Re: Simple yet Profound Metatheorem

On 16 Dec 2005 01:36:20 -0800, "sradhakr" <sradhakr@xxxxxxxxxx> wrote:

>
> *Any* proposition can be proven in intuitionistic logic if you start
> with the [assumption] P&~P.
>
No. That's false. But it is true that any proposition can be derived
as a /conclusion/ from the /premiss/ P & ~P.

Comment: Obviously you are not very familiar with systems
of natural deduction. There assumptions can be "discharged".
Hence the do not count as premisses of the final argument.

>
> The above "proof" is fundamentally flawed and *should not* be accepted
> as a valid proof of ~(P&~P).
>
Nonsense. The proof is completely valid.

>
> [...] What you could do is to make a straightforward, bald assertion
> of ~(P&~P) without claiming to prove it.
>
In logic we would call such a statement an /axiom/ then.

B u t we do not have to do that, since we can actually prove the
statement in the usual systems (calculi) of intuitionistic logic.
(See the other posts where several proofs in several different
systems [calculi] of intuitionistic logic have been posted.)


F.

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

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