3 ideas
9355 | One sort of circularity presupposes a premise, the other presupposes a rule being used [Braithwaite, by Devitt] |
Full Idea: An argument is 'premise-circular' if it aims to establish a conclusion that is assumed as a premise of that very argument. An argument is 'rule-circular' if it aims to establish a conclusion that asserts the goodness of the rule used in that argument. | |
From: report of R.B. Braithwaite (Scientific Explanation [1953], p.274-8) by Michael Devitt - There is no a Priori §2 | |
A reaction: Rule circularity is the sort of thing Quine is always objecting to, but such circularities may be unavoidable, and even totally benign. All the good things in life form a mutually supporting team. |
18198 | Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine] |
Full Idea: The mathematics wanted for use in empirical sciences is for me on a par with the rest of science. Transfinite ramifications are on the same footing as simplifications, but anything further is on a par rather with uninterpreted systems, | |
From: Willard Quine (Review of Parsons (1983) [1984], p.788), quoted by Penelope Maddy - Naturalism in Mathematics II.2 | |
A reaction: The word 'uninterpreted' is the interesting one. Would mathematicians object if the philosophers graciously allowed them to continue with their transfinite work, as long as they signed something to say it was uninterpreted? |
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? |