“The principles of logic and mathematics are true simply because we never allow them to be anything else.”

—  Alfred Jules Ayer , book Language, Truth, and Logic

Source: Language, Truth, and Logic (1936), p. 77.
Context: The principles of logic and mathematics are true 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.

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Alfred Jules Ayer photo
Alfred Jules Ayer 18
English philosopher 1910–1989

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