Dear Vinod,
On 05 Sep 2017, at 14:41, VINOD KUMAR SEHGAL wrote:
Dear Vinod,
Thank you for your attempt to understand what I try to explain. Let
us indeed try to find where we
might disagree. I think we disagree simply on our assumptions. You
assume primary stuff.
I assume elementary number relations.
But above is a great difference.
I think I see where we disagree.
On 01 Sep 2017, at 13:46, VINOD KUMAR SEHGAL wrote:
There are some more issues for numbers/arithmetic which requires to
be discussed
and explored further
i) Do numbers/arithmetic have some fundamental non-emergent
existence or do they
manifest in nature as the result of some emergent phenomenon.
I think numbers and arithmetic can't have any fundamental non-
emergent existence
since numbers per se are devoid of any "ontology with some
stuff" and for the
fundamental existence of anything, it should be possessed with
some "ontology
with some stuff"
OK. I might say that we differ on this. I do not believe in stuff. I
don't think that there are
evidences for stuff.
Yes, there could be no objective evidence for either of the
primordial existence of physical stuff
and numbers.
OK.
Now, assuming the numbers is not a lot. In fact assuming any universal
machinery, in the mathematical sense of Church, Turing, Kleene ...
(the discoverers of the plausible mathematical notion of (universal)
digital computation. It is made philosophically precise by the
assumption of Church's thesis, or Church-Turing thesis, but in my
opinion even better understood and discovered by Emil Post And Stephen
Kleene.
And the physicists assumes also the numbers when developing their
mathematical theories. Wigner asked where does the unreasonable
explanation power of mathematics in physics comes from.
What I only claim is that if mechanism is taken seriously enough into
account, and some thought experiences can help to see what this means,
eventually we can see that the physical reality is sort of derivative
of the mind of the universal Turing machines, which is incarnated
relatively to arithmetic, or any universal machinery, infinitely often
in a highly non computable way "at the bottom".
The universal numbers implemented in arithmetic (say) look inwards and
at first see the fermions and the bosons, the particles and the waves,
but then can see the root of the "illusion". Normally.
But for some thing ( phenomenal universe) to emerge out, we have to
start from
some thing -- some assumptions.
Absolutely.
In the absence of any objective evidence, let us examine this
issue from a logical feasibility point of view. When will any thing
exist?
That is the key issue.
My shorter answer: 0 exists. And if x exists, then the successor of x,
s(x) exists. So what exist is 0, s(0), s(s(0), etc. They are called
the natural numbers.
I assume classical logic, and the following axiom, with x + 1 for s(x):
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1) (Ey = it exists a number y such that)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
Although not in this form: this is taught already in all high school.
That theory is due to Raphael M. Robinson.
Then I use Gödel's arithmetization technic to define in the
arithmetical language a believer, which already believes a little more
than the axiom above: it believes in the induction axiom, which is
that if something (definable) is such that when true for x, it is true
for the successor of x, then, if 0 has that something true for itself,
then it is true for all numbers x.
That is long and tedious, but already done many times in the
literature. I intent to explain this here, in a sketchy way, so people
can see what I am talking about.
When it will be possessed
with some "ontology having stuff".
It is here that we might disagree. Why should we assume an ontology
having stuff?
Even just the physical theories, before and after the quantum, does
not promote a stuff, it seems to me.
And then I can explain that with mechanism, the notion of primary
physicalness does not make sense. Instead, mechanism provides a bigger
role to the physical by lowering the mechanist substitution level.
Numbers per se can't have any "ontology with stuff",
I agree. That is why the theory will only explain why the "cosmic
consciousness" will get deluded in believing in ontology with stuff.
I don't claim any truth here. Only that this follows from the digital
mechanist hypothesis.
therefore,
the primordial existence of the numbers is ruled out.
I don't see that. My spirit continues to make spiritual existence of
the goddess 0 and the god 1 and the goddess 2 and the god 3 and ...
I agree that it might seem a bit weird that we can have so long and
deep dreams as observations suggest, but mechanism expains why when we
look at ourself and the environment very close, we must see the traces
of the infinitely many computations which competes to brought our
states.
