Axiom

A purportedly uncriticizable foundation upon which a theoretical edifice is built.

In mathematics, axioms can be criticized externally and improved, distinguishing them from the axioms assumed by foundationalist epistemologies. Mathematical axioms are chosen, not discovered as bedrock truths — they are conjectures about what rules produce interesting or useful structures.

Connections

• •Central to Foundationalism — which erroneously treats axioms as unchallengeable
• •Contrasts with Critical Rationalism — where all ideas, including axioms, are open to Criticism
• •Related to Justificationism — which demands fixed foundations for knowledge
• •Mathematical axioms are actually conjectures that can be revised
• •Proof from axioms does not yield absolute certainty about the physical world