse 95 (95): 425-429. 1981.The paper purports to show, against Quine, that one can construct a language , which results from the extension of the theory of truth functions by introducing sentence letter quantification. Next a semantics is provided for this language. It is argued that the quantification is neither substitutional nor requires one to consider the sentence letters as taking entities as values.
-
10Notes and DiscussionsDialectica 57 (3): 315-322. 2003.This paper seeks to explain why the argument from analogy seems strong to an analogist such as Mill and weak to the skeptic. The inference from observed behavior to the existence of feelings, sensations, etc., in other subjects is justified, but its justification depends on taking observed behavior and feelings, sensations, and so on, to be not merely correlated, but connected. It is claimed that this is what Mill had in mind
-
University of Nebraska, LincolnRetired faculty
Lincoln, Nebraska, United States of America