[C] [Wittrs] !!!Re: Re: Metaphysical Versus Mystical
- From: "J D" <ubersicht@xxxxxxxxx>
- To: wittrsamr@xxxxxxxxxxxxx
- Date: Thu, 14 Jan 2010 00:37:59 -0000
JRS.
> 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.
And his point concerns the method of truth tables and of demonstrating the
truth of a tautology by inspection rather than by deriving it from logical
axioms such as the law of the excluded middle, De Morgan's laws, or what have
you.
Of course, higher orders of the predicate calculus are now accepted as part of
standard definitions of "logic", and on that reading 6.1265 would be more
problematic.
Consider what precedes and follows:
6.1262 Proof in logic is merely a mechanical expedient to facilitate the
recognition of tautologies in complicated cases.
6.1263 Indeed, it would be altogether too remarkable if a proposition that
had sense could be proved logically from others, and so too could a logical
proposition. It is clear from the start that a logical proof of a
proposition that has sense and a proof in logic must be two entirely
different things.
6.1264 A proposition that has sense states something, which is shown by its
proof to be so. In logic every proposition is the form of a proof. Every
proposition of logic is a modus ponens represented in signs. (And one
cannot express the modus ponens by means of a proposition.)
6.1265 It is always possible to construe logic in such a way that every
proposition is its own proof.
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.
JPDeMouy
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