more from this thinker | more from this text
Full Idea
Proof has as its goal not only to raise the truth of a proposition above all doubts, but additionally to provide insight into the interdependence of truths.
Gist of Idea
Proof aims to remove doubts, but also to show the interdependence of truths
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §02)
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Jacquette)', ed/tr. Jacquette,Dale [Pearson Longman 2007], p.18
A Reaction
This is a major idea in Frege's thinking, and a reason why he is the father of modern metaphysics as well as the father of modern logic. You study the framework of truths by studying the logic that connects them.
| 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] |