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Full Idea
Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another.
Gist of Idea
Proof reveals the interdependence of truths, as well as showing their certainty
Source
report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.2
A Reaction
This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts.
Related Idea
Idea 8559 Analysis aims at internal relationships, not reduction [Shoemaker]
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |