[FOM] The Lucas-Penrose Thesis vs The Turing Thesis
joeshipman at aol.com
Sun Oct 8 16:41:42 EDT 2006
From: jmc at steam.Stanford.EDU
Many worlds is not so exotic that a split might include
Pythagoras's theorem one way and its negation the other.
No, but it might, for example, result in one world where the axiom of a
real-valued measurable cardinal is accepted as "true" (along with its
arithmetical consequences such as Con(ZFC) and its higher-order
consequences such as ~CH), and a different, incompatible world where
CH, or "every set is accessible", or V=L, or even "every set is
strongly constructible" (which I discuss here :
), was a basic axiom.
I find it extremely hard to imagine alternate developments of
mathematics which disagree about any *arithmetical* sentences, though.
(Which means I might want to modify my earlier definition of "human
mathematics", resticting to arithmetical sentences rather than
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