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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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2537
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Types are properties, and tokens are events. Are they split between mental and physical, or not? [Sturgeon]
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Full Idea:
The question is whether mental and physical types (which are properties) are distinct, and whether mental and physical tokens (which are events) are distinct.
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From:
Scott Sturgeon (Matters of Mind [2000], Intro)
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A reaction:
Helpful. While the first one gives us the rather dodgy notion of 'property dualism', the second one seems to imply Cartesian dualism, if the events really are distinct. It seems to me that thought is an aspect of brain events, not a distinct event.
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2535
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The main argument for physicalism is its simple account of causation [Sturgeon]
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Full Idea:
The dominant empirical argument for physicalism is the Overdetermination Argument: physics is closed and complete, mind is causally efficacious, the world isn't choc-full of overdetermination, so the mind is physical as well.
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From:
Scott Sturgeon (Matters of Mind [2000], Intro)
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A reaction:
I find this argument utterly convincing. The idea that there is only one thing which is outside the interconnected causal nexus which seems to constitute the rest of reality, and that is a piece of meat inside our heads, strikes me as totally ridiculous.
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5994
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Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]
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Full Idea:
The four major disputes in classical cosmology were whether the cosmos is 'open' or 'closed', whether it is explained mechanistically or teleologically, whether it is alive or mere matter, and whether or not it has a beginning.
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From:
report of T.M. Robinson (Classical Cosmology (frags) [1997]) by PG - Db (ideas)
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A reaction:
A nice summary. The standard modern view is closed, mechanistic, inanimate and non-eternal. But philosophers can ask deeper questions than physicists, and I say we are entitled to speculate when the evidence runs out.
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