On 07 Jan 2015, at 21:12, meekerdb wrote:
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.
Yes, it is just a symbol, and all we need is your agreement with the
axioms and inference rule, in which that symbol is used. No
metaphysics, nor reification of anything.
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?
A program is defined as a word in some alphabet, and can be identified
with his Gödel number, or any encoding.
A computation is the doing of a program, and is defined relatively to
a universal system implementing that computation, in physics, or
arithmetic, or any fixed universal numbers/system.
A computation is NOT the description of a computation, which is itself
encodable as a number or as a sequence of numbers.
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?
The Sigma_1 sentences are Turing equivalent with the Universal
Doevtailer, which determine the measure brought by the global First
Person Indeterminacy (in "front" of the UD*).
Bruno
Brent
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