more from Michael D. Resnik

Single Idea 6299

[catalogued under 4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL]

Full Idea

Many axioms have been proposed, not on the grounds that they can be directly known, but rather because they produce a desired body of previously recognised results.

Gist of Idea

Axioms are often affirmed simply because they produce results which have been accepted

Source

Michael D. Resnik (Maths as a Science of Patterns [1997], One.5.1)

Book Reference

Resnik,Michael D.: 'Mathematics as Science of Pattern Recognition' [OUP 1999], p.84


A Reaction

This is the perennial problem with axioms - whether we start from them, or whether we deduce them after the event. There is nothing wrong with that, just as we might infer the existence of quarks because of their results.