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. Unlike a primitive truth, a tautology is a vacuous, empty truth. 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. Somehow or other, they must all be reducible to 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." 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. Nonetheless, I trust Russell and Pearce on this one. 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. [Since Ø has no members, in the standard set-theoretic definition of natural numbers it can be identified with the number zero, 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?)] 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. 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. 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! Best regards, Jon On Sep 20, 2:05 am, Roger <roger...@yahoo.com> wrote: > Jon, > > 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 > 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 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, > > > 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, > > > > Roger Granet > > > (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” 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". -- You received this message because you are subscribed to the Google Groups "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.
