On 28 Oct 2014, at 09:25, Peter Sas wrote:
First my apologies to you and Brent for the mix up. I'm new to this
wonderful forum, and the format still disorients me a bit...
No problem.
which is why the universe exists in the first place, that is, it is
not nothing (= ontological difference).
You wrote: 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.
Partly I am thinking of Heidegger here... not I have much respect
for him as a philosopher, on the contrary... but in the early phase
of his career he had some nice ideas, such as this one about
ontological difference: Being (with capital "B") as that which lets
beings be is not itself a being, it is rather a kind of Nothing
which acts like a counter foil to beings: we experience beings as
existing because we can contrast them with the Nothing which is
revealed to us through Angst and our being-unto-death...
Heidegger's approach to nothing is of course thoroughly
existentialist-phenomenological... According to me, this means that
he never really broke away from Kantian subjectivism: beings as
phenomena remain dependent on the subject's (Dasein's) orientation
to the nothingness of death... I would rather opt for an objectivist
approach to nothing, as 'something' that 'exists' independently and
prior to human beings (and indeed as prior to the universe as a
whole).
To me "nothing" (and "everything") are terms which are theory
dependent. It depends a lot of the *things*. The quantum vacuum is a
nice example of a quite complex notion of nothing. It is already
Turing universal, and it assumes more than most universal systems, for
its description.
My reasoning in this regard is very basic. To explain why there is
something rather than nothing we have to start with nothing,
Hmm... I don't think you can extract anything from just "nothing"
without adding some laws or principle. I can generate all the ordinals
from the empty set, but I need some strong axioms, like the reflection
principle.
since otherwise we end up either in an infinite regress or a vicious
circle.
Or we just get modest and have faith in some thing.
That is, as long as we start from some primordial being (e.g. God or
the Platonic realm of eternal truths) as the cause of all other
beings, we still have to explain why that primordial being existed/
exists in the first place.
But here there is a surprise, which might be seen as obvious, but
technically, it is not that obvious. We cannot derive the existence of
a universal machine without postulating the existence of a universal
machine. But all universal machine can understand that this is indeed
impossible.
And then we have to postulate either a still more primordial being
(regress) or suppose that the primordial being is self-causing,
which seems absurd.
OK.
The only possibility, then, is to start with the concept of nothing
and see if we can explain being on that basis.
Plotinus too describes the One as a kind of nothing
I am not sure. It just make the ONE distinct of the realm of ideas
(the Noùs), which is the realm of being. Both matter and the ONE, will
be outside that realm. Matter as an intrinsic limitation and
indetermination of the ONE, and the "universal SOUL".
The ONE of plotinus looks more like a big indifferentiate whole, than
a nothing.
but in my view that's because he holds a apophatic theology, where
the One transcends our conceptual capacities, so we can only
conceive it as a nothing whereas in fact it is rather the opposite,
an ontological plenitude.
I think Plotinus would not disagree on this. But it is the
transcendental character which makes it unable to put itself in the
picture (a bit like in most set theories, but not all, the collection
of all sets is not a set, or like Plotinus explains already the
collection of all numbers is not a number). But it is still something.
So in my view, a neo-Platonic approach is still not radical enough,
its conception of nothing is still not the absolute nothing with
which we have to start if we want to answer Leibniz' question
(Heidegger would say: Plotinus is still onto-theology, the confusion
of Being with a being).
I agree with onto-theology, as eventually we make clear the basic act
of faith with computationalism it is will take many form, like the
belief in principles, like x + 0 = 0, or Kxy = x) or the stronger "yes
doctor" (to the doctor who will replace your brain by a digital
transplant).
The onto needs faith, and that is why it is a theology.
So how to go from the absolute nothing to being? Here my intuition
is that nothing is a self-negating 'quantity' which as such
'produces' being. I know that's terribly vague and even a bit
mystical, and I'm struggling to make it more precise.
The unary set intersection of the empty set gives the whole universe
of set. But you need to assume the notion of set (which are much
stronger that the axioms of numbers).
You can get mathematically to a lot of things, from a notion of
nothing, but in all case you will have to assume *something*, for your
derivation making sense in some communicable way.
