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13416
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Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C]
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Full Idea:
The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true.
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From:
report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2
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A reaction:
This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks.
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21378
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We clearly feel responsible for our deeds, because we are quite certain that we did them [Schopenhauer]
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Full Idea:
Another fact of consciousness ...is the wholly clear and certain feeling of responsibility for what we do, of the accountability of our actions, which rests on the unshakable certainty that we ourselves are the doers of our deeds.
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From:
Arthur Schopenhauer (On the Freedom of the Will [1841], p.93-4), quoted by Christopher Janaway - Schopenhauer 7 'Freedom'
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A reaction:
The point is that we have this feeling even if we do not believe in free will. I am struck by the fact that responsibility is very obvious in our own case, even if it is not when we objectively consider other people. Even villains can feel guilty.
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