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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] |
| 1885 | Proof moves from agreed premises to a non-evident inference [Sext.Empiricus] |
| 8627 | Leibniz is inclined to regard all truths as provable [Leibniz, by Frege] |
| 17495 | Proof aims to remove doubts, but also to show the interdependence of truths [Frege] |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| 2898 | Anything which must first be proved is of little value [Nietzsche] |
| 19067 | A successful proof requires recognition of truth at every step [Dummett] |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |