Re: SUO: Re: SUOP Topic :> Definition Of Definition
That "paper" is actually an excerpt from Ch. 5 of my KR book.
I only gave a formal definition for formalized languages, such
as first-order logic, but the principle could be extended.
> I like your definition of "proposition". I look forward to
> reading your paper, in order to find out what you mean by
> "meaning-preserving". Something like "fluent speakers with
> respect to those sentences would assign the same truth-value
> to all of them" would be a necessary condition, I think,
> but not a sufficient one since it is an extensional criterion
> and the definiens is as intensional a term as they come.
Yes. Truth preserving is only a necessary criterion, but it
is too weak, as you observed. It is also too difficult to
enforce because it requires some way of checking truth,
which may require investigations that go beyond language.
My four criteria for preserving meaning are that a translation
must be invertible, proof preserving, vocabulary preserving,
and structure preserving.
Proof preserving (assuming sound rules of inference) is stricter
than truth preserving because it rules out equivalences that are
not provable. If two statements cannot be proved to be equivalent,
I would claim that there is a signicant difference in meaning.