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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9381
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If some inferences are needed to fix meaning, but we don't know which, they are all relevant [Fodor/Lepore, by Boghossian]
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Full Idea:
The Master Argument for linguistic holism is: Some of an expression's inferences are relevant to fixing its meaning; there is no way to distinguish the inferences that are constitutive (from Quine); so all inferences are relevant to fixing meaning.
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From:
report of J Fodor / E Lepore (Holism: a Shopper's Guide [1993], §III) by Paul Boghossian - Analyticity Reconsidered
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A reaction:
This would only be if you thought that the pattern of inferences is what fixes the meanings, but how can you derive inferences before you have meanings? The underlying language of thought generates the inferences? Meanings are involved!
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7071
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Life and rationality are pointless if we can only contemplate the freedom of our own ego [Jacobi]
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Full Idea:
If the highest upon which I can reflect, what I can contemplate, is my empty and pure, naked and mere ego, with its autonomy and freedom: then rational self-contemplation, then rationality is for me a curse - I deplore my existence.
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From:
Friedrich Jacobi (Letters to Fichte [1799], Ch.2), quoted by Simon Critchley - Continental Philosophy - V. Short Intro
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A reaction:
This is a rebellion against Fichte's interpretation of Kant. It is a lovely cry from the heart on behalf of everyone who resents lines of philosophical thinking that seem to imprison the mind and cut us off from the ordinary world and real life.
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