5 ideas
13418 | The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C] |
Full Idea: The difficulties historically attributed to the axiom of choice are probably better ascribed to the law of excluded middle. | |
From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
A reaction: The law of excluded middle was a target for the intuitionists, so presumably the debate went off in that direction. |
13419 | If functions are transfinite objects, finitists can have no conception of them [Parsons,C] |
Full Idea: The finitist may have no conception of function, because functions are transfinite objects. | |
From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §4) | |
A reaction: He is offering a view of Tait's. Above my pay scale, but it sounds like a powerful objection to the finitist view. Maybe there is a finitist account of functions that could be given? |
13417 | If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C] |
Full Idea: If experience shows that some aspect of the physical world fails to instantiate a certain mathematical structure, one will modify the theory by sustituting a different structure, while the original structure doesn't lose its status as part of mathematics. | |
From: Charles Parsons (Review of Tait 'Provenance of Pure Reason' [2009], §2) | |
A reaction: This seems to be a beautifully simple and powerful objection to the Quinean idea that mathematics somehow only gets its authority from physics. It looked like a daft view to begin with, of course. |
18545 | The disinterested attitude of the judge is the hallmark of a judgement of beauty [Shaftesbury, by Scruton] |
Full Idea: Shaftesbury explained the peculiar features of the judgement of beauty in terms of the disinterested attitude of the judge. | |
From: report of 3rd Earl of Shaftesbury (Characteristics [1711]) by Roger Scruton - Beauty: a very short introduction 1 | |
A reaction: Good. I take our vocabulary to mark a distinction between expressions of subjective preference, and expressions of what aspire to be objective facts. 'I love this' versus 'this is good or beautiful'. |
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? |