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17807
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To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry]
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Full Idea:
In the study of formal systems we do not confine ourselves to the derivation of elementary propositions step by step. Rather we take the system, defined by its primitive frame, as datum, and then study it by any means at our command.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The formalist')
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A reaction:
This is what may potentially lead to an essentialist view of such things. Focusing on bricks gives formalism, focusing on buildings gives essentialism.
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17806
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It is untenable that mathematics is general physical truths, because it needs infinity [Curry]
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Full Idea:
According to realism, mathematical propositions express the most general properties of our physical environment. This is the primitive view of mathematics, yet on account of the essential role played by infinity in mathematics, it is untenable today.
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From:
Haskell B. Curry (Remarks on the definition and nature of mathematics [1954], 'The problem')
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A reaction:
I resist this view, because Curry's view seems to imply a mad metaphysics. Hilbert resisted the role of the infinite in essential mathematics. If the physical world includes its possibilities, that might do the job. Hellman on structuralism?
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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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