8660
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There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
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Full Idea:
Aristotle developed his own distinction between potential infinity (never running out) and actual infinity (there being a collection of an actual infinite number of things, such as places, times, objects). He decided that actual infinity was incoherent.
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From:
report of Aristotle (works [c.330 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 1.3
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A reaction:
Friend argues, plausibly, that this won't do, since potential infinity doesn't make much sense if there is not an actual infinity of things to supply the demand. It seems to just illustrate how boggling and uncongenial infinity was to Aristotle.
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8404
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Explain single events by general rules, or vice versa, or probability explains both, or they are unconnected [Field,H]
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Full Idea:
Some think singular causal claims should be explained in terms of general causal claims; some think the order should be reversed; some think a third thing (e.g. objective probability) will explain both; and some think they are only loosely connected.
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From:
Hartry Field (Causation in a Physical World [2003], 2)
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A reaction:
I think Ducasse gives the best account, which is the second option, of giving singular causal claims priority. Probability (Mellor) strikes me as a non-starter, and the idea that they are fairly independent seems rather implausible.
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8401
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Physical laws are largely time-symmetric, so they make a poor basis for directional causation [Field,H]
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Full Idea:
It is sometimes pointed out that (perhaps with a few minor exceptions) the fundamental physical laws are completely time-symmetric. If so, then if one is inclined to found causation on fundamental physical law, it isn't evident how directionality gets in.
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From:
Hartry Field (Causation in a Physical World [2003], 1)
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A reaction:
All my instincts tell me that causation is more fundamental than laws, and that directionality is there at the start. That, though, raises the nice question of how, if causation explains laws, the direction eventually gets left OUT!
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8402
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The only reason for adding the notion of 'cause' to fundamental physics is directionality [Field,H]
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Full Idea:
Although it is true that the notion of 'cause' is not needed in fundamental physics, even statistical physics, still directionality considerations don't preclude this notion from being consistently added to fundamental physics.
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From:
Hartry Field (Causation in a Physical World [2003], 1)
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A reaction:
This only makes sense if the notion of cause already has directionality built into it, which I think is correct. The physicist might reply that they don't care about directionality, but the whole idea of an experiment seems to depend on it (Idea 8363).
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