On 1/7/2015 3:22 AM, Bruno Marchal wrote:
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).
So 0 is just a mark on paper, a symbol that is not a symbol "of" anything such as the
empty set.
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.
How is a "program" defined? Isn't it just a deterministic sequence of states?
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.
What is the justification for restriction to Sigma_1 sentences?
Brent
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