•  654
    Null Sentences
    Iyyun, The Jewish Philosophical Quarterly 48 23-36. 1999.
    In Tractatus, Wittgenstein held that there are null sentences – prominently including logical truths and the truths of mathematics. He says that such sentences are without sense (sinnlos), that they say nothing; he also denies that they are nonsensical (unsinning). Surely it is what a sentence says which is true or false. So if a sentence says nothing, how can it be true or false? The paper discusses the issue.
  •  644
    The Internal/External Question
    Grazier 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
  •  638
    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.
  •  453
    Are 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.
  •  398
    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
  •  385
    Bound Variables and Schematic Letters
    Logique 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.
  •  362
    What’s So Special About Sentences?
    Communication and Cognition: An Interdisciplinary Quarterly Journal 28 (4): 409-25. 1995.
    This paper is a discussion of Frege's maxim that it is only in the context of a sentence that a word has a meaning. Quine reads the maxim as saying that the sentence is the fundamental unit of significance. Dummett rejects this as a truism. But it is not a truism since it stands in opposition to a conception of meaning held by John Locke and others. The maxim denies that a word has a sense independently of any sentence in which it occurs. Dummett says this denial is inconsistent with the fact th…Read more
  •  302
    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
  •  253
    Offices and God
    Sophia 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.
  •  216
    Kripke on necessity and identity
    Philosophical Papers 27 (3): 151-159. 1998.
    It may be that all that matters for the modalities, possibility and necessity, is the object named by the proper name, not which proper name names it. An influential defender of this view is Saul Kripke. Kripke’s defense is criticized in the paper.
  •  158
    A problem about conversational implicature
    Linguistics and Philosophy 3 (1). 1979.
    Conversational implicatures are easy to grasp for the most part. But it is another matter to give a rational reconstruction of how they are grasped. We argue that Grice's attempt to do this fails. We distinguish two sorts of cases: (1) those in which we grasp the implicature by asking ourselves what would the speaker have to believe given that what he said is such as is required by the talk exchange; (2) those in which we grasp the implicature by asking ourselves why it is that what the speaker …Read more
  •  156
    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
  •  149
    Tarski and Proper Classes
    Analysis 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.
  •  137
    Quantifying over the reals
    Synthese 101 (1). 1994.
    Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us …Read more
  •  125
    Prior’s Theory of Propositions
    Analysis 37 (3): 104-112. 1977.
    Prior propounded a theory that, if correct, explains how it is possible for a statement about propositions to be true even if there are no propositions. The major feature of his theory is his treatment of sentence letters as bindable variables in non-referential positions. His theory, however, does not include a semantical account of the resulting quantification. The paper tries to fill that gap.
  •  116
    Moral relativism and deontic logic
    Synthese 85 (1). 1990.
    If a native of India asserts "Killing cattle is wrong" and a Nebraskan asserts "Killing cattle is not wrong", and both judgments agree with their respective moralities and both moralities are internally consistent, then the moral relativist says both judgments are fully correct. At this point relativism bifurcates. One branch which we call content relativism denies that the two people are contradicting each other. The idea is that the content of a moral judgment is a function of the overall mora…Read more
  •  105
    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.
  •  105
    Expressions and Tokens
    Analysis 41 (4): 181-187. 1981.
    The purpose of this paper is to uncover and correct several confusions about expressions, tokens and the relations between them that crop up in even highly sophisticated writing about language and logic.
  •  102
    Quine’s Way Out
    Analysis 36 (1): 28-37. 1975.
    As a way of dealing with the semantical paradoxes Quine has suggested: that semantical expressions such as ‘true’ and ‘true of’ be used with numerical subscripts; that when a truth locution T is applied to a sentence S, the subscript on T is greater than any within S; otherwise, the result of applying T to S is ill formed. A problem is that this introduces infinitely many semantical primitives. The paper suggests a way around the problem. The paper raises a further problem, leaving it open whet…Read more
  •  94
    Did 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.
  •  91
    Do we need quantification?
    Notre Dame Journal of Formal Logic 25 (4): 289-302. 1984.
    The standard response is illustrated by E, J. Lemmon's claim that if all objects in a given universe had names and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex proposition. It is because these two requirements are not always met that we need universal quantification. This paper is partly in agreement with Lemmon and partly in disagreement. From the point of view of syntax and semantics we can replace a universal prop…Read more
  •  91
    Relativism and ontology
    Philosophical 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.
  •  86
    The Lessons of the Liar
    Theory 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.
  •  77
    Mathematical Relativism
    with Sayward Charles
    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
  •  76
    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
  •  74
    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.
  •  69
    Indenumerability and substitutional quantification
    Notre 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
  •  67
    Quine's relativism
    Ratio 3 (2): 142-149. 1990.
    A doctrine that occurs intermittently in Quine’s work is that there is no extra-theoretic truth. This paper explores this doctrine, and argues that on its best interpretation it is inconsistent with three views Quine also accepts: bivalence, mathematical Platonism, and the disquotational account of truth.
  •  67
    Paradox and Semantical Correctness
    Analysis 39 (4): 166-169. 1979.
    In a series of papers R. L. Martin propounds a theory for dealing with the semantical paradoxes. This paper is a criticism of that theory.
  •  64
    Tractatus 6.2–6.22
    Philosophical Investigations 13 (2): 126-136. 1990.
    It is argued that Wittgenstein’s remarks 6.2-6.22 Tractatus fare well when one focuses on non-quantificational arithmetic, but they are problematic when one moves to quantificational arithmetic.