By: Olaf Gniechwitz
What is the connection between:
1. One's a priori intuition that there's no conceivable reason, or even explanation-space, for why anything at all exists. [This powerfully felt preconception is hard to express in natural language without spuriously reifying ("turning into a thing") non-existence or Nothingness i.e. asking "Why isn't there Nothing rather than Something?" and thus running the risk of lapsing into Heideggerian obscurantism. But see below].
2. The quantum-mechanical wave-function of the Universe, the (mathematically) complete and exhaustive formal description of the world, encodes how everything that physically can occur/exist does occur/exist with some density or other. Taken literally, this increasingly popular and deceptively "anything-goes"-sounding interpretation of the quantum formalism actually rules out all of the world's traditional cosmologies. This is because of their varying degrees of disguised internal inconsistency. Post-Everett "no collapse" interpretations of QM exclude a lot else besides. For Universal QM is far less permissive than it sounds in some ways. Yet tragically - at least to my negative utilitarian mind - its entailment of googolplexes of hell-branches means it is horrifically more prolific in others.
3. In the Universe as a whole, the conserved constants (electric charge, angular momentum, mass-energy) add up to/cancel out to exactly zero. There isn't any net electric charge or angular momentum. The world's positive mass-energy is exactly cancelled out by its negative gravitational potential energy. Provocatively, cryptically, elliptically, "nothing" exists. [What is so special about the conserved constants? Will everything internal to the universe, and analogously everything internal to black holes, turn out to be derivable from the conserved constants; and thus, in a sense to be explicated, be derivable from the properties of zero?]
4. Black holes: have [possible complications aside] "no hair". From an external observer's perspective, they are simply and exhaustively characterised by the conserved constants (internally, on the other hand, they may possess all sorts of properties, e.g. Shakespeare-loving infalling astronauts; you and me?). ultimately evaporate via Hawking radiation to 0.
5. The universe can itself be treated, contentiously, as a black/white hole (?? omega = 1, the critical value) Does the universe evaporate "hairlessly" backward/forward to 0???? ) [Notes: some non-standard physics: Are the Big Bang and Big Crunch not just type-identical(?), but token-identical?? Is the Big Bang a black hole evaporating??? Does the universe have an event horizon in our distant future/past when the (cold) universe (omega=1) is at maximal volume, eventually decaying via Hawking radiation? Are all time-like and space-like paths closed, entailing that spooky EPR correlations aren't really non-local?? Does the Multiverse 'expand' symmetrically both "backward" and "forward" in time from/to its final/initial low entropy condition (?) - granted that the entropy of a (universal?) black hole is given by the logarithm of the number of microstates consistent with the area of its shrinking/expanding event horizon?]
6. Mathematically : 0 can/must be construed as (a condition akin to our conception of?) a number. The whole of mathematics can, in principle, be derived from the properties of the empty set, Ø. [Since Ø has no members, it can be identified with the number zero, 0. 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.]
the existence of any number, in virtue of its properties, entails the existence of all the others i.e. a system of mathematics couldn't exist bereft only of the number, say, 42; and the existence of any number, in virtue of the full set of its properties/structural relationships, entails the existence of every other number. Thus there aren't any "atomic" facts in mathematics. Given, further, that mathematics exhaustively and uncannily encodes the world (Wigner's "unreasonable effectiveness" of mathematics in the natural sciences), then perhaps there aren't any "atomic" facts about the world either. The properties of any one thing [0?] entail the properties of all the others.
insofar as they are well-defined, the summed membership of the uncountably large set of positive and negative numbers, and every more fancy and elaborate pair of positive and negative real and imaginary etc terms, trivially and exactly cancels out to/adds up to 0. Alternatively: the sum of all infinities - starting at negative infinity and going to positive infinity - is zero. [actually, since there are powerful arguments that the subtraction of same-size infinite cardinals is not defined, any 'cancellation' isn't really trivial. Platonic abstracta are pathological beasts.] Immanent in 0 is their strict equivalence and consequent intersubstitutivity. (link to Everett?? Net energy etc of Multiverse = 0 = all possible outcomes) [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, then there just isn't anything substantive which needs explaining.]
Much ado about Nothing?
"Nothing comes from nothing"
(LUCRETIUS : The Nature of Things)
By most criteria we haven't got an explanation-space, let alone an explanation, for why anything exists. We can't imagine what an answer to the question would even look like. It's apt to seem so astonishing that there should be anything at all, in fact, that everything else about the world can - if one is of a philosophical cast of mind - appear as trivial detail in comparison. It is not clear whether this fundamental mystery of existence will ever be solved. For we don't know how, and with what conceptual resources, we might begin to start looking for an answer. We don't even know here what the amorphous notion of an "explanation" would amount to.
Misplaced optimism that a solution can be found isn't uncommon. Sometimes it derives from verbal manoeuvres aimed at damning the question as meaningless. Sometimes it derives from a confusion with deep but conceptually distinct puzzles such as: why there is [currently] a preponderance of matter over antimatter? Or what if anything came "before" the Big Bang? The latter problem at least "feels" deeper than the former. Yet it still doesn't address the fundamental enigma. Even if a Hawking-inspired "no boundaries" conjecture is correct, and there is no "before", the central problem of why anything exists remains as intractable as ever.
