•  73
    Mathematical Relativism
    with Philip Hugly
    History 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
  •  117
    Does scientific realism entail mathematical realism?
    Facta Philosophica 5 173-182. 2003.
    Hilary Putnam suggests that the essence of the realist conception of mathematics is that the statements of mathematics are objective so that the true ones are objectively true. An argument for mathematical realism, thus conceived, is implicit in Putnam's writing. The first premise is that within currently accepted science there are objective truths. Next is the premise that some of these statements logically imply statements of pure mathematics. The conclusion drawn is that some statements of pu…Read more
  •  41
    Definite Descriptions, Negation and Necessitation
    Russell: The Journal of Bertrand Russell Studies 13 (1): 36-47. 1993.
    The principal question asked in this paper is: in the case of attributive usage, is the definite description to be analyzed as Russell said or is it to be treated as a referring expression, functioning semantically as a proper name? It answers by defending the former alternative.
  • Editor's Introduction
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 11-21. 2006.
  •  44
    Taking actions seriously
    Behavior and Philosophy 23 (24): 51-60. 1995.
    Two kinds of functionalism are distinguished: intensional and extensional. The former is argued to be superior to the latter. The former is also defended against two objections independently put forth by Ned Block and John Searle.
  •  96
    Theories of truth and truth-value gaps
    Linguistics and Philosophy 16 (6). 1993.
    The fact that a group of axioms use the word 'true' does not guarantee that that group of axioms yields a theory of truth. For Davidson the derivability of certain biconditionals from the axioms is what guarantees this. We argue that the test does not work. In particular, we argue that if the object language has truth-value gaps, the result of applying Davidson''s definition of a theory of truth is that no correct theory of truth for the language is possible.
  •  36
    Are there infinitely many sorts of things?
    Philosophia 8 (1): 17-30. 1978.
    An argument is given for Fred Sommers's thesis that the number of sorts of things, that is, the number of types or categories, discriminated by any natural language is always infinite.
  • Chapter 4: The Peano Axioms
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 105-128. 2006.
  •  72
    The disquotational theory of truth is false
    Philosophia 22 (3-4): 331-339. 1993.
    It is argued that if there are truth-value gaps then the disquotational theory of truth is false. Secondly, it is argued that the same conclusion can be reached even without the assumption that there are truth-value gaps.
  •  65
    Anarchism and Rights Violations
    Critica 14 (40): 105-116. 1982.
    The justification of the existence of the state should precede the justification of any particular organization of the state. The paper tries to give a clear argument facing anyone who sets out to do the first thing, which is to justify the existence of the state. The problem facing such a person is to identify which premise of the argument is false and explain why it is false.
  • Chapter 7: Arithmetic and Rules
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 183-211. 2006.
  •  76
    On some much maligned remarks of Wittgenstein on gödel
    Philosophical Investigations 24 (3). 2001.
    In "Remarks on the Foundations of Mathematics" Wittgenstein discusses an argument that goes from Gödel’s incompleteness result to the conclusion that some truths of mathematics are unprovable. Wittgenstein takes issue with this argument. Wittgenstein’s remarks in this connection have received very negative reaction from some very prominent people, for example, Gödel and Dummett. The paper is a defense of what Wittgenstein has to say about the argument in question.
  •  3
    Quine' way out
    Analysis 36 (1): 28-37. 1975.
  •  65
    Frege on identities
    History and Philosophy of Logic 21 (3): 195-205. 2000.
    The idea underlying the Begriffsschrift account of identities was that the content of a sentence is a function of the things it is about. If so, then if an identity a=b is about the content of its contained terms and is true, then a=a and a=b have the same content. But they do not have the same content; so, Frege concluded, identities are not about the contents of their contained terms. The way Frege regarded the matter is that in an identity the terms flanking the symbol for identity do not hav…Read more
  •  41
    In this book a non-realist philosophy of mathematics is presented. Two ideas are essential to its conception. These ideas are (i) that pure mathematics--taken in isolation from the use of mathematical signs in empirical judgement--is an activity for which a formalist account is roughly correct, and (ii) that mathematical signs nonetheless have a sense, but only in and through belonging to a system of signs with empirical application. This conception is argued by the two authors and is critically…Read more
  •  83
    Malcolm on criteria
    Behavior and Philosophy 32 (2): 349-358. 2004.
