Reading Group: Frege's Logic: From Begriffsschrift to Grundgesetze

In his lifetime, Frege published two volumes in which he 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 sufficient 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 reading group, we 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, 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 find their initial articulation in Frege, among them the analysis of concepts as functions, predication as functional application, and that the composition of function and argument is a semantic entity.
The reading group will commence with an overview of Frege’s logical system, including an introduction to his logical notation and his method of proof as logical derivation. We will then move to a comparison of the systems of Begriffsschrift and Grundgesetze, with particular attention paid to the role of the horizontal, generalization, identity and the formalization of definitions.

Group Readings:

Frege, Grundgesetze der Arithmetik, Foreword
May, “Logic as Science”
Tichy, The Foundations of Frege’s Logic, Chapter Thirteen: Inference

Background Readings:
Frege Begriffsschrift, Part 1
Frege Grundgesetze, Part I, “Exposition of the Concept Script”

The Reading Group will have three sessions: Monday, May 6, Wednesday, May 8, and Friday May 10, 2024, 10-12 am. We will meet in the Statistics Library, Room 245, Ludwigstr. 33.