On 21 Sep 2011, at 08:01, nihil0 wrote:

Hi everyone,

I would like to reply to various people's comments since my post so
far. I'll try to be as clear as I can, though words aren't well cut
out for metaphysics, as you probably are aware.

I think we all want to know what principles and axioms we must accept
as primitives to construct a theory of everything. However, I want to
see how far we can get assuming no primitives. By primitives, I mean
truths (or as Nietzsche liked to call them, "assumptions") that can't
be proved with certainty, but can be used to derive and justify many
other truths. An example of a primitive is "I am not a brain in a
vat"; I can't prove it beyond an unreasonable doubt, but nonetheless I
take it for granted in my normal day-to-day theorizing about the
world. Bruno says he takes as primitives in his TOE axioms such as
comprehensibility and reflection, and 0 and succesor.

Not really. Well, not at all. comprehension and reflection are some possible axioms which together with some other axioms can axiomatize set theory (in first order logic). In that theory you can define 0, and successor and develop arithmetic. Set theory is a stupendously rich theory. far too rich, and personnaly I don't believe in it, even if I appreciate it a lot. Actually I use it also as an example of a Löbian machine, with much more power (in the ability to prove even just arithmetical statements) than Peano Arithmetic (my generic observer-being).

But the TOE, which is meta-extracted from the mechanist hypothesis, is a much weaker theory. It is Robinson Arithmetic. basically it is logic + the addition laws:

Ax x + 0 = x  (0 adds nothing)
AxAy  x + s(y) = s(x + y)   ( meaning x + (y +1) = (x + y) +1)

and the multiplication laws (axioms)

Ax   x *0 = 0
AxAy x*s(y) = x*y + x

with "A" = FOR ALL (the universal quantifier) and "E" = "IT EXISTS" (the existencial quantifier).

Unlike a primitive truth, a tautology is a vacuous, empty truth.

I don't think so. If that were true, we would not have axioms in propositional calculus, nor any weaker logic than classical logic. But there are an infinities of weaker logics than classical logic (like intuitionist logic, quantum logic, relevance logic, linear logic, etc.). It is even a fashion among some analytical philosopher to try to cast doubt on the classical tautologies, which indeed are actually very strong statements. There are quasi-operational definition of Platonism in math. They lead to the acceptation of non constructive proofs and object. For example intuitionists reject the excluded middle (p V ~p).

proposition "apples are apples" conveys no meaning. X = X is just the
Law of Identity.

I believe contra Bruno that all mathematical/logical/physical truths
are tautological.

You can't be serious. You extend the meaning of tautology too far.

Somehow or other, they must all be reducible to 0 =

Prove me that 17 is a prime number, from 0=0.

Bertrand Russell said, "Everything that is a proposition of logic
has got to be in some sense or the other like a tautology."

Bertrand Russell is a nice guy, but its philosophy of math did not survive the Gödel's discovery. Russell and Whitehead wrote Principia Mathematica to illustrates that everything in math is a tautology, but Gödel blew up that very idea. Gödel 1931 paper concerns a rigorous version of principia mathematica, and a proof that such approach can't work at all. It is a reason of joy, because it makes math FULL of unpredictibel surprises, of many varieties.

Unfortunately, I cannot back up this awfully ambitious thesis since
I'm not a mathematician, I'm just a philosophy major at the University
of Michigan. Many mathematicians (perhaps Gödel) might have already
disproven it or (worse) shown it to be unfalsifiable.

Gödel disprove it, indeed.

Nonetheless, I
trust Russell and Pearce on this one.


Pearce says in his article (http://www.hedweb.com/nihilism/

"The whole of mathematics can, in principle, be derived from the
properties of the empty set, Ø.

No, you can't.
In fact the whole of mathematics cannot be derived from anything, not even infinite structures. It probably does not even make sense.

[Since Ø has no members, in the
standard set-theoretic definition of natural numbers it can be
identified with the number zero, 0.

It is better to say that the empty set can implement, or represent, the number 0. You cannot identify them when thinking about conceptual issue. If you *do* math, you can identify them as an abuse of language to be shorter and more efficacious, but for conceptual reasoning, this can only be misleading. 0 is simply not the empty set. You can say that 0 is the number element of the empty set, and you can represent in set theoretical language, the arithmetical notion of 0.

(this is still problematic; should
0 be regarded, not as the empty set, but as the number of items in the
empty set? And what's the ontological status of the empty set?)]

In most set theories, you can usually prove the existence of the empty set. That is Ex(x = { }) can be proved from the axioms and inference rules.

number 1 can be defined as the set containing 0, i.e. simply the set
{0} that contains only one member. Since 0 is defined to be the empty
set, this means that the number 1 is the set that contains the empty
set as a member {Ø}. The number 2 can be understood as the set, {0,
1}, which is just the set {Ø, {Ø}}. Carrying on, the number 3 is
defined to be the set {0, 1, 2} which reduces to {Ø, {Ø}, {Ø, {Ø}}}
Generalising, the number N can be defined as the set containing 0 and
all the numbers smaller than N. Thus N = {0, 1, 2 ...N-1} is a set
with N members. Assuming only the concept of the empty set Ø, each of
the numbers in this set N can be replaced by its definition in terms
of nested sets. Proceeding to derive the rest of maths from the
properties of the natural numbers is more ambitious; but it's
conceivable in principle.