But physicality or cosmic consciousness can
have an "ontology having stuff:,
Not only we don't need stuff, but with mechanism it obstructs a
simpler and testable explanation, so why not just confess we don't
know, and let us do the test. Now, QM pass the test, unlike all
uniworld theory. So I take QM as confirming the more startling, and
admittdely shocking, consequence of mechanism. I mean the fact that
the soul has an infinity of (virtual) bodies (in arithmetic).
therefore, they primordial existence of CC or some physcality
is logically feasible
I see only humans betting on measurable numbers (temperature, length,
weight, ...), from which they infer mathematical relations, and
indeed, most of the time,
computable relations.
So numbers do manifest when humans measure temperature, length,
and weight. ( if there is nothing to measure, numbers will also not
exist)
Not really. It follows from just the axioms above that numbers get
involved in crazily complex relations, involving many numbers. Then
you must take into account the difference between the first person
memories and the third person local description of the most probable
histories. The first one are invariant of delays, and the first person
relies on infinite sums of big numbers. But there are renormalization,
and the problem are similar in quantum field theory.
But temp, length, and
weight can't manifest unless there is some heat energy, space, and
matter.
With the progress of virtual reality, the knocking on the table
argument will lose its power.
A digital typhoon cannot make you wet, unless you, and the typhoon,
have been digitalized at the correct substitution level. But then,
that emulation, in particular, is executed infinitely often in
arithmetic. Fortunately, computer science provides some gluing of the
computations, which in the limit can make you relatively rare, with
deep memories.
This, in turn, means,
numbers will manifest when energy, matter, and space appears in some
measurable formats
This will make numbers secondary to energy, matter, and space.
I am not even sure you can define energy, space, time without assuming
unities and the multiple of those unities, and their rational and
real, even complex cousins.
I see only person doing measurements and getting numbers, from which
they infer interesting and beautiful relations (also quite useful in
practice).
I see this as an evidence for a physical reality, but I am not sure it
is an evidence for some stuffy reality, still less for a primary
metaphysical reality.
Then they believe, like everyone, that they are conscious and have
first
person experience, and they usually assume an identity thesis
between their body and mind.
No belief, Ist person experience and any assumption of identity
thesis is feasible unless
consciousness is present as a priori.
I agree with you.
(This will force me to explain the "enlightenment" of the universal
machine. I can't do it just now, and it is subtle and can be prone of
misunderstanding).
A sone having NIl consciousness can neither believe
it to be conscious, have any Ist person experience or have any
identity thesis. So to hypothesize
that human's consciousness, Ist person experience, and identity
thesis come out of human's
belief does not stand the simple scrutiny of logic. ( Of course
logic also come out due to
consciousness)
If I understand correctly I still agree with this.
My work is a deductive argument (modulo definition/axioms) showing,
said shortly, that such
an identity thesis does not make sense when we assume Mechanism.
So we might agree, and you could appreciate the first half of the
result, which is that Mechanism
(in cognitive science) and Materialism (in the sense of assuming
the existence of primitive stuff,
or perhaps better assuming the primitive existence of stuff) are
incompatible. So, if you want
keep stuff, it is logically compelling to abandon Mechanism.
The first half of my studies shows that (Not Mechanism OR Not
Materialism.). That is equivalent
with the two following:
Mechanism -> Not materialism
Materialism -> Not Mechanism
I don't comprehend fully what makes you to not to accept materialism
despite Mechanism. I take
the mechanism as the state where materialism follows certain laws
and it unfolds, go forward
conforming to certain physical laws of nature with these Laws being
representable in numbers/
arithmetical forms. So whether physical laws or mechanism are the
two forms of the same reality
and both these act on the physicality in form of matter and/ or
energy.
You please elaborate on your concept of mechanism.
I use Digital Mechanism, where a computation is a symbol processing,
usually deterministic, which can be carried by elementary discrete,
digital, numerable, steps.
The notion has been discovered by mathematicians working in the
foundation of mathematics.
It has nothing to do a priori with matter or energy.
A key discovery is the discovery of the universal (digital) machine,
which can mimic all other digital machine or interacting collection of
digital machines.
It happens also that the physical reality has many Turing universal
facets, and when a universal digital machine is implemented,
incarnated in the physical reality it gives a general purpose computer.
