The Silent Revolution in Wittgenstein’s Later Philosophy of Mathematics

Abstract

It is customary to distinguish the early Wittgenstein of the Tractatus from the later Wittgenstein of the “Philosophical Investigations.” But I believe a revolution of a similar magnitude occurred in the middle of the “later” period of Wittgenstein, August 1937, which included a new approach to the philosophy of mathematics. This approach is a change in the way Wittgenstein perceives the relationship between mathematics and its canonical applications. Instead of seeing mathematical theorems as rules of “grammar” governing mathematical language, he suddenly began to see them as rules governing human activities like counting and measuring. Mathematical theorems became “supervenient” upon these activities, which eliminated the “problem” of the applicability of mathematics.