Nowadays, we know it is not. Even set theory itself (a quite powerful theory) cannot get all the "simple" arithmetical truth. There are just no complete theory at all.

All that then remains to be done is to
explain the empty set i.e. why (a condition analogous to our concept
of) the empty set must be the case]"

Pearce later concludes that "if, in all, there is 0, i.e no (net)
properties whatsoever, then there just isn't anything substantive
which needs explaining."  Jason and Roger, are you satisfied by this
explanation of why there doesn't need to be a meta-explanation of why
anything exists?

Bruno you might object and say that Pearce takes as a primitive "the
standard set-theoretic definition of natural numbers", in which zero
is identical with the empty set and sets can be nested inside others
to define other numbers (successor). But if zero and the empty set are
identical, then their equality doesn't require further proof, it just
is the Law of Identity. Also, I think Pearce's idea that reality is
constituted (somehow) by empty sets nested in other empty sets
supports the following idea of Roger's: "the existent state that is
what has been previously called "absolute non-existence" has the
unique property of being able to reproduce itself." Perhaps you guys
are saying the same thing just in different words.

You might be interested in what I am explaining on this list. From an assumption about the functioning of the brain, I derive that the TOE is any first order specification of any theory which can prove the existence of a universal machine. Amazingly, ver simple theories can do that, like addition and multiplication (like above), or the combinators laws Kxy = x and Sxyz = xz(yz). This already entails the existence of believer (or theories much richer that those theories, *in* the theory, and physics (both quanta and qualia) arise from a first person indeterminacy (which most on this list seems to have grasped, I think).

I think the Law of Identity (0 = 0) is the fundamental law of reality,
though it's a rather circular and vacuous law. Jason you say, "A meta-
reality with no laws permits the existence of any structure that can
exist." I think you imply here that only *some* things can exist. I
think you would agree with me, then, that the Law of Identity
determines what can and cannot be the case. For example, I cannot have
one hand and two hands at the same time and place (though I might have
two hands in one Hubble volume and one hand in another,

Stephen, you say "Existence exists". Heidegger said "Nothing
noths." (I just thought that might titillate you)

Any comments and critiques are welcome!

I really hate to look like patronizing, but I hate not to be honest, also, and I think you should study some good book on logic (or better to follow some good introductory course in both proof theory and model theory). I feel sorry, but Gödel's theorem impact is not just the destruction of HIlbert's program, but the whole philosophy of math by Russell.


On Sep 20, 2:05 am, Roger <roger...@yahoo.com> wrote:

Hi. Thanks for the feedback. The empty set as the building block
of existence is exactly the point I as making in my original posting
that started this thread.  What you're referring to as the empty set,
I was referring to as how what has previously been called absolute
"non-existence" or "nothing" completely describes, or defines, the
entirety of what is present and is thus an existent state, or
something. This existent state of mine is what others would call the
empty set.   The reason this is worth thinking about is because just
saying that the empty set is the basis of existence doesn't explain
why that empty set is there in the first place.  This is what I was
trying to get at.  Additionally, there has to be some mechanism
inherent in this existent state previously referred to as absolute
"non-existence" (ie, the empty set) that allows it to replicate itself
and produce the universe, energy, etc. This is needed because it
appears that there's more to the universe than just a single empty
existent state and that things are moving around. What I suggested in
the paper at my website was that:

1. Assume what has previously been called "absolute non-existence".

2. This "absolute non-existence" itself, and not our mind's conception
of "non-existence", completely describes, or defines, the entirety of
what is there and is thus actually an existent state, or "something".
This complete definition is equivalent to an edge or boundary defining
what is present and thus giving "substance" or existence to the the
thing. This complete definition, edge, or boundary is like the curly
braces around the empty set.

3. Now, by the assumption in step 1, there is also "absolute non-
existence" all around the edge of the existent state formed in step
2.   This "absolute non-existence" also completely describes, or
defines the entirety of what is there and is thus also an existent
state.  That is, the first existent state has reproduced itself.  I
think that the existenet state that is what has been previously called
"absolute non-existence" has the unique property of being able to
reproduce itself.

4. This process continues ad infinitum in kind of a cellular automaton-
like process to form in a big bang-like expansion a larger set of
existent states - our universe.

    This is described in more detail in the paper at my website at:

https://sites.google.com/site/ralphthewebsite/filecabinet/why- things-...

There's also some more detail on how the above process can lead to the
presence of energy in the universe.

