3 ideas
| 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. |
| 22312 | Facts can be both positive and negative [Wittgenstein, by Potter] |
| Full Idea: In 1913 Wittgenstein was explicit that there are both positive and negative facts. | |
| From: report of Ludwig Wittgenstein (Notes on Logic [1913], B7) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 47 'Mole' | |
| A reaction: This is a prelude to the Tractatus, in which negative facts are denied in T1.11 (and in a 1919 letter), but then affirmed in T2.06. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |