[hist-analytic] What do we need to represent syntax? was: Clarity Is Not Enough
steve bayne
baynesrb at yahoo.com
Tue Feb 24 15:10:49 EST 2009
Prof. Grandy is absolutely right to correct the impression I
may have made in pursuing the Godel theorems. What I had to
say was far less interesting than his following remark:
"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."
I have a small question here. We all remember Russell's Introduction
to the Tractatus, wherein Russell brings up the idea of levels of
languages that dispense with Wittgenstein's notion of showing. Prof.
Grandy accepts the basic strategy now widespread of Tarski and
Carnap, and those who followed. My question is this: suppose that an
analysis of syntax can only take place in M. That leaves an unanalyzed
notion of syntax, that of M itself. So no matter how high up the
hierarchy we go the analysis given is always given in a syntax
that, by Wittgenstein's lights (circa 1922) could only be shown
not "said."
Now if logic is not to have an ontology does this make a difference?
Suppose we say, following early Wittgenstein, that the logical form
of the world is shown and that somehow this is indicated by the
structure of an "ideal" language. If so, then quantification would
not provide a criterion of ontological commitment since any ontological
commitment on the part of M could only be shown; no existential,
even over concatenated expressions being given. One other question.
When we give a syntactical metalanguage what is the status of objects.
In Tarski's original paper, no individual constants are present. Is
this significant? In any case, thanks to Prof. Grandy for his
concise and informed reply.
Regards
STeve
--- On Tue, 2/24/09, Richard Grandy <rgrandy at rice.edu> wrote:
From: Richard Grandy <rgrandy at rice.edu>
Subject: What do we need to represent syntax? was: Clarity Is Not Enough
To: hist-analytic at simplelists.com, baynesrb at yahoo.com
Date: Tuesday, February 24, 2009, 3:03 PM
What do we need to represent syntax? was: Clarity
Is NotIt 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.
Richard
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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