Logic and Math are the Rules We Work Within

The principles of logic and mathematics are true universally simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying. In other words, the truths of logic and mathematics are analytic propositions or tautologies.

Alfred J. Ayer, Sir Alfred Jules Ayer, Language, Truth and Logic (1952-06-01)

• logic
• mathematics