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10203 | We apprehend small, finite mathematical structures by abstraction from patterns [Shapiro] |
Full Idea: The epistemological account of mathematical structures depends on the size and complexity of the structure, but small, finite structures are apprehended through abstraction via simple pattern recognition. | |
From: Stewart Shapiro (Philosophy of Mathematics [1997], Intro) | |
A reaction: Yes! This I take to be the reason why John Stuart Mill was not a fool in his discussion of the pebbles. Successive abstractions (and fictions) will then get you to more complex structures. |