|149||Special Topics in the Philosophy of Logic & Mathematics: Theories of Truth||Mancosu||MWF 1-2||220 Wheeler Hall|
The course is devoted to a detailed study of the two major formal theories of truth developed in the twentieth century, e.g. Tarski’s (1935) and Kripke’s (1975). When trying to articulate the principles capturing the logic of truth predicates in natural language our intuition leads immediately to the request that the theory should yield all biconditionals of the form “‘p’ is true iff p”. But the liar paradox shows that this naïve principle for truth, together with classical logic, leads to contradiction. Tarski’s solution rests on the distinction between object language (L) and metalanguage (ML) and on imposing as an adequacy condition for a theory of truth that the metalanguage be able to prove all the biconditionals of the above form, where p is restricted to sentences of the object language. Since the truth predicate for L is expressible in ML but not in L, the liar, and similar paradoxes, are blocked. Tarski’s approach dominated the field for forty years. Kripke in 1975 developed a formal theory of truth using a three valued logic. In his approach paradoxical statements turn out to be neither true nor false. Kripke’s construction leads to a theory of truth in which the truth predicate for L is expressible in L itself. The importance of Tarski’s and Kripke’s theories of truth cannot be overstated; indeed, they are required for a proper understanding of all other formal theories of truth that have been proposed in the last thirty years (revision theory, etc.). Students taking this course will be required to do a substantial amount of logical work. In the process they will learn topics such as, among others, basics of set theory, many valued logics, fixed points and inductive definitions. Of course, the philosophical implications of Tarski’s and Kripke’s theories will also be discussed. The formal prerequisite is 12A (Introduction to Logic). Familiarity with either Phil 140A or Phil 140B will be an advantage but material covered in those courses will not be presupposed.
Textbook: Vann McGee, Truth, Vagueness, and Paradox. An essay on the logic of truth, Hackett, 1988.