[Wittrs] !!!Re: Re: Metaphysical Versus Mystical
- From: "jrstern" <jrstern@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Thu, 14 Jan 2010 01:51:43 -0000
--- In Wittrs@xxxxxxxxxxxxxxx, "J D" <wittrsamr@...> wrote:
>
> > It is even harder to square statements like:
> >
> > 6.1265 It is always possible to construe logic in such a
> > way that every proposition is its own proof.
> >
> > ... with logic after Godel and Turing.
>
> The scope of "logic" in TLP may not be clear on this point. If he is
> describing the propositional calculus, then what Godel and Turing have to say
> about second and higher orders of the predicate calculus would be irrelevant.
Sure, but by what principle would one separate out only first-order statements?
But I don't think that's quite the direction that Wittgenstein would (did)
take.
...
> 6.127 All the propositions of logic are of equal status: it is not
> the case that some of them are essentially derived propositions.
> Every tautology itself shows that it is a tautology.
This is interesting. I have problems with it, serious problems, but
first let's see what is good about it (and related TLP points).
Even here as early as the TLP, we see Wittgenstein starting to avoid "method".
Not all method, to be sure, as TLP *is* method, which the
later Wittgenstein had to give up for consistency sake, I guess.
My take on this is per the linguistic turn, in that Wittgenstein
would not see individual statements as the kind of thing that one
either derives or proves, and certainly not in any way that depends
on others (what is the Quine quote, "our statements about the external world
face the tribunal of sense experience not individually but only as a corporate
body", none of that "corporate" stuff
for Wittgenstein).
Wittgenstein took this same approach contra Godel and Turing, or at
least that's (my interpretation of) Shanker's description: "so there
is one statement (or class of statements) that cannot be proven - so what?" I
have a lot of sympathy for this, btw. However, in general,
it seems most people do not. And it may not be pertinent to the
question.
Because then we come up to Turing and computing. I find it very
hard to look at a computer program in execution and say that nothing
there is a derived proposition. While a number of these TLP
statements support each other, I'm afraid that they are very
problematical when one considers computation - or even the process
of mathematical proof as Wittgenstein reviews in RFM.
Josh
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