more from Bernard Bolzano

Single Idea 17265

[catalogued under 7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation]

Full Idea

Mathematical proofs are philosophical in method if they do not only demonstrate that a certain mathematical truth holds but if they also disclose why it holds, that is, if they uncover its grounds.

Gist of Idea

Philosophical proofs in mathematics establish truths, and also show their grounds

Source

report of Bernard Bolzano (Theory of Science (Wissenschaftslehre, 4 vols) [1837]) by Correia,F/Schnieder,B - Grounding: an opinionated introduction 2.3

Book Reference

'Metaphysical Grounding', ed/tr. Correia,F/Schnieder,B [CUP 2012], p.6


A Reaction

I aim to defend the role of explanation in mathematics, but this says that this is only if the proofs are 'philosophical', which may be of no interest to mathematicians. Oh well, that's their loss.