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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17643
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Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam]
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Full Idea:
Relative to the description 'that statue', a certain shape is an essential property of the object; relative to the description 'that piece of clay', the shape not an essential property (but being clay is).
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From:
Hilary Putnam (Why there isn't a ready-made world [1981], 'Intro')
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A reaction:
Relative to the description 'that loathsome object', is the statue essentially loathsome? Asserting the essence of an object is a response to the object, not a response to a description of it. This is not the solution to the statue problem.
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17642
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The old view that sense data are independent of mind is quite dotty [Putnam]
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Full Idea:
Moore and Russell held the strange view that 'sensibilia' (sense data) are mind-independent entities: a view so dotty, on the face of it, that few analytic philosophers like to be reminded that this is how analytic philosophy started.
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From:
Hilary Putnam (Why there isn't a ready-made world [1981], 'Intro')
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A reaction:
I suspect the view was influenced by the anti-psychologism of Frege, and his idea that all the other concepts are mind-independent, living by their own rules in a 'third realm'. Personally I think analytic philosophy needs more psychology, not less.
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7667
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There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin]
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Full Idea:
Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius.
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From:
report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism
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A reaction:
This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny.
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