3 ideas
17606 | Axioms reveal the underlying assumptions, and reveal relationships between different areas [Kline] |
Full Idea: The axiomatic method ....revealed precisely what assumptions underlie each branch [of mathematics] and made possible the comparison and clarification of the relationships of various branches. | |
From: Morris Kline (Mathematical Thought from Ancient to Modern Times [1972], p.1027), quoted by Penelope Maddy - Defending the Axioms 1.3 | |
A reaction: I take this to be the 'fruitfulness' which marks out the discovery of the essence of something. |
16157 | Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M] |
Full Idea: No insurance company, presented with a policy written for 'Theoris' [the original ship] would pay for damages suffered if the ship contructed from the old planks had been shipwrecked. | |
From: Michael Frede (Individuals in Aristotle [1978]) | |
A reaction: A very nicely dramatic way of presenting what is taken to be the usual reading of the basic case - that the original identity tracks the continuity of the original structure, not the matter. |
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? |