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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. |
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). |