    Consider the general proposition that normally when people pain-behave they are in pain. Where a traditional philosopher like Mill tries to give an empirical proof of this proposition (the argument from analogy), Malcolm tries to give a transcendental proof. Malcolm’s argument is transcendental in that he tries to show that the very conditions under which we can have a concept provide for the application of the concept and the knowledge that the concept is truly as well as properly applied. The…Read more
  •  8
    Prior and Lorenzen on Quantification
    Grazer Philosophische Studien 41 (1): 151-173. 1991.
  •  286
    What is the Logic of Propositional Identity?
    Logic and Logical Philosophy 15 (1): 3-15. 2006.
    Propositional identity is not expressed by a predicate. So its logic is not given by the ordinary first order axioms for identity. What are the logical axioms governing this concept, then? Some axioms in addition to those proposed by Arthur Prior are proposed.
  •  69
    Dualism and the argument from continuity
    with Eric Russert Kraemer
    Philosophical Studies 37 (January): 55-59. 1980.
    One of the things C. D Broad argued many years ago is that certain 'scientific' arguments against dualist interactionism come back in the end to a metaphysical bias in favor of materialism. Here the authors pursue this basic strategy against another 'scientific' argument against dualism itself. The argument is called 'the argument from continuity'. According to this argument the fact that organisms and species develop by insensible gradations renders dualism implausible. The authors try to demon…Read more
  •  8
    Analysis “Problem” No. 15
    Analysis 36 (2): 49. 1976.
  •  41
    Four views of arithmetical truth
    Philosophical 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
  •  292
    Is Moral Relativism Consistent?
    Analysis 45 (1): 40-44. 1985.
    Let C1 and C2 be distinct moral codes formulated in English. Let C1 contain a norm N and C2 its negation. The paper construes the moral relativist as saying that if both codes are consistent, then, in the strongest sense of correctness applicable to moral norms, they are also both correct in the sense that they contain only correct moral norms. If we believe that the physical statements of English are true (false) in English, we will reject an analogous statement made of physical theories. We wi…Read more
  •  53
    The Received Distinction Between Pragmatics, Syntax and Semantics
    Foundations of Language 11 97-104. 1974.
    The distinction between pragmatics, semantics, and syntax, at least as traditionally construed, is argued to be defective in various respects.
  •  134
    Convention T and basic law V
    Analysis 62 (4). 2002.
    It is argued that Convention T and Basic Law V of Frege’s Grungesetze share three striking similarities. First, they are universal generalizations that are intuitively plausible because they have so many obvious instances. Second, both are false because they yield contradictions. Third, neither gives rise to a paradox.
  •  175
    Domains of Discourse
    Logique Et Analyse 117 (17): 173-176. 1987.
    Suppose there is a domain of discourse of English, then everything of which any predicate is true is a member of that domain. If English has a domain of discourse, then, since ‘is a domain of discourse of English’ is itself a predicate of English and true of that domain, that domain is a member of itself. But nothing is a member of itself. Thus English has no domain of discourse. We defend this argument and go on to argue to the same conclusion without relying on the supposition that English is …Read more
  •  229
    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
  •  8
    The Internal/External Question
    Grazer Philosophische Studien 47 (1): 31-41. 1994.
  •  101
    A defense of Sommers
    Philosophical Studies 29 (5). 1976.
    Jon Fjeld wrote a paper that he begins by nicely outlining why various criticisms of Fred Sommers theory of types and categories fail. Fjeld puts forth a criticism that avoids the problems with these other criticisms. But, it is argued, his criticism also fails.
  • Chapter 3: Objectivism and Realism in Frege's Philosophy of Arithmetic
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 73-101. 2006.