Re: The shocking truth about the naturals
- From: george <greeneg@xxxxxxxxxx>
- Date: Fri, 07 Sep 2007 06:34:44 -0700
On Sep 6, 9:31 pm, Boris Borcic <bbor...@xxxxxxxxx> wrote:
ng as this old argument is, it is curious it has
escaped the determined skeptic that the upward Löwenheim-Skolem
theorem incontrovertibly shows we can't really prove any collection
countable.
Since the above technically alludes to me (as current last representative), I
guess it is legitimate for me to remark on it... that (1) my /own/ use of
"incontrovertibly" indeed alluded to the unavoidability of "determined skeptics"
and further adepts of the church of univocity, and (2) that my alluding to the
necessity of counting with them is not sufficient cause to count myself among
these groups.
I am a little surprised that AK didn't give you credit for bringing
this up.
It is true that it is an intellectual point in its own right,
regardless of who
said it last, but since I wasn't reading the "physical process"
thread, I
didn't realize that you had inspired him.
The relevant point here (which is converging with the point of my long
thing
from Sept.6) is that the situations are INHERENTLY not symmetric.
"Prove" does not have just one meaning. Around here, we are
artificially
RESTRICTING the meaning of prove to "prove in classical finitary 1st-
order logic".
This paradigm is founded on the concept of a FIRST-ORDER LANGUAGE.
This language (or method of language-formation, founded on simple
"signatures") HAS A *DEFINITION*.
.
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