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Topic: Matheology § 220
Replies: 1   Last Post: Feb 13, 2013 11:21 AM

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Posts: 18,076
Registered: 1/29/05
Matheology § 220
Posted: Feb 13, 2013 9:29 AM
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Matheology § 220

PA {{Peano-Arithmetik}} already tells us that the universe is
infinite, but PA ?stops? after we have all the natural numbers. {{No,
Peano arithmetics never stops because it never reaches an end. Here
potential and actual infinity are confused.}} ZFC goes beyond the
natural numbers; in ZFC we can distinguish different infinite
cardinalities such as ?countable? and ?uncountable?, and we can show
that there are infinitely many cardinalities, uncountably many, etc.
{{and we can show that there is nothing of that kind other than in
dreams, but not in logic.}}
[Saharon Shelah: "Logical Dreams" (2002)]

Regards, WM

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