But I discovered them when studying the bacterium Escherichia Coli,
and would I have not found the little book on Godel theorem, I would
have become a biologist.
What fascinated me in the bacteria was already there in arithmetic, or
in simple relation between words.
Now, I can understand that you will not like the second half of my
study. Indeed, to be honest, even without Mechanism, I am skeptical
to the idea that some stuff exist: if I try to conceive it, I see
some infinitely rigid stuff, and can only changing this by changing
space, time energy relation, making me already open to the idea that
"physics" is an invariant of the observable from a person
perspective. A person, to me, is immaterial, even if to manifest
itself relatively to other persons and entities, it implements
itself in a logic with the good "linear and" or "tensor product".
It is more easy to explain the "illusion" of stuff to an immaterial
consciousness than to explain
the illusion of consciousness (if only that could mean anything) to
a piece of stuff, usually
described as inert (as it should be if it is primitive).
I agree to above but
The consciousness might be immaterial in terms of the known matter
or physical energy,
as known to the current science. But this should not imply to mean
that is devoid of any
"ontology with a stuff" otherwise it will have no primordial
existence. The consciousness
itself might be a unique ontology with some unique stuff.
I remain intrigued by your willing some stuff in the big picture, even
when we don't see it.
I, on the contrary, am very skeptical on what I see, and even super-
cautious how to interpret it.
But even the physicist in me (I am mathematician officialy, but I
think I am a theologian, actually) does not believe in stuff.
What could that be?
Assuming Mechanism, we do have a theory of an observer, which is
immaterial, like
numbers, yet partially rational. The observer is the universal
machine, in the purely
arithmetical sense of the terms (as apparent in the early proof of
the very important theorems
of Gödel 1931).
As indicated in the aforesaid, observer-- a conscious one, though
might be immaterial
in terms of the current knowledge of the matter/energy, but it is
possessed with some
"ontology with a stuff" with consciousness itself being some unique
unknown stuff.
This seems weird for me. I don't conceive consciousness as a stuff at
all. So much that eventually I prefer to ged rid of the stuff to ease
the mind-body problem, somehow.
I understand that the physical reality looks stuffy, spatial,
temporal, but mechanism go closer to Kant, the young Hegel, and more
generally toward idealism. Space, time, even more so with quantum
mechanics are observable (well, with some problem for time, but let it
go for now). Observation is a first person experience, and can be
dreamed.
In arithmetic, the physics is made "very solid", as it is not a dream
among all dreams, but a special non trivial sum on all dreams.
Other wise,
there can't be any primordial existence of the consciousness.
Only because you assume that some stuff is needed for existence. But
that is what I doubt.
Universal machine can't
be an observer since universal machine is nothing but the
manifestation of some physical
laws of nature and none of the Laws can emerge out but from the
cosmic consciousness.
This is what I will try to explain: the universal machine exists as a
special number (successor of successor of ... 0), when in special
relation with other numbers, and they do dream, in a technical sense,
and, with mechanism, in the human sense.
If you take universal machine as observer in the arithmetical sense
only then it can't have'
the primordial existence since arithmetic per se has no "ontology
with stuff:
and for the primordial
existence of any thing some "ontology with stuff" is necessary
That is what you should try to convince me. I do not see the necessity
of stuff in general, and I do see its incompatibility with mechanism.
But I propose a test, not claim any truth here.
Mechanism explains precisely where the illusion of stuff arise, and
should explain its shape, with the group theory, the number 24 (which
plays some role at many places in math and physics (the favorite
number of Ramanujan).
Then we can forget the hypothesis of mechanism, as the result shows
that for the ontology
we can use only the combinators and reduction, or the lambda
expressions and abstraction,
or the more familiar natural numbers with addition and
multiplication:
0 ≠ (x + 1)
((x + 1) = (y + 1)) -> x = y
x = 0 v Ey(x = y + 1)
x + 0 = x
x + (y + 1) = (x + y) + 1
x * 0 = 0
x * (y + 1) = (x * y) + x
All the above relations reflect the physical reality of nature. If
x= 2 tables ( or any discrete entity)
and if we produce I more table on the scene, we find that on the
scene, all the tables don't
vanish i.e it does not become 0. It is due to this observed
physical reality that we assume the realtion
0 is not = (x+1)
The human discovery of the natural numbers reflects the nature already
"using" the idea, but might be explained without a stuffy ontology.
