Ideas from 'The Logic of Boundaryless Concepts' by Ian Rumfitt [2007], by Theme Structure

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5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

9390	Logic guides thinking, but it isn't a substitute for it

			Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking.
			From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13)
			A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy.

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects

9389	Vague membership of sets is possible if the set is defined by its concept, not its members

			Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
			From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
			A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.