Single Idea 9344

[catalogued under 12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities]

Full Idea

At the end of the analytical method in mathematics there are simple ideas of which no definition can be given. Moreover there are axioms and postulates, in short, primitive principles, which cannot be demonstrated and do not need demonstration.

Gist of Idea

Mathematical analysis ends in primitive principles, which cannot be and need not be demonstrated

Source

Gottfried Leibniz (Monadology [1716], §35)

Book Reference

Marcus Aurelius: 'The Meditations', ed/tr. Grube,G.M.A. [Hackett 1983], p.153


A Reaction

My view is that we do not know such principles when we apprehend them in isolation. I would call them 'intuitions'. They only ascend to the status of knowledge when the mathematics is extended and derived from them, and found to work.