But here a word of caution and reality, 0 is not + (x+1) exist only
in arithmetic only as part of our
assumption. But otherwise, none of the two tables or any two
entities are exactly equal. Therefoe,
none of the arithmetical relation reflects the complete reality of
nature.
The explanation of the appearance of Nature requires the theology of
the universal machine. Nature is an object emerging from that sum on
infinitely many dreams, and structured by the points of view of the
universal machine available by incompleteness (and the fact that the
machine is aware of its incompleteness).
Here I depart from some Pythagorean which have a sort of stuffy view
of the numbers, and thought that material object were made of numbers.
Nothing is made of numbers, but their relations determine all the
computations, and the first person are particuliration of the
universal consciousness flux of the universal machine.
Nothing else is assumed, nor can be assumed if we assume Mechanism.
Infinity axiom leads to
internal inflation of histories, but the universal numbers cannot
avoid them from inside, and get lost
in what is, from inside, only the consequence of the axiom above.
But the whole arithmetic starts with 1+1=2 which is an assumption.
All the subsequent assumption
might be the extension of this assumption. Mechanism, as I
understand, is the manifestation of the
physical Laws, governing the course of movement.operation of
nature, as representable in some
number/arithmetic form
I will have to explain that the digital mechanism I talk about is a
recent discovery in math. The computer are physical being, but
physical will be explained in term of the arithmetcal dream of the
digital machine which are (relatively) active in the arithmetical
reality.
The observer is defined by any number believing in the axioms above,
together with
the "induction axioms", i.e. the infinitely many formula with the
shape
(F(0) & Ax(F(x) -> F(s(x))) -> AxF(x), with F(x) being a formula in
the arithmetical language.
Of course, it is long and tedious to define that observer in the
language of arithmetic. For example
you have to define list of symbols in arithmetic; but you can use
the uniqueness of prime
decomposition, or the "chinese lemma" to proceed, and this is how
Gödel did in his 1931 paper. The list (4, 3, 2) is coded by 2^4 *
3^3 * 5^2. The details are in the original paper of Gödel, or in
good textbook in mathematical logic.
One might adopt any methodology to define observer in the language
of arithmetic but that is not
going to change the real identity and status of the observer. The
observer is a conscious fundamental
entity having some "ontology with stuff".
In your theory. But you will need special infinities to avoid the
digital mechanist consequence.
It is, therefore, due to this it has some fundamental existence.
But none of the numbers has any 'ontology with stuff", therefore,
none of the numbers can be the
conscious observer though in arithmetic one may any assumption or
play with numbers.
One more thing worth noting. You can't define any thing with numbers
unless there is the priori
presence of the consciousness. So consciousness is prior to any
definition. An inert stone is unable'
to define any thing.
Once a machine believes enough arithmetical formula, she become
Turing Universal, and *then*,
if furthermore she believes in the induction axioms, she get enough
introspective power to know that
she is universal, and that she can only belong to a many-dream
structure. The view from inside is
infinitely more complex than the view from outside. Adding stuff
cannot help, unless you abandon
Mechanism
These beliefs in machines have not come on their own. These beliefs
have been incorporated in machine
by our consciousness when we started with the base assumption of
1+1=2.
Enough for today. Balance comments next time.
Thanks you for your effort. It is clear where we disagree. You assume
some stuff, and I am agnostic, but also I show that stuff makes no
sense with mechanism, except as phenomenological perception field of
some collection of number-machine in arithmetic.
We have just quite different metaphysical premise. But you have a sort
of physicalist conception of machine, so that I might need to train
you on the digital machine, in case you would like to better
appreciate my point, but of course, there is no obligation. I will
"annoy" only those who want both mechanism and materialism.
I will send a post with the definition of the observer soon, in the
coming weeks. I promised this on another list, and it will be useful
here for possible further reference. I will also try to say some word
on the arithmetical enlightenment (a risky task as we will be close to
give a name to the unnameable).
Best,
Bruno Marchal
http://iridia.ulb.ac.be/~marchal/
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