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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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6474
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Seeing is not in itself knowledge, but is separate from what is seen, such as a patch of colour [Russell]
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Full Idea:
Undeniably, knowledge comes through seeing, but it is a mistake to regard the mere seeing itself as knowledge; if we are so to regard it, we must distinguish the seeing from what is seen; a patch of colour is one thing, and our seeing it is another.
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From:
Bertrand Russell (The Analysis of Mind [1921], Lec. VIII)
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A reaction:
This is Russell's 1921 explanation of why he adopted sense-data (but he rejects them later in this paragraph). This gives a simplistic impression of what he intended, which has three components: the object, the 'sensibile', and the sense-datum.
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6476
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We cannot assume that the subject actually exists, so we cannot distinguish sensations from sense-data [Russell]
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Full Idea:
If we are to avoid a perfectly gratuitous assumption, we must dispense with the subject as one of the actual ingredients of the world; but when we do this, the possibility of distinguishing the sensation from the sense-datum vanishes.
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From:
Bertrand Russell (The Analysis of Mind [1921], Lec. VIII)
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A reaction:
This is the reason why Russell himself rejected sense-data. It is more normal, I think, to reject them simply as being superfluous. If the subject can simply perceive the sense-data, why can't they just perceive the object more directly?
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6475
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In perception, the self is just a logical fiction demanded by grammar [Russell]
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Full Idea:
In perception, the idea of the subject appears to be a logical fiction, like mathematical points and instants; it is introduced, not because observation reveals it, but because it is linguistically convenient and apparently demanded by grammar.
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From:
Bertrand Russell (The Analysis of Mind [1921], Lec. VIII)
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A reaction:
In 1912, Russell had felt that both the Cogito, and the experience of meta-thought, had confirmed the existence of a non-permanent ego, but here he offers a Humean rejection. His notion of a 'logical fiction' is behaviouristic. I believe in the Self.
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