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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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8430
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Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
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Full Idea:
The function of causal statements is 1) to explain events, 2) for predictive usefulness, 3) to help control events, 4) with agents, to attribute moral responsibility, 5) in physical theory. We should judge causal theories by how they account for these.
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From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.207)
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A reaction:
He suggests that Lewis's counterfactual theory won't do well on this test. I think the first one is what matters. Philosophy aims to understand, and that is achieved through explanation. Regularity and counterfactual theories explain very little.
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8429
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Counterfactuals can express four other relations between events, apart from causation [Kim]
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Full Idea:
Counterfactuals can express 'analytical' dependency, or the fact that one event is part of another, or an action done by doing another, or (most interestingly) an event can determine another without causally determining it.
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From:
Jaegwon Kim (Causes and Counterfactuals [1973], p.205)
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A reaction:
[Kim gives example of each case] Counterfactuals can even express a relation that involves no dependency. Or they might just involve redescription, as in 'If Scott were still alive, then the author of "Waverley" would be too'.
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4781
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Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]
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Full Idea:
Kim gives a range of examples of counterfactual dependence without causation, as: 'if yesterday wasn't Monday, today wouldn't be Tuesday', and 'if my sister had not given birth, I would not be an uncle'.
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From:
report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3
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A reaction:
This is aimed at David Lewis. The objection seems like commonsense. "If you blink, the cat gets it". Causal claims involve counterfactuals, but they are not definitive of what causation is.
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