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From: George Greene on 9 Jun 2010 21:50

> George Greene <gree...(a)email.unc.edu> writes:
> > Is Charlie EVEN REMOTELY QUALIFIED to be presenting such an
> > explanation?!?!?

On Jun 8, 9:21 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Surely he's eminently qualified to explain what he personally means by
> whatever technical terms he introduces into the discussion.

He may be OBLIGATED to so explain but that does NOT make him
ABLE, let ALONE qualified! Your statement here is factually refuted
by
the record. If by some miracle he possessed such intellectual
qualifications,
he has certainly done an excellent job of hiding them. And almost
NObody EVER GETS
to INTRODUCE a term IN ANY case!!! Almost EVERY term you could THINK
of TO use
has ALREADY BEEN USED (coherently) BY SOMEBODY ELSE ALREADY!

"Countable" and "covers" and "consists of" DO NOT mean precisely what
YOU or I or
C-B or WM may SAY that they mean! They mean what THEY already/always
HAVE meant,
DESPITE what the clueless are trying to say!
From: George Greene on 9 Jun 2010 21:54
On Jun 9, 9:50 pm, George Greene <gree...(a)email.unc.edu> wrote:
> > George Greene <gree...(a)email.unc.edu> writes:
> > > Is Charlie EVEN REMOTELY QUALIFIED to be presenting such an
> > > explanation?!?!?
>
> On Jun 8, 9:21 pm, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
>
> > Surely he's eminently qualified to explain what he personally means by
> > whatever technical terms he introduces into the discussion.
>
> He may be OBLIGATED to so explain but that does NOT make him
> ABLE, let ALONE qualified!  Your statement here is factually refuted
> by
> the record.  If by some miracle he possessed such intellectual
> qualifications,
> he has certainly done an excellent job of hiding them.  And almost
> NObody EVER GETS
> to INTRODUCE a term IN ANY case!!!  Almost  EVERY term you could THINK
> of TO use
> has ALREADY BEEN USED (coherently) BY SOMEBODY ELSE ALREADY!

It turns out that I am arguing with myself here:
> There are various uses and definitions of "representable",
> "definable", "expressible" in the literature. The above agrees with
> the terminology used in Smullyan's "Gödel's incompleteness theorems".

The "above" referred to is something that AK should have quoted.
It contrasts "expressible" with "representable", but C-B could not be
bothered to
further contrast "definable". The quoted sentiment is the
intellectually correct one.
The fact that YMMV is more important than any particular definition.
Using a term that is already known to be multiply defined is
problematic
in any case. But using the version that AK claims C-B wanted to use
is
doubly worse, since by that definition, THE provability predicate DOES
NOT
represent provability, since it represents what's provable, and no
unprovability
sentence is provable.
From: George Greene on 9 Jun 2010 21:55
On Jun 9, 9:54 pm, George Greene <gree...(a)email.unc.edu> wrote:

>  But using the version that AK claims C-B wanted to use is
> doubly worse, since by that definition, THE provability predicate DOES
> NOT represent provability, since it represents what's provable, and no
> unprovability sentence  is provable.

Which is precisely why C-B is not qualified to be pontificating.


From: Aatu Koskensilta on 12 Jun 2010 11:07
George Greene <greeneg(a)email.unc.edu> writes:

> But using the version that AK claims C-B wanted to use is doubly
> worse, since by that definition, THE provability predicate DOES NOT
> represent provability

Sure it does. Recall Charlie's explanation

A wff expresses (represents) the set of numbers that when substituted
for its free variables forms a true (provable) sentence.

Since PA is Sigma-1 sound the usual provability predicate for PA
represents in PA the set of theorems of PA.

--
Aatu Koskensilta (aatu.koskensilta(a)uta.fi)

"Wovon man nicht sprechan kann, dar�ber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: George Greene on 12 Jun 2010 12:49
On Jun 12, 11:07 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Sure it does. Recall Charlie's explanation
>
>   A wff expresses (represents) the set of numbers that when substituted
>   for its free variables forms a true (provable) sentence.

Which means that provability is representable WHILE UNPROVABILITY IS
NOT.

I'm sorry, this is just not acceptable.
If these were generally employed definitions, then, of course, it
would be,
but if you going to say "I want to do it this way", it does become
improtant
for your way not to be ridiculous.
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