Re: Skolem Again

William of Ockham wrote:

Chris Menzel wrote:

From the fact 
that a given interpretation of a theory makes all of its axioms true it
does not follow that it can properly be considered the theory's meaning.



But if grasp of meaning is grasp of truth-conditions, this is terribly
difficult to avoid.


May I irrupt with a little dialogue?

  Set-Semanticist: Ok, venerabilis inceptor,let us consider
the theory T1 given by just one axiom A1: \exists x P(x).
  Pseudo-Ockham: Not a big one...
  SS: Remember what posterity will attribute to you: 'Entia
non sunt multiplicanda', etc.
  PO: Placet, go on.
  SS: And now, would you be kind to give me a model for T1?
  PO: Of course! For example, consider M1 as follows: the
domain of T1 is the real world; the interpretation of P(x)
is "x is a good philosopher", as understood by common
English speakers. Since there are at least one object in
real world (for example, me) that falls inside the extension
of P(x), A1 is true in M1, hence M1 is a model of T1.
  SS: Terse exposition! Now I say that "Some people are not
good philosophers" is part of the meaning of T1.
  PO: Excuse me?
  SS: It is easily proven; in fact, is it true in M1, so
....'it is terribly difficult to avoid' that conclusion.
  PO: I haven't realized! Thanks!
  SS: You are welcome. Good look with your Ph.D.

.

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