more from Gerhard Gentzen

Single Idea 11023

[catalogued under 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives]

Full Idea

The introduction rules represent, as it were, the 'definitions' of the symbols concerned, and the elimination rules are no more, in the final analysis, than the consequences of these definitions.

Gist of Idea

The logical connectives are 'defined' by their introduction rules


Gerhard Gentzen (works [1938]), quoted by Stephen Read - Thinking About Logic Ch.8

Book Reference

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.229

A Reaction

If an introduction-rule (or a truth table) were taken as fixed and beyond dispute, then it would have the status of a definition, since there would be nothing else to appeal to. So is there anything else to appeal to here?