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All the ideas for 'Causes and Counterfactuals', 'Realism, Mathematics and Modality' and 'works'

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8 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

15941	For intuitionists excluded middle is an outdated historical convention [Brouwer]
	Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth.
	From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2
	A reaction: [Brouwer 1952:510-11]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy

18247	Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]
	Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities.
	From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6
	A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer.

6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics

8714	Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H]
	Full Idea: The fictionalist can say that the sense in which '2+2=4' is true is pretty much the same as the sense in which 'Oliver Twist lived in London' is true. They are true 'according to a well-known story', or 'according to standard mathematics'.
	From: Hartry Field (Realism, Mathematics and Modality [1989], 1.1.1), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 6.3
	A reaction: The roots of this idea are in Carnap. Fictionalism strikes me as brilliant, but poisonous in large doses. Novels can aspire to artistic truth, or to documentary truth. We invent a fiction, and nudge it slowly towards reality.

26. Natural Theory / C. Causation / 1. Causation

8430	Causal statements are used to explain, to predict, to control, to attribute responsibility, and in theories [Kim]
	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.
	From: Jaegwon Kim (Causes and Counterfactuals [1973], p.207)
	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.

26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation

8396	Many counterfactuals have nothing to do with causation [Kim, by Tooley]
	Full Idea: Kim has pointed out that there are a number of counterfactuals that have nothing to do with causation. If John marries Mary, then if John had not existed he would not have married Mary, but that is not the cause of their union.
	From: report of Jaegwon Kim (Causes and Counterfactuals [1973], 5.2) by Michael Tooley - Causation and Supervenience
	A reaction: One might not think that this mattered, but it leaves the problem of distinguishing between the causal counterfactuals and the rest (and you mustn't mention causation when you are doing it!).

8429	Counterfactuals can express four other relations between events, apart from causation [Kim]
	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.
	From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205)
	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'.

8428	Causation is not the only dependency relation expressed by counterfactuals [Kim]
	Full Idea: The sort of dependency expressed by counterfactual relations is considerably broader than strictly causal dependency, and causal dependency is only one among the heterogeneous group of dependency relationships counterfactuals can express.
	From: Jaegwon Kim (Causes and Counterfactuals [1973], p.205)
	A reaction: In 'If pigs could fly, one and one still wouldn't make three' there isn't even a dependency. Kim has opened up lines of criticism which make the counterfactual analysis of causation look very implausible to me.

26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims

4781	Many counterfactual truths do not imply causation ('if yesterday wasn't Monday, it isn't Tuesday') [Kim, by Psillos]
	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'.
	From: report of Jaegwon Kim (Causes and Counterfactuals [1973]) by Stathis Psillos - Causation and Explanation §3.3
	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.