Do independent sentences have truth-values?

Prof. Zeynep Soysal, UR Department of Philosophy

Thursday, November 29th, 2018
3:30 PM - 4:30 PM
Harkness 115

Kurt Gödel’s incompleteness theorems show that for every sufficiently strong consistent formal system of mathematics, there are mathematical sentences that are neither provable nor refutable in that formal system. Such sentences are said to be independent of the formal system. The existence of independent sentences raises two immediate questions: Are sentences that are independent of our standard mathematical formal systems nonetheless either true or false, i.e., do they have a truth-value? And, if independent sentences do have a truth-value, then how could we find out what is their truth-value? In this talk, I will first spell out the two main and opposing answers to these questions. I will then explain how both of these answers involve semantic commitments, i.e. commitments concerning the meanings of certain mathematical expressions. Finally, I will argue that the best approach for making progress on these questions is metasemantic: It starts by asking what would determine that our mathematical expressions have meanings to begin with.

Event contact: hazel dot mcknight at rochester dot edu