green numbers give full details | back to texts | unexpand these ideas
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. |
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. |