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2 ideas
| 17624 | To understand axioms you must grasp their logical power and priority [Frege, by Burge] |
| Full Idea: Understanding the axioms depends not only on understanding Frege's elucidatory remarks about the interpretation of his symbols, but also on understanding their logical structure - their power to entail other truths, and their reason-giving priority. | |
| From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 4) by Tyler Burge - Frege on Knowing the Foundations 4 | |
| A reaction: This is a distinctively Burgean spin put on what Frege has to say about axioms, but I like it, and it seems well enough supported in Frege's writings (e.g. 1914). |
| 17622 | We come to believe mathematical propositions via their grounding in the structure [Burge] |
| Full Idea: A deeper justification for believing in [mathematical] propositions [apart from pragmatism] lies in finding their place in a logicist proof structure, by understanding the grounds within this structure that support them. | |
| From: Tyler Burge (Frege on Knowing the Foundations [1998], 3) | |
| A reaction: This generalises to doubting something until you see what grounds it. |