[hist-analytic] What do we need to represent syntax? was: Clarity Is Not Enough
rgrandy at rice.edu
Tue Feb 24 15:03:03 EST 2009
It may be natural or habitual to think about ontology or domains of
discourse in this context, but if we are analyzing what is required
we need to think more carefully.
Godel's theorem for any specific system is strictly a proof theoretic
result, no models or domains required, thank you. "If S is omega
consistent neither G or ~G is provable in S"
Godel's generalized theorem ("For any formal system S ....")
requires recursion theory or something equivalent to give a precise
definition of "formal". Again no models or domains required.
I know that Godel's theorem was probably not what Steve had in mind,
but is the crispest example, and I don't see offhand why more is
needed for his purposes (e.g., measuring redundancy).
To put it more directly, I am arguing that what is required for a
metalanguage M to provide resources to analyze the syntax of language
L is that the syntax of M can represent the syntax of L.
Raised by proof-theoreticians and recursion theorists on the East
Coast, though later persuaded (during time on the sunny West Coast)
that model theory has its virtues)
>I'm pretty sure I get what you are talking about w.r.t
>the metalanguage stuff. But take this fragment:
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