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18244
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I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
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Full Idea:
Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.
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From:
Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4
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A reaction:
Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.
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14712
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A sentence is a priori if no possible way the world might actually be could make it false [Chalmers]
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Full Idea:
The Core Thesis for rationalist 2D semantics is that for any sentence S, S is apriori iff S has a necessary 1-intension. (That is, there is no possible way the world might be that, if it actually obtained, would make S false).
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From:
David J.Chalmers (Epistemic Two-Dimensional Semantics [2004], p.165), quoted by Laura Schroeter - Two-Dimensional Semantics 2.3.2
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A reaction:
[The parenthesis is by Schroeter] A '1-intension' is defined by a diagonal on a 2D semantic matrix. Chalmers defends conceivability as the guide to possibility. This is a very traditional view of the a priori, expressed in modern terms.
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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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