On Frege’s Logical Diagrams

Abstract

Modern logic has been provided since its very inception in 1879 with a diagrammatic outlook: Frege’s two-dimensional symbolism in his Begriffsschrift. This was supposed to surpass specific limitations both of natural and of other constructed languages. However, it did not receive the attention paid to Frege’s purely logical innovations. This fact was partly due to the common opinion, informed by logicians like Venn, Schröder and Peano, and heavily influenced by Russell’s overstatement that the symbolism was ’unfortunately so cumbrous as to be very difficult to employ in practice’ [1]. This was rather ironic, I believe, as Frege devised it exactly for the purpose of assisting our inferential practice: ’its chief purpose should be to test in the most reliable manner the validity of a chain of reasoning’ [2]. The main thrust of my paper is to show that a particular point raised by Schröder – that Frege’s conceptual notation fails to be modelled on the formula language of arithmetic – is based on a misunderstanding. I will describe then what it seems to me the most advantageous aspect of Frege’s diagrams, and give a serious reason for their eventual cast-off. But first let’s look at some of them.

Frege’s diagrams have been only recently noted as an endeavor to logically reason with diagrams (e.g., in [3]), but no analysis has yet been offered. The present paper is motivated by this state of affairs. I am very grateful to Patricia Blanchette for her comments and suggestions.