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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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21547
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On Meinong's principles 'the existent round square' has to exist [Russell]
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Full Idea:
To my contention that, on his principles, 'the existent round square' exists, Meinong replies that it is existent but does not exist. I must confess that I see no difference between existing and being existent, and I have no more to say on this head.
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From:
Bertrand Russell (Review: Meinong 'Uber die Stellung...' [1907], p.93)
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A reaction:
Russell is obviously invoking the famously dubious ontological argument for God's existence. Normally impossible objects are rejected because of contradictions, but there might also be category mistakes. 'The slow square'.
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15314
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Faraday's single field of variable forces introduces a criterion of Unity into what is ultimate [Faraday, by Harré/Madden]
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Full Idea:
In Faraday lines of force picture the directional structure of powers,...so the fundamental entity is a single, unified field. ...A new criterion of the ultimate has stepped in: Unity. The universal field is still the final explanation, but not invariant.
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From:
report of Michael Faraday (Experimental Researches in Electricity [1859]) by Harré,R./Madden,E.H. - Causal Powers 9.II.B
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A reaction:
Almost Parmenides, except that the field is not invariant. But that was always the ancient objection to the One - that it offered no explanation of change.
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