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 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.
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. It simply executes all possible sequences of states - it doesn't necessarily
compute anything in the Turing sense. In fact those threads that compute something halt
and will become of measure zero as the UD proceeds.
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?
Brent
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