9390
|
Logic guides thinking, but it isn't a substitute for it [Rumfitt]
|
|
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.
|
9226
|
If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
|
|
Full Idea:
Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects.
|
|
From:
Hartry Field (Recent Debates on the A Priori [2005], 7)
|
|
A reaction:
For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect.
|
9389
|
Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
|
|
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.
|