    Tegmark's assumption of a mathematical construct as the basis of
our existence doesn't explain where this construct comes from or how
it reproduces to form the universe.  Wheeler's idea that the
distinction between the observer and the observed could be the
mechanism of giving existence to non-existence could be fit into my
idea, I think, by saying that the observed is what has previously been
called "absolute non-existence", and the observer is the fact that
this "absolute non-existence" completely defines the entirety of what
is present and is like the edge or boundary defining what is there.
Speculating even further, one could say that this edge or boundary is
the same as the strings/membranes that physicists think make up the

    Anyways, thanks again for restarting this thread!


On Sep 19, 2:27 am, nihil0 <jonathan.wol...@gmail.com> wrote:

Hi everyone,

This is my first post on the List. I find this topic fascinating and
I'm impressed with everyone's thoughts about it. I'm not sure if
you're aware of this, but it has been discussed on a few other
Everything threads.

Norman Samish posted the following to the thread "Tipler Weighs In" on
May 16, 2005 at 9:24pm:

"I wonder if you and/or any other members on this list have an opinion
about the validity of an article athttp://www.hedweb.com/nihilism/nihilfil.htm
. . ."

I would like to continue that discussion here on this thread, because
I believe the article Norman cites provides a satisfying answer the
question "Why does anything exist?," which is very closely related to the question "Why is there something rather than nothing." The author
is David Pearce, who is an active British philosopher.

Here are some highlights of Pearce's answer: "In the Universe as a
whole, the conserved constants (electric charge, angular momentum,
mass-energy) add up to/cancel out to exactly zero. . . Yet why not,
say, 42, rather than 0? Well, if everything -- impossibly, I'm
guessing -- added up/cancelled out instead to 42, then 42 would have
to be accounted for. But if, in all, there is 0, i.e no (net)
properties whatsoever, then there just isn't anything substantive
which needs explaining. . . The whole of mathematics can, in
principle, be derived from the properties of the empty set, Ø" I think
this last sentence, if true, would support Tegmark's Mathematical
Universe Hypothesis, because if math is derivable from nothing (as
Pearce thinks) and physics is derivable from math (as Tegmark thinks)
and, then physics is derivable from nothing, and presto we have a
theory of everything/nothing.

I think Pearce's conclusion is the following: everything that exists
is a property of (or function of) the number zero (i.e., the empty
set, nothing). Let's call this idea Ontological Nihilism.

Russell Standish seems to endorse this idea in his book "Theory of
Nothing", which I'm reading. He formulates an equation for the amount
of complexity a system has, and says that "The complexity [i.e.,
information content] of the Everything is zero, just as it is of the
Nothing. The simplest set is the set of all possibilities, which is
the dual of the empty set." (pg. 40) He also suggests that Feynman
acknowledged something like Ontological Nihilism. In vol. 2 of his
lectures, Feynmann argued that the grand unified theory of physics
could be expressed as a function of the number zero; just rearrange
all physics equations so they equal zero, then add them all up. After
all, equations have to be balanced on both sides, right?

Personally, I find Ontological Nihilism a remarkably elegant,
scientific and satisfying answer to the question "Why is there
something instead of nothing" because it effectively dissolves the
question. What do you think?

Thanks in advance for your comments,


On Aug 8, 2:40 am, Roger <roger...@yahoo.com> wrote:

Hi. I used to post to this list but haven't in a long time. I'm
a biochemist but like to think about the question of "Why isthere
something rather than nothing?" as a hobby.  If you're interested,
some of my ideas on this question and on  "Why do things exist?",
infinite sets and on the relationships of all this to mathematics and
physics are at:


An abstract of the "Why do things exist and Why istheresomething
rather than nothing?" paper is below.

    Thank you in advance for any feedback you may have.

Sincerely ,

Roger Granet (roger ...@yahoo.com)


In this paper, I propose solutions to the questions "Why do things
exist?" and "Why istheresomething rather than nothing?"  In regard
to the first question, "Why do things exist?", it is argued that a
thing exists if the contents of, or what is meant by, that thing are completely defined. A complete definition is equivalent to an edge or boundary defining what is contained within and giving “substance” and existence to the thing. In regard to the second question, "Why istheresomething rather than nothing?", "nothing", or non- existence, is
first defined to mean: no energy, matter, volume, space, time,
thoughts, concepts, mathematical truths, etc.; and no minds to think
about this lack-of-all.  It is then shown that this non-existence
itself, not our mind's conception of non-existence, is the complete
description, or definition, of what is present. That is, no energy, no matter, no volume, no space, no time, no thoughts, etc., in and of
itself, describes, defines, or tells you, exactly what is present.
Therefore, as a complete definition of what is present, "nothing", or
non-existence, is actually an existent state.  So, what has
traditionally been thought of as "nothing", or non-existence, is, when seen from a different perspective, an existent state or "something". Said yet another way, non-existence can appear as either "nothing" or
"something" depending on the perspective of the observer.   Another
argument is also presented that reaches this same conclusion.
Finally, this reasoning is used to form a primitive model of the
universe via what I refer to as "philosophical engineering".

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