Single Idea 13004

[catalogued under 5. Theory of Logic / K. Features of Logics / 1. Axiomatisation]

Full Idea

Aristotle's way with axioms, rather than Euclid's, is as assumptions which we are willing to agree on while awaiting an opportunity to prove them

Gist of Idea

Aristotle's axioms (unlike Euclid's) are assumptions awaiting proof

Source

report of Aristotle (Posterior Analytics [c.327 BCE], 76b23-) by Gottfried Leibniz - New Essays on Human Understanding 4.07

Book Reference

Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.419


A Reaction

Euclid's are understood as basic self-evident truths which will be accepted by everyone, though the famous parallel line postulate undermined that. The modern view of axioms is a set of minimum theorems that imply the others. I like Aristotle.