There is another formidable problem. We don't have any idea how to block the vicious regress of explanation, causal or acausal, facing various otherwise conceivable prospective candidates we might one day arrive at. For instance, many cosmologists currently speculate that, for instance, our universe is the product of a spontaneous fluctuation of the quantum vacuum (again, net energy = 0). Subsequent symmetry-breaking phase-transitions in this very early era triggered off a brief period of exponential inflation. Its effects account for the large-scale properties of the "visible" universe today. Inflationary scenarios are certainly intriguing. Indeed, there are other models, such as variants on Linde's eternal chaotic inflation, in which elsewhere - beyond our parochial little multiverse - there is nothing to stop inflation ever ending. This is an utterly dizzying prospect. None of these options as they stand, however, offer any obvious prospect of blocking the explanatory regress. Even so, scientific inquiry still seems more likely to yield fruitful answers than armchair metaphysics. For if we could ever come fully to understand the properties of what fundamentally exists, and unravel its causal history, then we might have a better chance of coming to understand why it - or indeed anything - exists too.
Physicists sometimes say that all the really interesting things in the world happened during the first second. Today many theorists think we understand most of that second rather well. Yet we have no idea why the underlying reality of the world is, say, a rich quantum vacuum(?)(?) (or stringy vibrations, M-branes, etc.). This ignorance persists even though we now fondly suppose that we know some of a quantum vacuum's properties. So unless all forms of meaning holism are false, then perhaps we won't really understand the QM vacuum's properties at all, or anything else either, until we understand why, in some sense, the quantum vacuum exists. Worse, if the history of science and philosophy is any guide, then the ultimate answer may depend on a radical revision of our concept of what it is to be an explanation, too. Yet this revision wouldn't be available until we were well on the way towards knowing the solution on which it depended. So can we "bootsrap" our way to an answer? Let's hope so.
These reflections may seem unduly pessimistic. Yet scientific rationalism and the whole epistemic enterprise depend, not just on (at least a large methodological measure of) physical reductionism, but in practice on a large measure of semantic atomism too. This is so in the sense that they presuppose that our ignorance of the solution to such mysteries as the nature of consciousness, and an explanation for existence itself, doesn't systematically infect and stultify the content of everything else we think we know; and that the solution to these mysteries wouldn't revolutionise or render obsolete the semantic significance of all our previous terms.
Yet perhaps such semantic quarantine isn't feasible. Our position on learning the ultimate answers might be like that of a religious devotee whose loss of faith transforms his conceptual scheme though he retains its lexical shell; or like that of a rationalist philosopher who thinks he understands consciousness prior to expanding and radically re-ordering his semantic and evidential base with psychedelic drugs. Or, possibly more relevantly, since we don't have even a conceptual shell to be getting by with in the case of explaining the world itself, perhaps it's like trying to understand life without any understanding at all of the principles of Darwinian evolution. Such a feat simply isn't possible.
Admittedly, and in an unknown way, the question of why anything exists is probably ill-posed. The question may reflect some erroneous Collingwood-style Absolute Presupposition or background assumption that humans can't access. Or alternatively, its flaw may lie in a (false) proposition that is too trivially and glaringly obvious (to us) to appear worth formally articulating and defending. Yet it would seem too facile to write off the Fundamental Question, and any better formulated successor, as cognitively meaningless without some no-less-deep explanation of why this referential failure should be so. Treating the question of why anything exists seriously is not the same as saying that ultimately anything really could, in some obscure, non-epistemic sense, be otherwise than it actually is. Asking why there is Something rather than nothing at all isn't saying that non-existence was a substantive(!)(?) possibility. Indeed an implication of the zero ontology to be argued here is that the existence of anything else other than what exists is - if what does exist is properly understood - logically incoherent, including the notion of unrealised ontic possibility itself. For perhaps in all but a heuristic sense there is no difference between x and necessarily x. Given this is the case, then the notion of real contingency turns on a psychologistic misconception of the link between possibility and the imagination, because everything must be exactly how it is on pain of one lapsing into incoherence. In the case of the notion of nothing at all ever having existed when construed as a real possibility, then even the link with imagination breaks down. This is because one can't imagine nothing whatsoever existing.
But scepticism about real contingency isn't in itself very helpful to solving the riddle of existence. For one will still want to know why things can't be otherwise. A working assumption in this context is that the ascription of possibility is always relative to background conditions. If the background condition is simply everything [net = 0??] that (tenselessly) exists, then the possibility of it being otherwise in anything but the epistemic sense is incoherent. The task is to explain why. Such modal scepticism might seem incompatible with the Everett interpretation - superficially the fan of modal contingency's ultimate free lunch. Yet all the nominal Everret "branch" worlds are equally real. Moreover, properly understood, there is only one world; it's just that most of its classically inequivalent coarse-grained "branches" don't interfere with each other very much. [This is perhaps simplistic. There may in fact be (cf Lee Smolin) a (pseudo?)-infinite population of zero-rated multiverses(!) whose evolution and complex interconnection via black-hole "umbilical cords" can be described by Darwinian principles. "Hairy"? I'm betting not]
Unfortunately, one can often pose the right questions embodying the right concepts only when one already half-knows the answers. Here we don't have them. So these notes really amount to a hunt for an explanation-space, not an offer of an explanation. The woolliness of the proposed answer is redeemed only because the zero ontology propounded illuminates how the ultimate explanation might in principle be exact, rigorous, predictive and exhaustive: not wordy and philosophical at all.
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