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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11214
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We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
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Full Idea:
The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
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From:
Ian Rumfitt ("Yes" and "No" [2000], IV)
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A reaction:
[compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).
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15314
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Faraday's single field of variable forces introduces a criterion of Unity into what is ultimate [Faraday, by Harré/Madden]
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Full Idea:
In Faraday lines of force picture the directional structure of powers,...so the fundamental entity is a single, unified field. ...A new criterion of the ultimate has stepped in: Unity. The universal field is still the final explanation, but not invariant.
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From:
report of Michael Faraday (Experimental Researches in Electricity [1859]) by Harré,R./Madden,E.H. - Causal Powers 9.II.B
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A reaction:
Almost Parmenides, except that the field is not invariant. But that was always the ancient objection to the One - that it offered no explanation of change.
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