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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 Ref
'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.
| 17262 | Aristotle's formal and material 'becauses' [aitiai] arguably involve grounding [Aristotle, by Correia/Schnieder] |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| 14268 | Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K] |
| 17274 | Philosophical explanation is largely by ground (just as cause is used in science) [Fine,K] |
| 17290 | Only metaphysical grounding must be explained by essence [Fine,K] |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| 17296 | We must accept grounding, for our important explanations [Audi,P] |
| 17268 | Grounding is metaphysical and explanation epistemic, so keep them apart [Correia/Schnieder] |