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Ideas for 'Philosophy of Mathematics', 'Popular Scientific Lectures' and 'Intuitionism: an Introduction'

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2 ideas

9. Objects / A. Existence of Objects / 1. Physical Objects

10272	The notion of 'object' is at least partially structural and mathematical [Shapiro]
	Full Idea: The very notion of 'object' is at least partially structural and mathematical.
	From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.1)
	A reaction: [In the context, Shapiro clearly has physical objects in mind] This view seems to fit with Russell's 'relational' view of the physical world, though Russell rejected structuralism in mathematics. I take abstraction to be part of perception.

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects

10275	A blurry border is still a border [Shapiro]
	Full Idea: A blurry border is still a border.
	From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.3)
	A reaction: This remark deserves to be quoted in almost every area of philosophy, against those who attack a concept by focusing on its vague edges. Philosophers should focus on central cases, not borderline cases (though the latter may be of interest).