Reference and realism in philosophy of language and philosophy of mathematics

Most realists accept some version of the correspondence theory of truth, and most hold that reference is not subject to much indeterminacy. My central project is to defend these semantic doctrines against some influential recent attacks.; The body of my dissertation consists of exposition and criticism of sample members of two groups of arguments: Hilary Putnam's model theoretic arguments against mathematical realism, and Donald Davidson's arguments for the thesis that reference in natural language is inscrutable. I also discuss in detail related arguments due to Bas van Fraassen, Thoralf Skolem, Jonathan Lear, John Wallace, and Hartry Field. The Putnamian arguments discussed here primarily concern reference in pure mathematics, whereas the Davidsonian arguments primarily concern reference in natural language, but both groups of arguments purport to show that the reference of singular terms and predicates is indeterminate, and to do so in similar ways. Insofar as the correspondence theory of truth depends on the opposite view that term reference is fixed and determinate, these arguments also threaten to undercut the correspondence theory.; Davidson claims (i) that a trivial permutation argument shows that reasonable formal and evidential requirements on interpretations of a language do not single out a correct interpretation, or even a small class of acceptable interpretations, and (ii) that indeterminacy of reference follows almost trivially. I show by counterexample that (i) is false, and argue that (ii) rests on an implausible verification principle. According to Putnam, a version of the same argument shows that reference is not determined by the truth conditions of whole sentences. I show that the main theorem to which Putnam appeals in this context does not hold in a reasonable semantics for a language with intensional operators. I show that the truth conditions of certain existential, modal, and counterfactual sentences place constraints on reference that block these arguments.; Davidson and Putnam also claim that causal accounts of reference do not defeat their arguments for inscrutability. Putnam's objections to the causal theory of reference have been criticized extensively and are not discussed here. I discuss a similar, but distinct, objection to the causal theory due to Davidson, and argue that it is mistaken. I also argue that Putnam's attempt to revive Skolemism fails, and that mathematical realism is not undermined by any of the familiar theorems of modern logic and set theory, including the Lowenheim-Skolem family, reflection arguments, trivial and nontrivial isomorphisms, and independence results. I discuss the relevant concepts of set theory and model theory in some detail, and expose a technical error in Putnam's discussion of the Lowenheim-Skolem Theorem.; The arguments I discuss all purport to undermine central realist doctrines on the basis of theorems of mathematical logic. But all of these arguments also rely on further extramathematical assumptions, some of which are controversial and unsupported--indeed, unnoticed. Some of the arguments involve misinformation and technical mistakes as well. The arguments I discuss are representative of those designed to show that realism is not compatible with the facts of mathematics. In discrediting them, I show that there is no reason to suspect such an incompatibility, and provide indirect evidence for the view that no such incompatibility exists.