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2 ideas
| 2145 | In mathematics certain things have to be accepted without further explanation [Plato] |
| Full Idea: The practitioners of maths take certain things as basic, and feel no further need to explain them. | |
| From: Plato (The Republic [c.374 BCE], 510c) |
| 9154 | Frege agreed with Euclid that the axioms of logic and mathematics are known through self-evidence [Frege, by Burge] |
| Full Idea: Frege maintained a sophisticated version of the Euclidean position that knowledge of the axioms and theorems of logic, geometry, and arithmetic rests on the self-evidence of the axioms, definitions, and rules of inference. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Tyler Burge - Frege on Apriority Intro | |
| A reaction: I am inclined to agree that they are indeed self-evident, but not in a purely a priori way. They are self-evident general facts about how reality is and how (it seems) that it must be. It seems to me closer to a perception than an insight. |