On 17 Nov 2014, at 16:25, Peter Sas wrote:
Here is a new blog piece I wrote:
http://critique-of-pure-interest.blogspot.nl/2014/11/the-inconsistency-of-nothing-objective_17.html
OK. I print the quite clear and well written introduction of your
article:
Peter Sas wrote in his blog:
<<
In my previous post on this blog I argued that if we want to answer
Leibniz' famous question ("Why is there something rather than
nothing?") we have no choice but to start with the assumption
thatnothing at all exists and then investigate how we might derive
existence from this state of nothingness. The rationale behind this
approach is obvious: as long as we start with some primordial being
(e.g. God or the laws of physics) as the cause of all other beings, we
will not have truly answered Leibniz' question, since in that case we
still have to explain why the supposedly primordial being existed. Why
does God exist? Or where did the laws of nature come from? The late
Robert Nozick put this problem succinctly as follows: "The question
[of Leibniz] appears impossible to answer. Any factor introduced to
explain why there is something will itself be part of the something to
be explained". (Nozick 1981: 115) Hence, only if we start with the
assumption that nothing at all exists will Leibniz' question become
answerable.
>>
First, note that you stay in the Aristotelian tradition of suggesting
a choice between the two gods of Aristotle: the creator and the
creation, that is God or the laws of physics.
Xeusippes (-300), Tegmark and myself and others would add the laws of
mathematics. Indeed I show that if we assume that consciousness is
invariant for some digital permutation at some level of description,
then we cannot distinguishes an arithmetical God from an analytical
God nor from a physical God, although we *can* have 3p clues if we
attempt to look at ourselves below the computationalist level of
description.
Now you will asks me where does the laws of mathematics come from?
Well, computationalism answers that question, not entirely, but it
justifies entirely why it doesn't make sense to hope for an entire
answer here. It actually isolates the tiniest thing that we can't
understand, but need to explain everything.
Let me try to explain. Since the failure of logicism, we know today
that we cannot derive the existence of the natural numbers 0, s(0),
s(s(0)), ..., or 0, 1, 2, 3, ... if you prefer, from logic alone. So
we need axioms, we need a theory, we need hypotheses on which we can
hopefully agree to just talk about the natural numbers. Like wize, we
can't derive addition from logic, and then even assuming addition, we
cannot yet derive multiplication, even with the induction axioms.
Whatever will be your notion of "nothing", to be enough rich to get
the natural number, will make you assuming the natural number, or
something Turing equivalent, which is such that if you don't assume
it, you cannot get it at all.
Then, once we have both assumes the addition laws and multiplication
laws, we arrive at the Turing universal level, and this contains *all*
the machine dreams. Sharable first person plural dreams ("video-game")
exists and can cohere to define some multi- or multi-multi-verses.
Advantage: the math forces us to distinguish many modalities for the
"knowing", "believing", "observing", etc. The person and its
consciousness is not eliminated: it is one which put the equations and
the fire in the equations. Bute the fundamental equations are the laws
of addition and multiplications, all the rest is the pôssible
epistemologies of the numbers.
What are you hoping for? The relation between nothing and everything
is a relation of complementarity, you can't define one without having
the other one. take the unary intersection of sets. That int x = the
usual intersection of all sets y belonging to x. Classical logic will
make the unary intersection of the empty set equal to the collection
of all sets. Or take the number, with multiplication, You get
"infinity" when attempting to divide 1 by zero. Or take the quantum
emptiness, which assumes often by default some large portion of set
theory (much more assumption that elementary arithmetic). But the
quantum vacuum contains the universal waves in its partial
superposition states, which leads to internal multiverses.
The point is that all precise enough notion of nothingness will
assume ... many things, if only at the meta-level. In logic we agree
both on the axioms, and of the rules making it possible to derive new
formula from those axioms. If you want (but it might be you don't want
that) make an explanation of everything from nothing, you will need to
make a choice for a notion of "thing", on which we can agree to exist
in at least some sense. If that notion is not Turing-universal, you
will not be able to explain even just our belief in universal numbers.
If it is Turing universal, then it is equivalent to assuming the
natural numbers.
In that sense, I think that computationalism does explain (modulo its
possible refutation by physics) where everything comes from, including
the computable and many things which concern us but are non
computable, and some even non nameable.
The only problem, but it is the price of the conceptual solution, and
it makes a classical naïve form of computationalism testable, is that
we have to derive the laws of physics from arithmetic and number's
self-reference abilities, relative to truth, consistency, etc.
Advantage and disadvantage: time to buy some books in math, computer
science, mathematical logic.
About -∃x(Ex) My problem is that the "reverted E" is a quantifier,
and the second E is a property, but I doubt existence can be made into
a property. That reify existence, and introduces a problem that we
don't need, unless you believe in one or both Aristotelian God(s).
Computationalist have not that problem: only 0, s(0) , etc. exist in a
clear definite sense. All the rest will be the hallucinations, say,
made possible by the relations in between numbers inherited from
addition and multiplication. No existence at all is reifed. The basic
ontology is 0, s(0), ..., and the physical existence will be when some
numbers believe correctly modal proposition of modal existence, like
[] <>Ex []<> P(x) (the first E being the usual quantifier, the
physical becomes a point of view on the arithmetical reality "see from
inside". There is a bit of: everything from not a lot: as arithmetic
seen from inside is much bigger than arithmetic seen from outside
(that's somehow the roots of incompleteness).
Very nice and clear article. I think. But I think that Gödel's
theorem, and others by Tarski, Skolem, have shed much light on this
question, and computationalism even more, by associating to each
(universal) number, a theology, containing physics, so the numbers can
evaluate its degree of non-computationalism or emulation-order (not
that this easy, but QM could confirm (not prove) that we are NOT in an
emulation.
Peter, you are on the territory of philosophy/theology which has a non
empty intersection with mathematics, once we assume computationalism.
Bruno
Here I use some of the tools of analytical philosophy to analyze the
logical impossibility of nothinness... For the philosophically
inclined among you...
Peter
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