15896
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Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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Full Idea:
Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
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From:
report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
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A reaction:
I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.
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20062
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If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm]
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Full Idea:
If someone wants to kill his uncle to inherit a fortune, and having this desire makes him so agitated that he loses control of his car and kills a pedestrian, who turns out to be his uncle, the conditions of the causal theory seem to be satisfied.
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From:
Roderick Chisholm (Freedom and Action [1966]), quoted by Rowland Stout - Action 6 'Deviant'
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A reaction:
This line of argument has undermined all sorts of causal theories that were fashionable in the 1960s and 70s. Explanation should lead to understanding, but a deviant causal chain doesn't explain the outcome. The causal theory can be tightened.
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20054
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There has to be a brain event which is not caused by another event, but by the agent [Chisholm]
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Full Idea:
There must be some event A, presumably some cerebral event, which is not caused by any other event, but by the agent.
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From:
Roderick Chisholm (Freedom and Action [1966], p.20), quoted by Rowland Stout - Action 4 'Agent'
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A reaction:
I'm afraid this thought strikes me as quaintly ridiculous. What kind of metaphysics can allow causation outside the natural nexus, yet occuring within the physical brain? This is a relic of religious dualism. Let it go.
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