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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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23794
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Some representational states, like perception, may be nonconceptual [Evans, by Schulte]
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Full Idea:
Evans introduced the idea that there are some representational states, for example perceptual experiences, which have content that is nonconceptual.
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From:
report of Gareth Evans (The Varieties of Reference [1980]) by Peter Schulte - Mental Content 3.4
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A reaction:
McDowell famously disagree, and whether all experience is inherently conceptualised is a main debate from that period. Hard to see how it could be settled, but I incline to McDowell, because minimal perception hardly counts as 'experience'.
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16366
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The Generality Constraint says if you can think a predicate you can apply it to anything [Evans]
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Full Idea:
If a subject can be credited with the thought that a is F, then he must have the conceptual resources for entertaining the thought that a is G, for every property of being G of which he has conception. This condition I call the 'Generality Constraint'.
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From:
Gareth Evans (The Varieties of Reference [1980], p.104), quoted by François Recanati - Mental Files 5.3
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A reaction:
Recanati endorses the Constraint in his account of mental files. Apparently if I can entertain the thought of a circle being round, I can also entertain the thought of it being square, so I am not too sure about this one.
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