Re: If (P & ~P) -> Q is not derivable then Goedel's formula is not derivable


Newberry wrote:
Confutus wrote:
Newberry wrote:
Confutus wrote:
If you aren't going to accept the classical Tertaim non Datur in
either of its forms, (P v ~P) or ~(P & ~P), you might as well face
this excluded middle squarely, name it, symbolize it, and then
explore, understand, and accept the consequences rather than sskirt
around it.

This is in fact exactly what he has done;
he has just added "x means unknown" as a third/middle
value to all his truth-tables, which might as well therefore
be called ignorance-tables, since he insists that x must mean
that we are ignorant of which of the other 2 values is really
happening (obviously, it needn't mean that, or anything).

Newbery replied:
Well, I am not sure what the equivalence of (~P v Q) with (P -> Q) has
to do with excluded middle.

Excluded middle is (TALK about lack of self-awareness) relevant to
Newberry's whole treatment of all these issues simply because he
is REFUSING to exclude the middle.

In the meantime let me give you a third
answer to your question:

3) Q is not relevant to the conclusion that (P v ~P) v Q is a
tautology. (Please se my reply to R. Srinivasan.) Then (P v ~P) v Q is
not an o-relevant tautology.

You had to re-include the formerly excluded middle, in order to
conclude that.

If you define P ->Q as ~P v Q then
obviously (P & ~P) -> Q is not an o-relevant tautology either.

But that conclusion, via the equivalence, now depends on your
having not excluded the middle. THAT'S what they have to do with
each other. YOU ARE USING both of them. It's YOUR fault.

In summary, the notion of o-relevance automatically takes care of the
paradoxes of material implication.

Which, again obviously, ARE NOT paradoxical.

Rejection of the excluded middle principle implies a multi-valued
logic.

***. *2* values ALREADY constitute MULTIPLE values.
Going from 2 to 3 is not a big deal.

So the question is if it can be justified and what the third,
fourth ... value should be.

You're being a complete idiot.
THERE IS NO question, at least not FOR YOU.
The third value IS "x" and you have ALREADY BEEN
publishing AND CHAMPIONING truth-tables for it.

.