FOM: truth and provability

[Torkel Franzen]

Randall Holmes says:


  >I have a feeling that Kanovei is actually disputing this much more
  >dubious assertion:
  >There is a sentence expressible in mathematical notation which is true
 >(in some metaphysical sense) and not provable (in _any_ mathematical
 >system).
  >It is perfectly possible to dispute this assertion (which is not a 
  >consequence of Godel's theorem).
  >Any comments from any of the parties to the discussion?

  I had a comment on this in an earlier message, which didn't appear
on the list:


  V.Kanovei says:

  >The only sound ontological meaning of the Goedel theorem is 
  >that there is no theory (of certain kind) which is both 
  >complete and consistent. The misinterpretation of it claims 
  >that there exist (ontologically) sentences which are true 
  >(ontologically) but not provable (mathematically) -- this 
  >misthesis was expressed by several contributors to this list. 

  Although this is indeed a misconception which is often encountered,
I don't believe it has been expressed by any contributor to the list.
Rather, what has been said is that Godel's theorem shows that there
is, for any consistent extension T of PA (say), a true arithmetical
statement which is not provable in T. Indeed you yourself assented
to this, as you must, since it is a mathematical theorem. However,
it seems you wish to underline that we must not in this theorem
understand "true" in the sense of "ontologically true". As far as
I can see, your strictures in this regard have nothing in particular
to do with Godel's theorem, but apply to anything we say in or about
arithmetic. 

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Torkel Franzen