Re: Recursivity vs. Provability

Babylonian wrote:
> Charlie-Boo wrote:
> >
> > But there are properties of truth that hold for all models, e.g. if
P
> > is true then ~P is false. These we can rely on.
> >
> > I had considered also asking the question of what general
properties
> of
> > truth are there, and can we show the relationships among them, but
> > didn't want to mix the 2 questions. However, now that I have, here
> are
> > a few:
> >
> > 1. If P is true then ~P is false.
> > 2. If P is false then ~P is true.
> > 3. P has the same value as ~~P.
> > 4. P is either true or false.
> > 5. P is not both true and false.

> Not all of these are the case in some multi-valued formal logics, or
> even informal intuitionist logic.

They also do not hold for CB2-Logic (unpublished) in which ~TRUE is
TRUE. But that is not a reflection of the real world use of the
notions of truth and falsity.

(This is an example of misuse of references - the case where we try to
redefine an existing concept because someone wrote about such. The
solution is to clearly label the work as being something else.

For example, it was recently claimed here that certain authors produced
a proof but had to first redefine what the word "proof" means.
Earlier, someone claimed that a Turing Machine can both halt yes and
halt no because someone redefined what "Turing Machine" means.)

C-B

.

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