Combining Texts

All the ideas for 'fragments/reports', 'Review of Bob Hale's 'Abstract Objects'' and 'Lecture on Applicability of Mathematics'

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4 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis

9184	We can't presume that all interesting concepts can be analysed [Williamson]
	Full Idea: We have no prior reason to suppose that philosophically significant concepts have interesting analyses into necessary and sufficient conditions.
	From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
	A reaction: We might think that they are either analysable or primitive, and that failure of analysis invites us to take a concept as primitive. But maybe God can analyse it and we can't.

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism

9183	Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
	Full Idea: The Fregean argument for platonism is that some true assertions contain singular terms which denote abstract objects if they denote anything; since the assertions are true, the singular terms denote.
	From: Timothy Williamson (Review of Bob Hale's 'Abstract Objects' [1988])
	A reaction: I am perplexed that anyone would rest their view of reality on such an argument. The obvious comparison would be with true remarks about blatantly fictional characters, or blatantly invented concepts such as 'checkmate'.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

8732	It is spooky the way mathematics anticipates physics [Weinberg]
	Full Idea: It is positively spooky how the physicist finds the mathematician has been there before him or her.
	From: Steven Weinberg (Lecture on Applicability of Mathematics [1986], p.725), quoted by Stewart Shapiro - Thinking About Mathematics 2.3
	A reaction: This suggests that mathematics might be the study of possibilities or hypotheticals, like mental rehearsals for physics. See Hellman's modal structuralism. Maybe mathematicians are reading the mind of God, but I doubt that.

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

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?