On 09 May 2012, at 21:39, R AM wrote:
On Wed, May 9, 2012 at 8:23 PM, Bruno Marchal <marc...@ulb.ac.be>
wrote:
On 09 May 2012, at 17:09, R AM wrote:
"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.
I was using the analogy between items contained in sets and things
contained in bags. The curly brackets would represent the bags.
Removing things from a bag leaves it empty. Removing the bag
leaves ... nothing.
Nothing in the universe of sets. But this makes not much sense. And
you have still an empty universe. Then you will tell me to remove all
universes, but you will still get an empty multiverse. Oh, you can get
rid of all multiverses, but you will still have an empty multi-
multiverse. Oh, you can reiterate this in the transfinite, ... but you
need some rich theory at the metalevel, then. Absolute nothingness
does not make sense in my opinion.
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).
Yes, these concrete nothings are well behaved, unlike the absolute
nothing, which we don't know what rules it obey (in case it is a
meaningful concept, which it might not be).
OK.
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 I guess that is because the UD generates internally all possible
inputs for all possible programs, isn't it.
Right.
Bruno
Ricardo.
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