Gottlob Frege (1848-1925) was a mathematician who became interested in logic and whose Begriffschrift (1879) transformed conceptions of logic. He went on suggest (in his Grundlagen der Arithmetik of 1884 and Grundgesetze der Arithmetik of 1893 and 1903) to show how the whole of mathematics might be derived from purely logical principles. His approach to mathematics rested on deep and systematic thinking about its language, and that thinking extended to features of language with little role in the language of mathematics.

Frege’s style is different from Peirce’s, and he gets to the point very quickly. Most of his key ideas show up in the first few pages, but he has things to say about them later that have also attracted attention and generated controversy.

Assignment for Mon. 1/27: pp. 209-214

The key idea here lies in the distinctions among sense (Sinn), reference (Bedeutung), and conception (Vorstellung). Translation is something of issue: many leave the term Bedeutung untranslated and Frege’s Vorstellung is more often translated in as ‘idea’. The idea of “indirect reference” is also important and we will recur frequently in the rest of the article.

Assignment for Wed. 1/29: pp. 214-221

The main topic here is the application of Frege’s distinctions to sentences—in particular, his claim that the reference of a sentence is a truth value. But Frege also uses his idea of indirect sense to offer an account of range of philosophically important constructions in language (and ones that play relatively little role in mathematics).

Assignment for Fri. 1/31: pp. 221-230

In this last part of the article, Frege offers analyses of a still wider range of linguistic constructions. This important (and controversial) of these is the first, which leads him to present his views on the problem of the logical properties of definite descriptions (i.e., phrases of the form ‘the …’).