Paradoxes and the foundations of semantics and metaphysics

Abstract

Numerous philosophical problems, otherwise quite different in character, are of the following form. Certain claims which seem not only obviously true, but even constitutive of the meanings of the expressions employed, can be shown to lead to absurdity when taken together (perhaps in conjunction with contingent facts about the world). All such problems can justly be called paradoxes. The paradoxes I examine are the liar paradox, the sorites paradox, and the personal identity paradox posed by the fission problem. I argue that, in all of the cases examined, the claims that jointly lead to absurdity really are constitutive of the meanings of the expressions employed, in the following ways. First, semantic competence with the expressions involves being disposed to accept these claims. Second, the claims are reference-determining, in that the semantic values of the expressions employed are constrained by the condition that these claims should come out true, or as nearly true as possible. If a claim or principle is constitutive of meaning in both of these ways, I call it meaning-constitutive. When the meaning-constitutive principles for some expressions of a language are inconsistent, I call the language inconsistent. This is a stipulative definition; but it accords well with what other theorists who have talked about languages being inconsistent, for example Alfred Tarski, have had in mind. In chapters one and two, I argue that our language is inconsistent. In chapter three, I relate my theses to Frank Jackson's and David Lewis's views on how reference is determined. Another problem posed by the liar paradox concerns important theses in the philosophy of language. The liar reasoning shows that under certain conditions, a natural language cannot contain a predicate satisfying the T-schema. But many theses in the philosophy of language presuppose that truth satisfies the T-schema. I resolve this conflict in a Tarskian way: by saying that truth then is expressed only in an essentially richer metalanguage. However, I argue that taking this route means having to embrace the existence of absolutely inexpressible properties - and even to embrace the conclusion that some properties of which we appear to have concepts are absolutely inexpressible. All this is dealt with in chapter four. In the fifth chapter I show that my arguments of the previous chapters have (dis)solved the liar paradox. And finally, in the sixth chapter, I discuss the philosophical significance of truth and logic, and argue that these questions are significant only if understood in a new way. In this last chapter I also discuss the implications of the liar paradox for metaphysics; more specifically, its implications for the issue of how metaphysical claims are justified.