Hi! On 9/19/2011 5:24 AM, Bruno Marchal wrote:

On 19 Sep 2011, at 08:27, nihil0 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.

`Welcome to the party! Please feel free to express your ideas and`

`thoughts. :-)`

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 opinionabout 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,

`I think I could agree with this reasoning so long as the`

`explanation does not go to an argument for meaninglessness. While we can`

`accept that in the totality of existence all differences dissolve and`

`this the expressibility itself of our questions vanishes, this should`

`not be used as a reasoning to abandon the possibility of meaningfulness`

`at our level of existence. A similar argument and response exists on the`

`nature of Time. While all notions of temporal transitivity vanish in`

`the limit of a total system, as exemplified by the Wheeler-Dewitt`

`equation <http://arxiv.org/abs/physics/9806004>, this does not act to`

`void finite subsets of the Totality from having a real notion of time as`

`a measure of change`

`<http://faculty.uca.edu/rnovy/Aristotle--Time%20is%20the%20Measure.htm>.`

`A great article discussing this particular reasoning can be found here:`

`http://arxiv.org/pdf/gr-qc/9708055`

We have of course already discussed this a lot.In a nutshell, you cannot derive anything just from the empty setalone: you need some mathematical principles or axioms, like thecomprehension and the reflection axioms. This leads to an axiomaticset theory, which is nice but somehow too much powerful. But OK, settheory is already a Löbian observer, and you can derive everythingfrom this, although you still need some definition, notably of theinternal observers. Assuming mechanism, to proceed in that direction,then, as I have often explained, you get the derivation of everythingincluding a notion of "God" (truth), souls and the precise laws ofphysics (but this is a sequence of hard number theoretical problems,yet the conceptual solution already exist. Note that such a derivationis not a derivation from nothing: it is a derivation from the emptyset + rich powerful axioms. I use traditionnally 0, successor,addition, and multiplication (in this list), but the combinators +application are quite handy for that task too.Note also, that, contrary to what Tegmark defined, if mechanism iscorrect, the physical universe is not a mathematical structure, butmore the border of something which can be made 99% into a mathematicalstructure, together with a non reductible element, which is related tothe theological aspect of consciousness. The theory of everythingbecomes the mind theory of the (universal) numbers, and physicsappears to be a sum or measure on all computations.In that setting nothing and everything are equivalent dual notions,but they makes sense only in some theory with some rules ofmanipulation of the concept of nothing (like 0, or the empty set, orthe quantum vaccum: but this last one is assuming too much, and I haveprovided an argument showing that we have to derived it from numbers(or from combinators) if we want to be able to explain both the qualiaand the quanta. See my URL for proof of those statements if you areinterested.

`What about the axiom of choice? Is it included in the collection of`

`necessary mathematical principles that are needed for our`

`derivations/explanations of cosmogony`

`<http://en.wikipedia.org/wiki/Cosmogony>? It is becoming clear that we`

`need a principle that acts to induce a measure algebra on our universes`

`of entities as the usual axiom of choice has a fatal flaw`

`<http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox>. One`

`possibility is to use the property of compactness to generate the needed`

`finiteness via the idea expressed here:`

http://en.wikipedia.org/wiki/Locally_compact

`"All discrete spaces <http://en.wikipedia.org/wiki/Discrete_space> are`

`locally compact and Hausdorff (they are just the zero`

`<http://en.wikipedia.org/wiki/0_%28number%29>-dimensional manifolds).`

`These are compact only if they are finite."`

`My thought is that the requirement that the Stone duals of our`

`abstract algebras (which would include all of our notions of mechanism!)`

`are given as compact and (via Pontryagin duality`

`<http://en.wikipedia.org/wiki/Pontryagin_duality>) discrete spaces. When`

`and if compactness does not naturally exist, the compactness can be`

`induced by the use of the Stone-C(ech compactification`

`<http://en.wikipedia.org/wiki/Stone-Cech_compactification>.`

Some notes on this idea: From http://en.wikipedia.org/wiki/Locally_compact The point at infinity

