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.

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.

Psychological egoism says that a purposive action is self-interested in a certain sense. The trick is to say in what sense. On the one hand, the psychological egoist wants to avoid a thesis that can be falsified by trivial examples. On the other hand, what is wanted is a thesis that lacks vacuity. The paper’s purpose is to arrive at such a thesis and show that it is a reasonable guess with empirical content.

The fundamental thought of moral relativism is set out as follows: moral criteria, derived from overall moral points of view, are used to derive particular moral judgments. Thus such a judgment might be correct relative to one overall moral point of view and incorrect relative to another. The evaluation of an overall moral point of view does not involve the application of moral criteria. Rather, the evaluation of a morality takes us outside the province of morality. The result of sharpening (...) this view is a doctrine called system relativism. System relativism is contrasted with other conceptions of moral relativism that have recently been propounded. It is argued that system relativism is the most defensible version. (shrink)

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.

An account of the logic of bivalent languages with truth-value gaps is given. This account is keyed to the use of tables introduced by S. C. Kleene. The account has two guiding ideas. First, that the bivalence property insures that the language satisfies classical logic. Second, that the general concepts of a valid sentence and an inconsistent sentence are, respectively, as sentences which are not false in any model and sentences which are not true in any model. What recommends this (...) approach is (1) its relative simplicity, and (2) the fact that it leaves the fundamental features of classical logic intact. (shrink)

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’.

In ANARCY, STATE AND UTOPIA Robert Nozick says that the fundamental question of political philosophy, one that precedes questions about how the state should be organized, is whether there should be any state at all. In the first part of his book he attempts to justify the state. We argue that he is not successful.

Quine argues that if sentences that are set theoretically equivalent are interchangeable salva veritate, then all transparent operators are truth-functional. Criticisms of this argument fail to take into account the conditional character of the conclusion. Quine also argues that, for any person P with minimal logical acuity, if ‘belief’ has a sense in which it is a transparent operator, then, in that sense of the word, P believes everything if P believes anything. The suggestion is made that he intends that (...) result to show us that ‘believes’ has no transparent sense. Criticisms of this argument are either based on unwarranted assertions or on definitions of key terms that depart from Quine’s usage of those terms. (shrink)

A conception of pragmatics distinguishes pragmatics from semantics proper in terms of indexicality: semantics is conceived as the quest for a truth definition for languages without indexical expressions; pragmatics is conceived as a quest for a truth definition for languages with indexical expressions. I argue that indexicality is not a feature that can be used to capture anything like what Morris and Carnap had in mind.

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.

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 paper concludes (...) that these ordinary methods of inquiry, when employed in these limited cases, put us in a position in which we actually cannot know. Thus our ability to know will be a function of the added contextual elements that are found in ordinary cases. A second conclusion is that we come literally to observe bodily behaviour in the course of the sceptical inquiry; while in ordinary cases we observe pain-behaviour. (shrink)

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 into equivalence classes. These are the types discriminated by the language. This paper criticizes an attempt by Peter Strawson to explain terms peculiar to type theory in terms of other notions not peculiar to type theory. (shrink)

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 suggests that further clarification of the concepts of spanning and category mistakenness should be sought in reflection upon the more familiar concepts of a sort of thing and a predicate category. (shrink)

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.

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.

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 the (...) best of four views. It is also defended against objections. (shrink)

Quine criticizes Strawson’s account of the province of logic. Robert Hadley proposes a refutation of Quine. This paper proposes a refutation of Hadley.

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.

This paper reaches the conclusion that, while there are ordinary cases in which the pretending possibility is reasonable, these cases always contain some element that makes it reasonable. This will be the element we ask for when we ask why pretending possibility is raised. Knowledge that someone else is in pain is a matter of eliminating the proposed element or neutralizing its pain-negating aspect.

Two cases are distinguished. In one case two predicates belong to distinct languages. A straight-forward argument is presented that the predicates might be synonymous without being coextensive. In the second case the predicates belong to the same language. Here the issue is more involved, but the same conclusion is reached.

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.

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 demonstrate that this argument fails to (...) establish the implausibility of dualism. (shrink)

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’.

The paper’s purpose is to get clearer on what it is to express a proposition. A proposition is understood as anything that can be asserted, assumed, conjectured, stated, believed, and so on. It is not something that can be asked, ordered, requested, and so on. The paper tries to provide groundwork for a successful analysis by making distinctions and clarifying problems.

Quine’s way of dealing with the semantical paradoxes (Ways of Paradox, pp. 9-10) is criticized. The criticism is based on three premises: (1) no learnable language has infinitely many semantical primitives; (2) any language of which Quine’s theory is true has infinitely many semantical primitives; (3) English is a learnable language. The conclusion drawn is that Quine’s theory is not true of English.

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.

In an earlier paper Sayward argued that a speaker could not make an assertion by uttering a sentence of form “p, but I believe not-p” given that the speaker spoke honestly and literally. Robert Imlay criticized some things said in that earlier paper. This paper responds to those criticisms.

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.

The paper argues that two apparently attractive conceptions of an eternal sentence are defective. An alternative conception is presented which the authors think allows greater insight into the nature of semantic concepts.

Nicholas Sturgeon has claimed that moral explanations constitute one area of disagreement between moral realists and noncognitivists. He claims that the correctness of such explanation is consistent with moral realism but not with noncognitivism. Does this difference characterize all other anti-realist views. This paper argues that it does not. Moral relativism is a distinct anti-realist view. And the correctness of moral explanation is consistent with moral relativism.

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.

This paper is written in opposition of various antecedent discussions of Moore’s paradox. It concludes that one cannot make an honest and primary truth-claim by producing ‘p, but I believe not-p’.

Some of Austin's general statements about the doctrines of sense-datum philosophy are reviewed. It is concluded that Austin thought that in these doctrines "directly see" is given a new but inadequately explained and defined use. Were this so, the philosophical use of "directly see" would lack a definite sense and this would correspondingly affect the doctrines. They would lack definite truth-value. Against this, it is argued that the philosopher's use of "directly see" does not support Austin's general thesis that the (...) sense-datum doctrines lack truth-value. (shrink)

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.

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.

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.

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.

A perplexity about singular existence statements is that for their negations to be true their subject terms do not name anything. For example, in ‘Pegasus does not exist’ ‘does not exist’ is not said in respect to the referent of ‘Pegasus’ since there is none. But, then, in respect to what is that said? The paper answers the question by proposing a metalinguistic interpretation of singular existence statements, according to which singular existence statements are about names. It is argued that (...) this interpretation fits in well with Frege’s views on existence, presupposition, and his idea that names have senses. (shrink)

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.

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.

Two philosophical theories, mathematical Platonism and nominalism, are the background of six dialogues in this book. There are five characters in these dialogues: three are nominalists; the fourth is a Platonist; the main character is somewhat skeptical on most issues in the philosophy of mathematics, and is particularly skeptical regarding the two background theories.

In a recent paper Nicholas Sturgeon claims moral explanations constitute one area of disagreement between moral realists and noncognitivists. The correctness of such explanation is consistent with moral realism but not with noncognitivism. Does this difference characterize other anti-realist views? I argue that it does not. Moral relativism is a distinct anti-realist view. And the correctness of moral explanations is consistent with moral relativism.

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 pure mathematics are objectively true. (...) A key principle assumed is that if one statement logically implies a second, then if the first is objectively true so is the second. A question about this principle is raised and answered. The problem with the argument is with the second premise. (shrink)

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.

There are plausible objections to substitutional construals of generalization. But these objections do not apply to a substitutional construal of generalization proposed by Peter Geach several years ago. This paper examines Geach’s conception.