[FOM] The Lucas-Penrose Thesis vs The Turing Thesis

joeshipman@aol.com joeshipman at aol.com
Sun Oct 8 16:41:42 EDT 2006

 -----Original Message-----
 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 
set-theoretical sentences.)

 -- JS

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