I thought I had found one indication for this point of view in the
idea of the zero-energy universe,
You assume a physical universe. With computationalism, it is
undecidable if there is anything more than numbers and the laws of
addition and multiplication. from this you can derive the existence of
all finite piece of computations
and we are indeminate on them, and the physical realities are
persistent hallucinations, obeying laws themselves.
where positive and negative energy precisely cancel each other out,
so that perhaps we can describe the origination of the universe as a
kind of splitting of 0 into 1 and -1 (i.e. into positive and
negative energy). But now I've learned from the contributions on
this forum that the idea of the zero-energy universe is much more
problematic than figures like Hawking and Krauss make it appear.
What I also found very congenial is the notion of quantum
fluctuation, with particle-antipartice pairs popping into existence
from the fluctuating 'zero'-energy level of the vacuum (I wonder: is
the energy of the vacuum positive or negative or neither?).
Well, it is full of energy, so much that physicists find more and more
sophisticate ways to put them under the rug: it is the renormalization
field. In fact there are relation with knot theory, Hopf algebra,
quantum groups.
You can see a knot as a space-time diagram of a vacuum fluctuations.
If QM and quantum filed theories are correct, I would bet "we" are in
a quantum fluctuations, burt with computationalism that is something
we must derive this from the a-physical) number relations.
But as you also suggested, the vacuum is not the absolute nothing
since the vacuum is spatial and seething with quantum activity.
Anyway, I still feel that this splitting of the vacuum into
particles andd antiparticles fits hand in glove with a dialectical
approach to nothing as self-negating (for on that account, nothing
is both itsef and its own antibeing of sorts). But I admit, these
are just highly speculative intutions.
You might read the book by Louis Kauffman, and search for his paper.
My approach is more systematic, I sudy the consequence of the
assumption that my body or brain is Turing emulable, then this put
constraints, indeed all constraints but the geographico-historical, on
what matter can be. It explains partially consciousness also, without
any magic, and with explanation why they are gaps, and how to get over
them. But it shows also, that we are far more ignorant about "reality"
than the current Aristotelianism/naturalism/materialism let us think.
As for the contradiction inherent in the concept of nothing, this
seems to be a well-known idea, thought hard to make precise. Carnap
of course famously argued against Heidegger that his concept of
nothing is inconsistent. Partly Carnap's reasoning goes as follows:
define Nothing as N such that if x exists then x is not equal to N,
so if N exists (i.e. if N = x) then N is not N, hence a contradiction.
Carnap, of course, takes this to show that the concept of nothing is
nonsensical. But given the fact that we can only answer Leibniz'
question by starting with nothing, I think we have to see this
contradiction as an objective reality which explains why there is
being at all.
Well, to assert that there is nothing seems to me just a blattant lie.
That some notion of nothing can exist, I experience everyday. There
might be nothing in the fridge, at times.
I thought I had also found a way to show the inconsistency of
nothing through set theory, but that too turns out to be more
complicated than I expected. The reasoning is quite simple and goes
as follows: First consider the axiom of extensionality: sets are
identical iff they have all their elements in common. Then consider
the empty set and note that, since it doesn't have any elements, it
can't have elements in common with itself,
yes. The binary intersection of { } with { } gives { }.
But the unary intersection gives all sets. But a bit like my computer
tells me "error" when I ask it to divide by zero.
zero and infinity, nothing and everything are old friends, that's for
sure.
so it is disjoint with itself. But then from the axiom of
extensionality it follows that the empty set is not identical with
itself! But as it turns out, it seems that the axiom of
extensionality is formulated in such a way that this contradiction
cannot arise.
A good thing.
Still, the fact that the empty set has no elements makes it in my
view a very troublesome set with no clear identity-conditions. The
late philosopher E.J. Lowe argued something similar and concluded
that set theory should do away with the empty set.
It took so much time to the mathematician to accept that zero is a
number, like the others. Set theoricians learned to lesson, and knows
that the empty set is very important. It is an initial or final
elements in the categories of sets.
I wouldn't argue that, however, since I'm quite smitten with the set-
theoretic derivation of math recursively from the empty set (the Von
Neumann approach). Perhaps what I am looking for is a kind of
paraconsistent approach to the empty set, where it is precisely the
contradiction in the concept of the empty set that will allow us to
derive math from it.
Hmm... Paraconsistent logic is useful for handling some fuzziness in
informal reasoning, but I am a bit conservative on having clear and
crisp starting logic. Then you can see how ideally correct machines
get "paraconsietnt naturally" already. But OK? it is in some weak form.
In this regard I am also intrigued by Frege's definition of the
empty set as the set of all things that are not self-identical.
