Hi Peter,
You are replying to my post (I am Bruno, not Brent, although I am open
that we are all the same person, it is better to keep the name right
for helping in future references)
On 26 Oct 2014, at 17:52, Peter Sas wrote:
Thanks for your comments, which are very useful, even if the more
technical comments are beyond me (I have to study up on that).
Thanks for the tip about category theory, I vaguely heard about
it... I know it is a rival to set theory when it comes to founding
math (insofar that is possible given Goedel).
You write: "Note also that a "universe" is usually considered only
for its intrinsic quality. A universe has a priori no relation with
something else, as everything is or should be part of a universe, by
definition."
I would say: what is outside the universe is precisely nothing,
That might already be too much. Also, the notion of nothing is theory
dependent. The quantum nothingness is not the same as the nothingness
in set theory, etc.
which is why the universe exists in the first place, that is, it is
not nothing (= ontological difference).
That looks like a play with word, which does not mean that there is
not some truth behind, but you will have to elaborate a lot.
So even for the universe it holds that it is what it is by differing
from what it is not. And if it differs from nothing, then it must
also be determined (internally differentiated = ontic difference)
otherwise it would be indeterminate and thus as good as nothing.
Hmm...
i.e. a thing IS its difference form something else.
Not sure I wrote this.
OK, you might say God is what is different from all beings.
But I did say that.
In that sense I would say: God is really nothing, since it makes all
things be by differing from them.
That idea is made precise in Plotinus' theory (for which I provide a
way to interpret it in arithmetic, with God played by the notion of
Arithmetical truth or reality, the Noùs is interpreted by Gödel's
provability predicate, and then soul and matter are intensional
variants from that predicate, restricted to computationnaly accessible
states).
In that case God is responsible for the beings (the natural numbers
and their "ideas"), but is not a being itself. In fact in plotinus,
and in the machine's classical theology, both God and Matter are
outside the universe (the realm of being, the Noùs).
You write: "If we assume that the brain (or whatever my
consciousness supervene on) is Turing emulable, we must recover
physics from a special self-referential statistics on the
computations. Physics becomes a branch of machine's psychology, or
better machine's theology (in the greek original sense of the word)
itself branch of arithmetic or mathematics."
I wrote that indeed.
I don't get this. I see how the brain/consciousness might correspond
to self-referential loops in computations, but why does this have
implications for the whole of physics?
That was the object of a life of research, and thus is not that easy
to understand without some amount of work. I have not so much time in
this period, and so I refer you to my most simple paper, though a bit
concise, and the second part needs some familiarity with mathematical
logics and theoretical computer science. Nevertheless, the implication
for physics does not need special knowledge but passive computer
science:
http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
I assume Mechanism, actually its digital version, which makes a lot of
sense thanks to the Church (Post-Turing-Kleene) thesis. It forces to
generalise Everett embedding of the physicists and engineers into the
physical realm, into an embedding of the mathematicians and dreamers
into the arithmetical realm. The quantum wave should emerge
phenomenologically from the statistical "interference" of all
computations, independently of any languages describing the
computation. If digital mechanism, alias computationalism, is correct
we get a many-dreams interpretation of arithmetic, and the physical
realities (or reality) percolate(s) from coherence conditions that
some computations have. But we have to derive them constructively to
verify that statement, and the math of self-reference has made
possible to derive the arithmetical quantization, and up to now, it is
enough quantum-like to say that computationalism is not (yet) refuted.
It is my main point: that some problem in philosophy and theology can
be approached with the scientific method, notably when using the
computationalist hypothesis, which makes the ideally correct case
amenable to pure mathematics.
Do you mean to say that there must be a compuational approach to God
as the creator of physical nature?
Not really. I say that it has to be like that, if we assume that our
brain (quantum or classical) are Turing emulable.
Then God appears to be highly non computable (in fact not even
definable by the machine) as it is the whole arithmetical truth a
highly non computable set, it is at the top of the arithmetical
hierarchy which classifies the degrees of non-computability or non-
solvability). Then it does not ring so well to see that God as a
creator, it looks more like the TAO, or the ONE of Plotinus. The
arithmetical reality implements by itself all computations, but also
many levels of truth about those computations. The difference which
play the important role in all of this, is the difference between what
the machine will be able to justify (in different senses) and what she
can conceive or imagine, and with reality/truth.
You write: "We can doubt this, notably for the numbers where many
particular numbers can be individuated through its special
property." Could you give an example? I would say: even for unique
numbers (unique primes?) it holds that they are only what they are
because of their place in the number system; take the system away
and the number is just a meaningless mark.
I can agree with that. But the same reasoning in quantum field theory
would lead that only the vacuum exist. But in science we can adopt the
semi-axiomatic approach, and never try to say what things are, but
trying only to agree on some axioms about them. So I am OK with what
you say, but if only by methodology, I apply this on all things.
Now, some mathematical object are intended to instanciate many
different things, like the theory of groups (there are many different
groups). Other theories, like number theory, or machine's theory, talk
about only one structure (the natural numbers). We can't define
completely the structure N, with only the means in N, we need sets to
do that, or second logical axioms, so like groups, there are many
"natural numbers" systems. Unlike groups, we can focus on the standard
N structure, and the non standard play a bit a role of reservoir of
simplification tools, like analysis.
Eventually all this reduce the mind-body problem, and the reason why
there is nothing, to the mystery of our understanding and beliefs
about arithmetic, and this provides a tool for explaining why machines/
number can't sole that question. So, computationalism seems to offer
the best we can hope: a testable theory which justifies indirectly the
existence of a mystery: your belief in 0, and in 1, etc.
I am aware that some philosophers are not glad with the idea that,
using some hypothesis, we can translate a problem of philosophy into a
problem of math. They take that as bad news.
Some scientists also dislike the idea, but usually, they have missed
some points, or simply not look at the subject. Many "non-logicians"
have a "pre-Turing-Gödelian conception of the machines, or of the
finite entities in general.
It is not well know probably because few logicians like "philosophy of
mind", or knows about Everett QM (which can help to conceive the type
of reality computationalism leads us too), and physicists get often
wrong when venturing in mathematical logic. Nevertheless this has been
peer reviewed enough, but I am astonished that the testable classical
form of comp is not yet refuted.
Bruno
Peter
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