On 06 Jan 2015, at 20:21, meekerdb wrote:
On 1/6/2015 1:48 AM, Bruno Marchal wrote:
On 03 Jan 2015, at 06:05, 'Roger' via Everything List wrote:
Even if the word "exists" has no use because everything exists, it
seems important to know why everything exists.
But everything does not exist. At the best, you can say everything
consistent or possible exist.
Anyway, as I said, the notion of nothing and everything, which are
conceptually equivalent, needs a notion of thing. That notion of
thing will need some thing to be accepte
It is often ambiguous in this thread if people talk about every
physical things, every mathematical things, every epistemological
things, every theological things, ...
So, we cannot start from nothing.
We light try the empty theory: no axioms at all. But then its
semantics will be all models, and will needs some set theory (not
nothing!) to define the models. The semantics of the empty theory
is a theory of everything, but in a sort of trivial way.
Computationalism makes this clear, I think. We need to assume 0 (we
can't prove its existence from logic alone, we need also to assume
logic, if only to reason about the things we talk about, even when
they do not exist).
What does it mean to "assume 0". Is it to assume a collection of
things
No. If we assume a collection, we would do set theory, or something.
We might assume some intended collection at the metalevel, but if we
build a formal theory (a machine), we will not assume a collection at
the base level.
such that every element has a unique successor (per some ordering
relation) and there is one element that is not the successor of any
other element, which we call zero? That seems to assume things too.
Assuming zero means here that we add a symbol ("0") in the language
alphabet, and we assume some logical formula. The non logical symbol
that we have introduced are "0, s, + and *", and we assume some
formula like:
~(0 = s(x)), for any x (the x are always supposed to denote the
object of our universe, here the intended standard natural numbers)
also:
0 + x = x
0 * x = 0
We don't assume anything else (about zero).
Then once we have the numbers, the addition and multiplication
axioms, we have a Turing universal system and all its relative
manifestations, i.e. all computations or all true sigma_1
sentences, and the physical reality is an illusion coming from the
internal statistics on the computations.
But in your UDA the fact that the computer executing the UD is
Turing universal seems irrelevant.
The UD is a universal machine, programmed to generate and execute all
programs. A computer is by definition a Universal machine.
It simply executes all possible sequences of states - it doesn't
necessarily compute anything in the Turing sense.
It does not generate all possible sequences of states. It genuinely
execute each programs, on each input in the Turing sense. It just do
it litlle pieces by little pieces, but the computations are genuine
computations. You might look at the code. I am not sure why you say
that it generates all sequence of states. You confuse perhaps with the
library of Babel.
In fact those threads that compute something halt and will become
of measure zero as the UD proceeds.
Intuitively, but the incompleteness breaks the intuition, and the
measure is determined by the logic of self-reference restricted to the
Sigma_1 sentences (which represents both sates and finite halting
computations).
That works. We do get a quantization which behaves up to now as it
should, if computationalism and quantum mechanics are correct.
How is it that a thing can exist?
With computationalism, we cannot answer that question, but we can
entirely explain why. We need to assume one universal system (be it
numbers, fortran programs, or combinatirs, ...). Then the physical
is a sum of all the computations.
What I suggest is that a grouping defining what is contained
within is an existent entity.
That is similar to some comprehension set theoretical axioms. The
origianl comprehension axiom (by Frege) was shown to be
inconsistent by Bertrand Russell, and this leads to the
sophisticate set theory, like ZF (Zermelo-Fraenkel) or NBG (von
Neuman Bernays Gödel).
Note that set theories assumes much more than arithmetic. Set
theories are handy in math, but is a bit trivial in metaphysics. It
assumes too much. It contains Quantum mechanics, and all possible
variants, including non linear QM, Newtonian mechanics, etc.
Can you prove that arithmetic does not contain those variants?
No, because arithmetic does contain those variants, but not with a
measure compatible with the logic of self-reference and the material
intensional variants. The logic of physics, or observable, is given by
the modal logic of []p & p, []p & <>t, []p & <>t & p, with p limited
to sigma_1 sentences (equivalent with sentences having the shape
ExP(x) with P sigma_0 (recursive).
Bruno
Brent
--
You received this message because you are subscribed to the Google
Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it,
send an email to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
