Single Idea 10053

[catalogued under 5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism]

Full Idea

We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true.

Gist of Idea

Geometrical axioms imply the propositions, but the former may not be true

Source

Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4

Book Reference

-: 'British Soc for the Philosophy of Science' [-], p.109


A Reaction

Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism.