14305
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In the truth-functional account a burnt-up match was soluble because it never entered water [Carnap]
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Full Idea:
If a wooden match was completely burned up yesterday, and never placed in water at any time, is it not the case, therefore, that the match is soluble (in the truth-functional view). This follows just from the antecedent being false.
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From:
Rudolph Carnap (Testability and Meaning [1937], I.440), quoted by Stephen Mumford - Dispositions
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A reaction:
This, along with Edgington's nice example of the conditional command (Idea ) seems conclusive against the truth-functional account. The only defence possible is some sort of pragmatic account about implicature.
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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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