Re: Help with a problem

On 24 Nov 2005 14:13:18 -0800, "George Dance" <georgedance04@xxxxxxxx>
wrote:

> >
> > Throw the rule book at 'em. [...]
> >
> > Those should suffice for
> > |- p v ~p
> > as was shown in previous post.
> >
> I wouldn't argue that they're insufficient to prove anything.
>
That's a rather good idea. Since they are sufficient to prove *every*
valid formula of propositional logic.

>
> But I'd question the idea that those are 'the' rules of natural deduction.
>
Actually, they are. Those are essentially the rules introduced by
Gentzen (the -or one- inventor of ND).

>
> They're the rules of one system of nd; but there are many sound and
> complete nd systems, just as there are many sound and complete
> axiomatic systems.
>
In a certain sense t h i s set of rules is distinguished:

"The claim that the essential deductive operations have been isolated
[in Gentzen's calculi] is not to be understood as the claim that these
operations mirror all informal deductive practices, which would be an
unreasonable demand in view of the fact that informal practices may
sometimes contain logically insignificant irregularities. What is
claimed is that the essential logical content of intuitive logical
operations that can be formulated in the language considered can be
understood as composed of the atomic inferences isolated by Gentzen.
It is in this sense that we may understand the terminology _natural_
deduction."

(Prawitz)


F.

--
"I do tend to feel Hughes & Cresswell is a more authoritative
source than you." (D. Ullrich)
.