Though I am not sure if from this it follows that the empty set too
is not self-identical.
Why. Frege just used a contradiction to make sure his set is empty. I
could define the empty set by the set of all french higher than 42 km,
and lesser than 1 mm.
Now if ever you find a french lesser than 1mm, or higher than 42 km, I
will change the definition, instead of clailing that the empty set is
not empty.
I let you know that I don't really believe in sets, nor do I
disbelieve in them. I am agnostic, but most interesting sets are
numbers in disguise, in my opinion. I do not assume set theory in the
TOE extracted from computationalism, which is a tiny segment of the
arithmetical reality.
After all, the set of all cars is not itself a car. On the other
hand, if we define sets extensionally, and we adopt Frege's
definition, than the extension of the empty set is not-self-
identical, which then seems to imply that the set itself is not-self-
identical as well.
?
Of course, if we start with a contradiction, then ex falso sequitur
quodlibet and the entire system will be vitiated.
In most logic, but not in the relevance logics. But there are more
useful in artificial intelligence than in the fundamental matter, I
thinK.
Unless we find a way to somehow contain the contradiction of the
empty set (or nothing). My intuition here is that dialectics may be
of use here. It seems clear to me that we can say: since nothing is
inconsistent, and since being is the negation of nothing, being must
be consistent.
Both nothing and being can be consistent, without being real.
I wish I could develop such ideas in a more formal fashion. Perhaps
looking into paraconsistent set theory might be of use. If you have
any suggestions I would be very much obliged.
I guess you know the books by Graham Priest. He wrote also a nice
introduction to non-classical logics.
personnaly I am interested in the mind body problem, and I assume what
is needed to define a universal Turing machine. Obviously we get that
truth *about* machines escape what the machines can know, belief,
observe, and so classical logic is the simplest to talk about those
ignorance and limitations.
I am not in any way connected to a university. I got a PhD in
philosophy in 2000, but I did not have an academic career. So forums
like this one are the only means I have for discussing these things
with others and I am sincerely grateful for that!
You are welcome.
Also thanks for you paper. I will certainly read it (i.e. I will
attempt to read it, since math and formal logic are not my forte,
unfortunately).
The UDA (Universal Dovetailer Argument does not require much). The
translation of the UDA in aruthmetic requires familiarity with Gödel's
method of arithmetization of meta-arithmetic, and the works which
followed that. There are good book, but it is technically demanding
(alas).
The very idea of a computational approach to neo-platonism certainly
seems very original. By the way, I am not such a philosopher who is
averse to a scientific approach, quite the contrary, as you may have
guessed already.
Nice.
I do think however that presupposing a mathematical reality from
which physical somehow derives is still not enough to answer
Leibniz' question, for why then is there the mathematical reality to
begin with?
It comes from the dream of numbers. But we have to assume the numbers,
and the laws of addition and multiplication. (or anything Turing
equivalent).
Addition only gives rise already to an incredibly complex reality,
likewise for multiplication, but they are not rich enough to sustain a
universal machine. That comes when you marry addition and
multiplication, you get the universal machines, the prime numbers, and
they put some mess in Plato heaven.
We can say logic and math are timelessly true, but I think we still
want to know why that is so.
You can even forget logic and most of math. just some identity axioms
and few rules will do, and you get the Turing universality, then you
get a sort of God which cannot not lose itself in innumerable stories,
and develop beliefs in gods or other realities.
It is bit like aurobindo answers to the question of this thread (that
I like to quote sometimes):
What, you ask, was the beginning of it all?
And it is this ...
Existence that multiplied itself
For sheer delight of being
And plunged into numberless trillions of forms
So that it might
Find
Itself
Innumerably (Aurobindo)
The Mandelbrot set illustrates this already, in some way.
Moreover: there is also a certain subjectivity involved here, since
WE think they are timeless because WE cannot imagine a situation in
which logic and math were not true,
I don't know what is "math". But I agree for what has been called the
separable part of math, where intuitionists and classical logicians
agrees: the natural numbers, and simple laws.
but then the timelessness is predicated on our cognitive
limitations, which does not show that math and logic are in
themselves timelessly true.
Indeed. But I do not see why simple arithmetical facts (like machine j
stop on input k after 78 steps) can be said to depend on times in
anyways.
Peter
I guess Richard was referring to you, and not to Peter Jones. OK.
Bruno
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