On 02 Mar 2014, at 10:49, Chris de Morsella wrote:
the null set... the set of nothing at all. The null set is a lot more
than nothing.
Sure. The set { { } } is not empty. { } *is* something.
>>Yes, with the set theoretical principles of reflexion and
comprehension, you can get almost all sets from the null set.
In some ways all other possible sets naturally emerge from the null
set; in a way as all numbers emerge from the bit.... The bit, if
infinitely replicated can express any number; if you can get this
infinitely self-auto-replicating bit off and running like inflation
then the universe is in business.
Except that here you seems to take fro granted that "universe" is a
well defined term, but it is not, and apparently, if comp is true, the
physical and the mathematical universe are epistemic construction in
the mind of numbers, relatively to infinities of number relations. By
the First Person Indeterminacy, our mind are distributed through
infinitely many computations occurrences in arithmetic, and the
physical is somehow determined by the statistics which can exist (or
not, but the first results go in the direction that it can exist) on
*all* (relative) computations.
This makes physics, including experimental physics, into arithmetic.
It takes a great leap to get from nothing to the null set. At this
most reductionist of levels; is this where everyone gives up,
perhaps because it is unknowable.
I can see the logical progression from 1+1=2 to an ever inflating
infinite forest of numbers with infinite overlays of dynamism
operating over layer and layers of stochastic boundaries.
>>OK. But the point is that we can't prove the existence of null
set, or of the umber 0. We can't prove this from logic alone (=
failure of Russell and Whitehead "logicism").
Yes, I agree, I can only imagine how Kurt Gödel's incompleteness
theorem must have hit Russell and Whitehead like a ton of bricks.
It is a real (creative) bomb. Few realize the deep impact that theorem
has on basically everything fundamental.
It is often misused, and so, some expert logicians infer that all its
use out of logic are misused, but this is refuted in computer science
and in computationalist physics and theology.
Bruno
http://iridia.ulb.ac.be/~marchal/
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