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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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22489
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'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]
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Full Idea:
Geach puts 'good' in the class of attributive adjectives, such as 'large' and 'small', contrasting such adjectives with 'predicative' adjectives such as 'red'.
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From:
report of Peter Geach (Good and Evil [1956]) by Philippa Foot - Natural Goodness Intro
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A reaction:
[In Analysis 17, and 'Theories of Ethics' ed Foot] Thus any object can simply be red, but something can only be large or small 'for a rat' or 'for a car'. Hence nothing is just good, but always a good so-and-so. This is Aristotelian, and Foot loves it.
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