[FOM] Axiomatic Syntax

[Torkel Franzen]

Arnon Avron says:

  >The two might be equivalent in PA, but
  >self-reference is not a property that is preserved by equivalence in PA
  >(well, to my opinion it is not a property that a sentence of PA
  >can possibly have, so I am talking myself on a rather semi-intuitive,
  >vague level).

  A general characterization of reference in an intensional sense for
statements in the language of PA is hardly to be expected. There is
nothing special about self-referential statements in this regard.
How would you propose to characterize the statements of PA expressing
"Every natural number has a unique prime decomposition", keeping in
mind that a representation of finite sequences of numbers as numbers
must be used in expressing this in the language of PA? I think your
various misgivings would become clearer if stated in terms that do
involve the business of self-reference.

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Torkel Franzen