Abstract:

In his lifetime, Frege published two volumes in which he systematically laid out his logical system, Begriffsschrift in 1879, and Grundgesetze der Arithmetik in 1893. Notationally, the logic that Frege presents in these works appears the same, but this masks great changes that occurred in the interim: Between 1879 and 1893, Frege was occupied with a wholesale rethinking of the foundations of logic. The innovations he introduces reflect Frege's articulation of the notion of logical form, and the development of a semantic framework that is suffcient for carrying out his
logicist reduction of arithmetic to logic, a framework that would allow for logical terms to be interpreted as referring to numbers, and the arithmetic operations that operate on them. In this talk, I will explore these developments, focusing on two central theses: First, that Frege was following a broadly Kantian perspective on logic, Begriffsschrift being a manifestation of a pure, general logic, and Grundgesetze a transcendental logic, (albeit channeled through his novel conception of logical form), and second, that there is a transition from a non-compositional logical language in Begriffsschrift to a fully compositional language in Grundgesetze. In this context emerges many of the core semantical ideas that  nd their initial articulation in Frege. The talk will briefly outline Frege's notation, and discuss how Frege's views on functional application, logical terms and value-ranges, generalization, identity and definitions evolve.