9626
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A structure is an abstraction, focussing on relationships, and ignoring other features [Shapiro]
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Full Idea:
A structure is the abstract form of a system, focussing on the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.
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From:
Stewart Shapiro (Structure and Ontology [1989], 146), quoted by James Robert Brown - Philosophy of Mathematics Ch.4
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A reaction:
I find this account very attractive, even though it appeals to supposedly outmoded psychological abstractionism. It seems pretty close to Aristotle's view of things. Shapiro's account must face up to Frege's worries about these matters.
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14014
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Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]
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Full Idea:
Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
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From:
Hermann Minkowski (Space and Time [1908], Intro)
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A reaction:
Notice the qualification that it is a 'kind of' union. Deep confusion arises from exaggerating the analogy between space and time. Craig Bourne remarks (2006:157) that this shows independence of measurement, not of reality
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