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).`

The 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 = 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.

Hmm....

Pearce says in his article (http://www.hedweb.com/nihilism/ nihilfil.htm): "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.`

The 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, unfortunately). 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.`

Bruno

On Sep 20, 2:05 am, Roger <roger...@yahoo.com> wrote:Jon,Hi. Thanks for the feedback. The empty set as the buildingblockof 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 replicateitselfand produce the universe, energy, etc. This is needed because it appears that there's more to the universe than just a single emptyexistent state and that things are moving around. What I suggestedinthe 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'sconceptionof "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 boundarydefiningwhat is present and thus giving "substance" or existence to the thething. This complete definition, edge, or boundary is like thecurlybraces 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. Ithink that the existenet state that is what has been previouslycalled"absolute non-existence" has the unique property of being able to reproduce itself.4. This process continues ad infinitum in kind of a cellularautomaton-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 tothepresence 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 myidea, I think, by saying that the observed is what has previouslybeencalled "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 universe. Anyways, thanks again for restarting this thread! Roger 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 WeighsIn" onMay 16, 2005 at 9:24pm:"I wonder if you and/or any other members on this list have anopinionabout the validity of an article athttp://www.hedweb.com/nihilism/nihilfil.htm . . ."I would like to continue that discussion here on this thread,becauseI believe the article Norman cites provides a satisfying answer thequestion "Why does anything exist?," which is very closely relatedtothe question "Why is there something rather than nothing." Theauthoris 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, inprinciple, be derived from the properties of the empty set, Ø" Ithinkthis last sentence, if true, would support Tegmark's Mathematical Universe Hypothesis, because if math is derivable from nothing (asPearce thinks) and physics is derivable from math (as Tegmarkthinks)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 ofNothing", which I'm reading. He formulates an equation for theamountof 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 rearrangeall physics equations so they equal zero, then add them all up.Afterall, 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,JonOn 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'ma 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 mathematicsandphysics are at:https://sites.google.com/site/ralphthewebsite/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,RogerGranet(roger...@yahoo.com)Abstract:In this paper, I propose solutions to the questions "Why dothingsexist?" and "Why istheresomething rather than nothing?" In regard to the first question, "Why do things exist?", it is argued that athing exists if the contents of, or what is meant by, that thingarecompletely defined. A complete definition is equivalent to anedge orboundary defining what is contained within and giving “substance”andexistence to the thing. In regard to the second question, "Whyistheresomething rather than nothing?", "nothing", or non-existence, isfirst defined to mean: no energy, matter, volume, space, time,thoughts, concepts, mathematical truths, etc.; and no minds tothinkabout this lack-of-all. It is then shown that this non-existence itself, not our mind's conception of non-existence, is the completedescription, or definition, of what is present. That is, noenergy,no matter, no volume, no space, no time, no thoughts, etc., inand ofitself, describes, defines, or tells you, exactly what is present.Therefore, as a complete definition of what is present,"nothing", ornon-existence, is actually an existent state. So, what hastraditionally been thought of as "nothing", or non-existence, is,whenseen 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".--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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