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17697
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The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
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Full Idea:
The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
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From:
David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
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A reaction:
Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.
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14629
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If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
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Full Idea:
If we ask why A must be the case, and A is then proved from B, that explains it if B must be so. If the eventual source cites some truth F, then if F just is so, there is strong pressure to feel that the original necessity has not been explained.
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From:
Simon Blackburn (Morals and Modals [1987], 1)
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A reaction:
[compressed] Ross Cameron wrote a reply to this which I like. I'm fishing for the idea that essence is the source of necessity (as Kit Fine says), but that essence itself is not necessary (as only I say, apparently!).
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14529
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If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
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Full Idea:
Blackburn asks of what theorists propose as underlying the necessity of a proposition, the question whether they themselves are conceived as obtaining of necessity or merely contingently.
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From:
report of Simon Blackburn (Morals and Modals [1987], p.120-1) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 1
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A reaction:
I've seen a reply to this somewhere: I think the thought was that a necessity wouldn't be any less necessary if it had a contingent source, any more than the father of a world champion boxer has to be a world champion boxer.
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