`"Since every locally compact Hausdorff space /X/ is Tychonoff, it can be`

`embedded <http://en.wikipedia.org/wiki/Embedding_%28topology%29> in a`

`compact Hausdorff space b(/X/) using the Stone-C(ech compactification`

`<http://en.wikipedia.org/wiki/Stone-Cech_compactification>. But in fact,`

`there is a simpler method available in the locally compact case; the`

`one-point compactification`

`<http://en.wikipedia.org/wiki/One-point_compactification> will embed /X/`

`in a compact Hausdorff space a(/X/) with just one extra point. (The`

`one-point compactification can be applied to other spaces, but a(/X/)`

`will be Hausdorff if and only if`

`<http://en.wikipedia.org/wiki/If_and_only_if> /X/ is locally compact and`

`Hausdorff.) The locally compact Hausdorff spaces can thus be`

`characterised as the open subsets`

`<http://en.wikipedia.org/wiki/Open_subset> of compact Hausdorff spaces.`

`Intuitively, the extra point in a(/X/) can be thought of as a *point at`

`infinity*. _The point at infinity should be thought of as lying outside`

`every compact subset of /X/._ Many intuitive notions about tendency`

`towards infinity can be formulated in locally compact Hausdorff spaces`

`using this idea. For example, a continuous`

`<http://en.wikipedia.org/wiki/Continuous_function_%28topology%29> real`

`<http://en.wikipedia.org/wiki/Real_number> or complex`

`<http://en.wikipedia.org/wiki/Complex_number> valued function`

`<http://en.wikipedia.org/wiki/Function_%28mathematics%29> /f/ with`

`domain <http://en.wikipedia.org/wiki/Domain_%28function%29> /X/ is said`

`to /vanish at infinity`

`<http://en.wikipedia.org/wiki/Vanish_at_infinity>/ if, given any`

`positive number <http://en.wikipedia.org/wiki/Positive_number> /e/,`

`there is a compact subset /K/ of /X/ such that |/f/(/x/)| < /e/ whenever`

`the point <http://en.wikipedia.org/wiki/Point_%28geometry%29> /x/ lies`

`outside of /K/. This definition makes sense for any topological space`

`/X/. If /X/ is locally compact and Hausdorff, such functions are`

`precisely those extendable to a continuous function /g/ on its one-point`

`compactification a(/X/) = /X/ ? {?} where /g/(?) = 0.`

`The set C_0 (/X/) of all continuous complex-valued functions that vanish`

`at infinity is a C* algebra`

`<http://en.wikipedia.org/wiki/C-star_algebra>. In fact, every`

`commutative <http://en.wikipedia.org/wiki/Commutative> C* algebra is`

`isomorphic <http://en.wikipedia.org/wiki/Isomorphic> to C_0 (/X/) for`

`some unique <http://en.wikipedia.org/wiki/Unique> (up to`

`<http://en.wikipedia.org/wiki/Up_to> homeomorphism`

`<http://en.wikipedia.org/wiki/Homeomorphism>) locally compact Hausdorff`

`space /X/. More precisely, the categories`

`<http://en.wikipedia.org/wiki/Category_theory> of locally compact`

`Hausdorff spaces and of commutative C* algebras are dual`

`<http://en.wikipedia.org/wiki/Duality_%28category_theory%29>; this is`

`shown using the Gelfand representation`

`<http://en.wikipedia.org/wiki/Gelfand_representation>. Forming the`

`one-point compactification a(/X/) of /X/ corresponds under this duality`

`to adjoining an identity element`

`<http://en.wikipedia.org/wiki/Identity_element> to C_0 (/X/)."`

Querry:

`Is this idea invertible such that we can consider the notion of an`

`observer as 'existing at' or 'being a homunculus' at the point as`

`infinity. What would allow the 'Cartesian Theater' schemata a means to`

`generate this identification, if possible? Does the 'infinite regress'`

`that we see in the hall of mirrors act as a finite approximation of the`

`property of"lying outside every compact subset of X" ?`

`This follows the line of reasoning that Bruno explained above in`

`the sense that the missing .0000..1% is that "point at infinity"`

`necessary for compactness of manifolds as used in our physics to`

`represent space-time and its content. Additionally, it makes the concept`

`of an ideal 'observer at infinity' coherent and resolves the kinds of`

`problems that people like Daniel C. Dennett have pointed out. It also`

`gives us a natural way of expressing the sets of sets of sets of .. that`

`we see in the representation of numbers as " empty set + rich powerful`

`axioms" that Bruno mentions. For example see:`

`http://www.math.utah.edu/~pa/math/sets.html`

In a nutshell: we have still to postulate some primitive elements.Assuming the empty set + some rules, is equivalent with assuming allthe sets, or all the numbers. Once you have all the numbers (or allthe sets) you can derive the quanta and the qualia, by assuming themechanist hypothesis (or any of its multiple weakenings).

`Bruno, I am unable to read your paper titled "Theoretical computer`

`science and the natural sciences", as it is behind a paywall.`

`(http://www.sciencedirect.com/science/article/pii/S1571064505000242 )`

`therefore I need an alternative source that discusses the mechanism`

`thesis that we can quote from to avoid unintentional straw men. Would`

`the wiki article, found here`

`http://en.wikipedia.org/wiki/Mechanism_%28philosophy%29 and/or`

`http://en.wikipedia.org/wiki/Digital_philosophy, suffice?`

We cannot explain the numbers (or the sets) in any theory which doesnot postulate them. This is well known by mathematical logicians. Soit looks like the numbers constitute an irreducible mystery.Bruno

`Would it not be a wonderful coincidence if this irreducible mystery`

`of number was just a counterpart of the apparent irreducibility of`

`matter? Any finite expression of existence would have both a concrete`

`implementative expression and an abstract qualitative expression once we`

`understand the relation between the abstract (for example: numbers) and`

`the concrete (for example: particles).`

`A nice article on the problem that we are considering can be found`

`here: http://www.spiritone.com/~brucem/666.htm`

Onward! Stephen

Jon 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: 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 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” 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 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".--http://iridia.ulb.ac.be/~marchal/

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