Vann McGee

Tarski showed how to give satisfactory theories of truth for a wide variety of languages, but he required that the theory of truth for a language be formulated in an essentially richer metalanguage. Since there is no human language essentially richer than a natural language and since we would like to develop consistent theories of truth for natural languages, we would like to learn how to formulate a theory of truth for a language within that very language. ;Toward this end, I consider a class of formalized languages called partially interpreted languages, derived from the work of Carnap, in which sentences are classified as definitely true, definitely false, and intermediate. I give a condition of adequacy, analogus to Tarski's Convension T, requiring that is true be definitely true iff is definitely true , and show that it is possible to give, effectively and explicity, a theory of truth that meets the condition. Theories of truth that meet the condition are shown to have various pleasant properties. The construction depends heavily upon the work of Saul Kripke. ;In addition to the work of Tarski and Kripke, the "naive semantics" of Gupta and Herzberger is discussed. Of the paradoxes other than the liar, only Montague's paradox about necessity is discussed in any detail. To solve this paradox, I recommend a provability interpretation of modal logic of the type studied by Solovay. Prospects for extending Solovay's results into quantified modal logic are discussed. ;The work is entirely concerned with formal languages, although it is hoped that the tools developed can be usefully applied to natural languages.

This is not an overly ambitious paper. What I would like to do is to take a thesis that most people would regard as wildly implausible, and convince you that it is, in fact, false. What's worse, the argument I shall give is by no means airtight, though I hope it's reasonably convincing. The thesis has to do with the fuzzy boundaries of terms that refer to familiar middle-sized objects, terms like ‘Kilimanjaro’ and ‘the tallest mountain in Africa.’ It is intuitively clear that Kilimanjaro has a fuzzy boundary, so that there are some clods of earth at the base of the mountain for which there isn't anything, either in our practices in using the word ‘Kilimanjaro’ or in the facts of geography, that determines an answer to the question whether the clod is a part of Kilimanjaro.

There is no preferred reduction of number theory to set theory. Nonetheless, we confidently accept axioms obtained by substituting formulas from the language of set theory into the induction axiom schema. This is only possible, it is argued, because our acceptance of the induction axioms depends solely on the meanings of aritlunetical and logical terms, which is only possible if our 'intended models' of number theory are standard. Similarly, our acceptance of the second-order natural deduction rules depends solely on the meanings of the logical terms, which implies, it is argued, that our second-order quantifiers have to be standard.

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal

Deflationists about truth embrace the positive thesis that the notion of truth is useful as a logical device, for such purposes as blanket endorsement, and the negative thesis that the notion doesn’t have any legitimate applications beyond its logical uses, so it cannot play a significant theoretical role in scientific inquiry or causal explanation. Focusing on Christopher Hill as exemplary deflationist, the present paper takes issue with the negative thesis, arguing that, without making use of the notion of truth conditions, we have little hope for a scientific understanding of human speech, thought, and action. For the reference relation, the situation is different. Inscrutability arguments give reason to think that a more-than-deflationary theory of reference is unattainable. With respect to reference, deflationism is the only game in town.