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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14665
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We can call the quality of Plato 'Platonity', and say it is a quality which only he possesses [Boethius]
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Full Idea:
Let the incommunicable property of Plato be called 'Platonity'. For we can call this quality 'Platonity' by a fabricated word, in the way in which we call the quality of man 'humanity'. Therefore this Platonity is one man's alone - Plato's.
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From:
Boethius (Librium de interpretatione editio secunda [c.516], PL64 462d), quoted by Alvin Plantinga - Actualism and Possible Worlds 5
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A reaction:
Plantinga uses this idea to reinstate the old notion of a haecceity, to bestow unshakable identity on things. My interest in the quotation is that the most shocking confusions about properties arose long before the invention of set theory.
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