On 08 Jan 2015, at 04:23, 'Chris de Morsella' via Everything List wrote:
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From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com
] On Behalf Of meekerdb
Sent: Wednesday, January 07, 2015 12:12 PM
To: everything-list@googlegroups.com
Subject: Re: Why is there something rather than nothing? From
quantum theory to dialectics?
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.
I get the feeling that '0' has a lot more meaning for Bruno than
merely being a vertically oriented oval drawn on a paper (or
computer screen), that it is a symbolic notational reference to a
rather profound concept, which eluded the world for much of its
recorded history. It wasn't until the fifth century A.D. in India
that mathematicians fully conceived of it giving it conceptual
existence, though it was used earlier as a kind of decimal place
holder as far back as 300BC or thereabouts -- in Babylon. It was the
Italian mathematician Fibonacci who introduced the concept back into
the church darkened intellectual deserts of Europe in 1200 AD.
Placeholder type zero's -- to differentiate an empty number column
seems to have been adopted in ancient Sumer. It is only however much
later that the concept of zero was really understood.
Read somewhere that the concept of zero was independently arrived at
by three different cultures -- as far as we currently know that is
-- including the Olmecs (the mother culture of meso-America) from
whom the Mayans later adopted it -- A Mexican anthropologist friend
of mine told me this while I was living down there in the Veracruz
cloud forests some years ago. Most accounts, attribute the meso-
American discovery of the concept of zero to the Mayans, but he
insisted that the Mayans had picked it up from the much earlier
Olmec mother civilization.
Yes, 0 is a very deep notion, but in the mathematical TOE derived from
computationalism, it is just a symbol obeying to the axioms mentioned.
In logic, proofs are defined in a way such that the theorem are
independent of any interpretation of the symbols, as long as the
axioms are verified, and that the rules of inference are syntactically
valid.
That is logic. validity is independent of interpretations, semantics,
etc. This makes it possible to study the semantics itself
mathematically (not in the theory, but in a metatheory, which usually
presuppose the whole of possible mathematics).
This makes logic independent of philosophy, and indeed it makes it
into a branch of math, like any other one. Unfortunately, this makes
some logicians allergic to (re)apply logic to metaphysics or theology,
but this is a philosophical category error.
Since Gödel, we know of course that the natural number theoretical
reality is far beyond what we can axiomatize in any theory.
Bruno
-Chris
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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