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.
|
9874
|
Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege]
|
|
Full Idea:
The contradiction in Frege's system is due to the presence of second-order quantification, ..and Frege's explanation of the second-order quantifier, unlike that which he provides for the first-order one, appears to be substitutional rather than objectual.
|
|
From:
comment on Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], §25) by Michael Dummett - Frege philosophy of mathematics Ch.17
|
|
A reaction:
In Idea 9871 Dummett adds the further point that Frege lacks a clear notion of the domain of quantification. At this stage I don't fully understand this idea, but it is clearly of significance, so I will return to it.
|
18252
|
Real numbers are ratios of quantities, such as lengths or masses [Frege]
|
|
Full Idea:
If 'number' is the referent of a numerical symbol, a real number is the same as a ratio of quantities. ...A length can have to another length the same ratio as a mass to another mass.
|
|
From:
Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893], III.1.73), quoted by Michael Dummett - Frege philosophy of mathematics 21 'Frege's'
|
|
A reaction:
This is part of a critique of Cantor and the Cauchy series approach. Interesting that Frege, who is in the platonist camp, is keen to connect the real numbers with natural phenomena. He is always keen to keep touch with the application of mathematics.
|
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.
|
9190
|
A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett]
|
|
Full Idea:
In later Frege, a concept could be taken as a particular case of a function, mapping every object on to one of the truth-values (T or F), according as to whether, as we should ordinarily say, that object fell under the concept or not.
|
|
From:
report of Gottlob Frege (Grundgesetze der Arithmetik 1 (Basic Laws) [1893]) by Michael Dummett - The Philosophy of Mathematics 3.5
|
|
A reaction:
As so often in these attempts at explanation, this sounds circular. You can't decide whether an object truly falls under a concept, if you haven't already got the concept. His troubles all arise (I say) because he scorns abstractionist accounts.
|
7903
|
The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
|
|
Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
|
|
From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
|
|
A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
|