Logic & Philosophy of Science Colloquium


Thomas Hofweber
University of North Carolina at Chapel Hill

"Logicism Without Logic"


There is a puzzle about the occurrence of number words in natural language that goes back to Frege. Number words like "two" and "four" can occur as singular terms, but also as adjectives or determiners. These two syntactic occurrences correspond to two quite different semantic functions, and these two semantic functions are related to two rather different philosophical visions of arithmetic. The puzzle is how number words can do both of these things. I will argue that this puzzle has never been properly solved, but that a solution is forthcoming once we take a close look at number words as determiners. The solution I will propose will overcome what I take to be the biggest obstacle in a defense of logicism. Logicism will, however, not be understood as the claim that math is reducible to logic, but rather as a defense of the grand philosophical vision of mathematics that such a reduction was supposed to establish.

Friday, April 28, 2006
SST 777
3 pm

Refreshments will be served