[FOM] Re: Godel's Theorems

Torkel Franzen torkel at sm.luth.se
Thu May 1 01:12:28 EDT 2003

V. Kanovei says:

  >The answer depends on the meaning of "true sentence". 
  >If this means: "a sentence provable in ZFC" then {*) is as 
  >established as any mathematical theorem.
  >If this refers to something external with respect to 
  >the system of mathematical proofs, for instance, to the 
  >"standard model of PA" as a phenomenon of physical existence, 
  >then (*) should be considered as a physical law, that is, in 
  >principle, a subject of change and amendments.

  These are strange alternatives. How would you interpret "If T
is consistent, then the Godel sentence for T is true" in a case
where we have no idea whether or not T is consistent?

Torkel Franzen

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