On 09 May 2012, at 17:09, R AM wrote:
PM, Bruno Marchal
Yes.
"Nothing", in set theory, would be more like an empty *collection*
of sets, or an empty "universe" (a model of set theory), except that
in first order logic we forbid empty models (so that AxP(x) ->
ExP(x) remains valid, to simplify life (proofs)).
"nothing" could also be obtained by removing the curly brackets from
the empty set {}.
Noooo... Some bit of blank remains. If it was written on hemp, you
could smoke it. That's not nothing!
Don't confuse the notion and the symbols used to point to the notion.
Which you did, inadvertently I guess.
{ } is a set and "{ }" is a string with 3 symbols, ... which should be
differentiated even from the paper and ink, or stable picture on a
screen, representing physically the symbols to you, and then from the
image made by your brain, and the neuronal 'music' trigged by it, and
the consciousness filtered locally by the process, etc.
Or removing the (empty) container. I guess this would be equivalent
to "removing" space from the universe. Except that this doesn't make
any sense in Set Theory (maybe it doesn't make any sense in reality
either).
Still, {} is some sort of nothing in Set Theory,
Sure, like 0 is some sort of nothing in Number theory, and like
quantum vacuum is some sort of nothing in QM. Nothing is a theory
dependent notion. (Not so for the notion of computable functions).
Extensionally, the UD is a function from nothing (no inputs) to
nothing (no outputs), but then what a worker!
Extensionally it belongs to { } ^ { }. It is a function from { } to { }.
But that is a bit trivial, I think. It is due to the fact that
computability theory is not dimensional. Dimensions also have to be
derived from the internal points of view (with comp), like the real
and complex numbers and the physical laws.
given that it is what is left after all that is allowed to be
removed, is removed.
OK.
Bruno
Ricardo.
Bruno
http://iridia.ulb.ac.be/~marchal/
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