Le 28-juil.-12, à 20:37, Stephen P. King a écrit :
On 7/28/2012 9:35 AM, Bruno Marchal wrote:
This is a "degeneracy" problem, everything looks, acts and even is
one and the same thing, so how is there any differentiation that
allows a plurality to obtain?
0 ≠ s(0) ≠ s(s(0)) ≠ ....
I need to explain myself on this claim for the sake of others
that might be confused and yet open to understanding.
The non-equivalence that Bruno points out here with "0 ≠ s(0) ≠
s(s(0)) ≠ .... " is correct, but that correctness changes
?
when we introduce Godel Numbering. Godel numbering is the coding of
statements about numbers as numbers and so has the effect of making
the " ≠ " ambiguous
?
(it is just a translation. Why would a translation make a statement
ambiguous?)
and thus making the non-equivalence of numbers degenerate. Once we
introduce the idea that numbers can code for other numbers then it
follows that numbers are no longer uniquely different from each other.
Therefore the plurality of numbers with regard to their ability to
define multiple unique quantities vanishes.
QED
?
Bruno
http://iridia.ulb.ac.be/~marchal/
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