retraction

Rupert wrote:
There is not, as you imply, any good reason to privilege the standard
model in the context of Con(T) but not in the context of G_T (by the
way, G_T and Con(T) are equivalent in Sigma-1-Induction Arithmetic).

I mis-reacted to this.
When people mis-characterize what I have said, it makes me so
mad that sometimes I just can't think straight.

Initially, *I* was the one championing the position that one might
as well take G_T to be Con(T). *I* was the one talking stressing
SIMILARITIES between the two. Rupert was the one insisting
that there was some deep chasm that could only be bridged by
sigma-1- completeness. In other words, I am simply not implying
what Rupert has alleged that I am implying.

The relevant contexts here ARE NOT "the context of G_T"
and "the context of Con(T)". The relevant contexts ARE
the context of the first incompleteness theorem and of the
second. Con(T) is introduced in the context of the first but it
is NOT proved that both it AND its denial are UNproved by T
UNTIL the 2nd. It is specifically the fact that ~Con(T) is not
also provable that requires sigma-1-completeness.

So FUCKING what?? We are TALKING about *T* and
THEY ARE NOT equivalent in all models of T!!

Well, if T is PA, they are. That was just a mistake.
It was also, in any case, not my intended point.
*I* was the one who was insisting that they WERE, for
all practical purposes, equivalent to each other, in all
the relevant models (inTRA-model). My INTENDED point
was that they are not equivalent inTER-model (in some
models, they are both true, and in others they are both
false).

The immediate argument was about privileging one
as opposed to the other of Con(T) vs. G_T.
Obviously, simply BECAUSE Con(T) IS SPELLED
"Con(T)", models in which it has THE SAME truth-
value as "T is consistent" have to be privileged.
G_T, BY CONTRAST, is NOT fore-ordained or even
semantically intended to MEAN ANYthing: it is MERELY
intended to be unprovable, i.e., INTENDED to have DIFFERENT
truth-values in models of the SAME theory (T). This in some
sense implies it is intended NOT to mean anything in particular.
The fact that G_T means the same thing as Con(T) IS FROM THE
SECOND incompleteness theorem.

Of course, a context in which you understand G1 but not yet
G2 is one in which G2 IS STILL TRUE, whether
you understand it yet OR NOT. But that is not the point.
The point is that meaning PRE-imputed and assigned by us is
present and relevant in the case of Con(T), and in the case of
G_T, it isn't, at least not initially. This argument is getting
RIDICULOUSLY
petty. *I* was originally the one who said the equivalence was
trivial.
Rupert was the one saying it depended on something deep. If he
really felt that way then he should now be arguing MY side of this
question. On this one, we have truly passed each other going in
opposite
directions. This sort of thing does NOT happen when people are
committed to clarifying the technical points.

.

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