•  143
    Mathematical Relativism
    with Hugly Philip and 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.
  •  339
    Convention T and Basic Law V
    Analysis 62 (4): 289-292. 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.
  •  73
    Various authors of logic texts are cited who either suggest or explicitly state that the Gödel incompleteness result shows that some unprovable sentence of arithmetic is true. Against this, the paper argues that the matter is one of philosophical controversy, that it is not a mathematical or logical issue.
  •  37
    The Internal/External Question
    Grazer Philosophische Studien 47 (1): 31-41. 1994.
  •  175
    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 1: Introduction
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 35-42. 2006.
  •  97
    Should persons be sacrificed for the general welfare?
    Journal of Value Inquiry 16 (2): 149-152. 1982.
    It is argued that Robert Nozick is wrong in asserting that persons should not be sacrificed for the general welfare.
  •  112
    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.
  •  93
    Redundant truth
    Ratio 5 (1): 24-37. 1992.
    A strong and weak version of the redundancy theory of truth are distinguished. An argument put forth by Michael Dummett concludes that the weak version is vitiated by truth-value gaps. The weak version is defended against this argument. The strong version, however, is vitiated by truth-value gaps.
  •  119
    A fregean principle
    History and Philosophy of Logic 19 (3): 125-135. 1998.
    Frege held that the result of applying a predicate to names lacks reference if any of the names lack reference. We defend the principle against a number of plausible objections. We put forth an account of consequence for a first-order language with identity in which the principle holds
  •  200
    Prior’s Theory of Truth
    Analysis 47 (2): 83-87. 1987.
    This paper is a critical exposition of Prior’s theory of truth as expressed by the following truth locutions: (1) ‘it is true that’ prefixed to sentences; (2) ‘true proposition’; (3) true belief’, ‘true assertion’, ‘true statement’, etc.; (4) ‘true sentence’.
  •  198
    Prior on Propositional Identity
    Analysis 36 (4): 182-184. 1976.
    Let A, B, C stand for sentences expressing propositions; let A be a component of C; let C A/B be just like C except for replacing some occurrence of A in C by an occurrence of B; let = be a binary connective for propositional identity read as ‘the proposition that __ is the very same proposition as …’. Then authors defend adding ‘from C = C A/B infer A = B’ to Prior’s rules for propositional identity, appearing in OBJECTS OF THOUGHT.
  •  83
    Is 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.
  •  186
    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
  •  1300
    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.
  •  71
    Anderson and Belnap devise a model theory for entailment on which propositional identity equals proposional coentailment. This feature can be reasonably questioned. The authors devise two extensions of Anderson and Belnap’s model theory. Both systems preserve Anderson and Belnap’s results for entailment, but distinguish coentailment from identity.
  •  198
    Determining whether the law of excluded middle requires bivalence depends upon whether we are talking about sentences or propositions. If we are talking about sentences, neither side has a decisive case. If we are talking of propositions, there is a strong argument on the side of those who say the excluded middle does require bivalence. I argue that all challenges to this argument can be met.
  •  262
    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.
  •  157
    Williams’ Definition of ‘X is true’
    Analysis 30 (3): 95-97. 1970.
    C. J. F, Williams proposed ‘for some p ___ states that p & p’ as a satisfactory analysis of ‘___ is true’. This paper takes issue with this claim.
  •  103
    What is an infinite expression?
    Philosophia 16 (1): 45-60. 1986.
    The following syllogism is considered: a string is not an expression unless it is tokenable; no one can utter, write, or in anyway token an infinite string; so no infinite string is an expression. The second premise is rejected. But the tokenability of an infinite sentence is not sufficient for it being an infinite expression. A further condition is that no finite sentence expresses that sentence’s truth-conditions. So it is an open question whether English contains infinite expressions.
  •  408
    A Wittgensteinian Philosophy of Mathematics
    Logic 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 8: Thesis One
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 215-240. 2006.
  •  164
    Thompson Clarke and the problem of other minds
    International Journal of Philosophical Studies 13 (1): 1-14. 2005.
    The force of sceptical inquiries into out knowledge of other people is a paradigm of the force that philosophical views can have. Sceptical views arise out of philosophical inquiries that are identical in all major respects with inquiries that we employ in ordinary cases. These inquiries employ perfectly mundane methods of making and assessing claims to know. This paper tries to show that these inquiries are conducted in cases that lack certain contextual ingredients found in ordinary cases. The…Read more
  •  262
    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
  •  93
    Absurdity and spanning
    with Stephen H. Voss
    Philosophia 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
  • Chapter 6: Arithmetic and Necessity
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 159-182. 2006.
  •  63
    Roman Suzuko on Situational Identity
    Sorites 15 42-49. 2004.
    This paper gives a semantical account for the (i)ordinary propositional calculus, enriched with quantifiers binding variables standing for sentences, and with an identity-function with sentences as arguments; (ii)the ordinary theory of quantification applied to the special quantifiers; and (iii)ordinary laws of identity applied to the special function. The account includes some thoughts of Roman Suszko as well as some thoughts of Wittgenstein's Tractatus.
  • References
    Poznan Studies in the Philosophy of the Sciences and the Humanities 90 285-287. 2006.
  •  192
    Is heaven a possible world?
    with Douglas Erlandson
    International Journal for Philosophy of Religion 12 (1). 1981.
    The goal of theodicy is to show how God could create our world with all its evil. This paper argues that the theodicist can achieve her goal only if she gives up one of these three propositions: (1) evil does not exist in heaven; (2) heaven is better than the present world; (3) heaven is a possible world. Second, it is argued that the theodicist can reject (3) without giving up her belief that heaven exists, so that (3) is her best alternative.