The Zero Ontology - David Pearce on Why Anything Exists

Arthur Witherall

What is the Zero Ontology?

David Pearce has described a proposal which outlines an explanation space within which the question "Why is there something instead of nothing?" can be given a legitimate answer. This is how he describes his endeavour, and he makes it clear that his ideas are purely speculative. He does not have a straightforward answer to the question, nor even a theory. All that he has is a sketch of what a theory which "explains existence" might be like, and how it might arrive at its conclusions. While I must admit that I find his sketch compelling in many ways, there are problems and paradoxes lurking in the very idea that one could explain why the world exists. In the case of Pearce's proposal, the explanation takes the form of showing that there is (in a sense) nothing to explain. As such, it is similar to necessitarian responses to the problem, which claim that there is no alternative to the existence of the world since something - God, for example - exists as a matter of logical necessity. Pearce does not exactly endorse a traditional necessitarian theory, but he comes awfully close. In my opinion, there is a recognition of balance and proportion in his thesis which makes his thesis more appealing than any reliance upon a deus-ex-machina.

What makes his suggestion interesting, in my opinion, is that it invokes a powerful intuition that the totality of the real, "substantial" world (the world of physical things) is ultimately indistinguishable from the void. That is, the substance of the world as a whole is identical with nothingness, and reality is interpreted as the realisation of Zero. This Zero, however, need not be interpreted as a number. Whether it is a number or not, it has more complexity, in this context, than has hitherto been imagined, for it includes the entire universe - indeed it is the "final result" of all the properties and processes of the universe. It is the ultimate emptiness of existence. Pearce sometimes uses terminology which reflects the fact that 0 is to be treated as a state of affairs rather than a number, when he says that his hypothesis is "that zero is the case".

This "Zero ontology", an interpretation of the void which treats it as the summation of all substantial reality (or vice versa - an interpretation of substantial reality in terms of the void), appears as either unintelligible or highly counter-intuitive from the perspective of our everyday worldview. We are used to dealing with substantial things, and we tend to think of 0, or the void, as the absence of things rather than their ultimate "summation". But this may be a problem of language rather than intelligibility. We do not have the right terms at present to describe the great totality of the world, considered as a single unit when all of its properties are taken into account. Such an entity is beyond our experience, and certainly beyond our powers of manipulation. When modern physics tells us that the ultimate value of the conserved constants of the physical universe is exactly zero, or as Pearce puts it:

"In the Universe as a whole, the conserved constants (electric charge, angular momentum, mass-energy) add up to/cancel out to exactly 0. 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)"
our normal conceptual resources seem to stall. Does this really mean that the substance of the world is not really substantial at all, or is it a bizarre mathematical trick which should be interpreted in some other way? It is important to understand, of course, that there really is some positive mass-energy in certain parts of the world. That is not being denied. When it is said that the quantity of mass-energy is Zero, this is only true for the world as a whole. We think that mass-bearing material things exist because we are located in a particular part of the world where they appear to exist. Only when we have a perspective on the whole world can we see that they are effectively wiped out in the overall structure of things.

Pearce's position is similar to other philosophies of the void, including Buddhist mysticism and western nihilism, but there are also important differences. There were apparently three tenets in the philosophy of the ancient Greek philosopher Gorgias: 1) nothing exists; 2) if anything does exist, it cannot be known, and; 3) if anything does exist and can be known, it cannot be communicated. This is nihilism at its most stark, but also its most implausible. Gorgias is too extreme. Pearce's position is distinguishable from it, and from the Buddhist version of nihilism, in at least one significant respect. It employs physics and mathematics, and addresses the question of existence within this context. Recent theories about black holes, the Big Bang, and the Everett-Wheeler interpretation of quantum mechanics, are brought in to explicate his thesis. I have nothing much to say about his use of these theories. In fact, I am less impressed with the scientific aspects of his proposal than I am with the overall picture he paints, although I do appreciate the necessity for explaining the physical details of the world. What we really want is an explanation space which can account for why the world exists as well as the equally perplexing question of why it is exactly the way it is. If we are going to address the problem of existence properly, it does seem that we will have to explain everything else as well, at least in a general way. Existence is not an isolated topic of investigation.

Pearce's proposal has the virtue, if only it could be worked out properly, of wrapping everything up in a completed explanatory framework. It would account for all that we experience, all that we theorise, and all that there is to the substance of the cosmos. All of this, according to his picture, must somehow work itself out to be equal to zero. That is, all of the properties of things must cancel themselves out completely, leaving nothing at all to explain. The number zero itself is recast in a new conceptual and ontological garb, so that it is not merely nothingness but also at the same time somethingness (ie. substance). When properly worked out, this means that all of the properties of substances must be taken into account in the final equation or calculation, which is the final explanation, simply because they must all be used together to "sum up" to zero. As such, when this explanation is forthcoming, it will necessarily account for all of the properties of everything that exists. If anything is missing, the summation might be different, and the explanation would not go through.

With such an magnificent picture of the cosmos on the cards, and so many details to uncover, we must surely pause before crying "contradiction!" at his paradoxical mode of expression (ie. in saying that nothingness or Zero is ultimately identical with the world-as-a-whole). We must pause, not merely because so much is at stake - an explanation-space for existence - but also because Pearce clearly knows that he is using a paradoxical mode of expression, and is not trying to be deliberately obtuse. He is envisaging a space for which we have yet to develop the right concepts. Paradox is inevitable, so we may let it go as long as we can make some sense of his proposal.

A Theory of Absolute Nothingness?

My first inclination is to defend the proposal that, in some yet-to-be-fully-devised theoretical structure, the properties of everything in reality add up to or cancel out to zero. This inclination comes from a particular interpretation of what it means, and my intuitive comparison of the ideas it employs. It seems to me that in this context we are not to compare "something" with "nothing" as quantificational idioms, but instead we should compare totalities. That is, we should look at the world and the void, and ask whether they could in some way be equivalent. The totality of the world, that is the real world whatever it includes (eg. planets, people, numbers, feelings, Everett's "branch-worlds", and so on), shares certain features with absolute nothingness, which is the total emptiness of everything (to be expressed in a way as yet inconceivable to us). Comparing them reveals that they could be identical, although it does not reveal a perspicuous way of expressing this identity in the English language.

To begin with, Pearce provides us with a fairly good image of his explanation space by comparing it with the system of numbers. As he says, if you literally add up all of the numbers, positive and negative, the result is 0:

" 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."
This is not very interesting by itself, but it supplies a way of imagining a more inclusive role for 0. Given that we can extrapolate and imagine things that are yet to be done, we can envisage a system of mathematical equations which perfectly describe the physical world, and which have the feature that all of the substantive quantities of the universe add up to 0. Then, just like the series of numbers, we will have a perfect symmetry of magnitudes (though not of a mathematical kind) with 0 in the exact centre of the symmetry. This is what the Zero ontology proposes: that reality, understood as the totality of our experiential and theoretical knowledge (ie. mathematics, physics, and phenomenology), is "equal" in some sense to 0. Perhaps we could say that reality is perfectly "centred" on 0. And perhaps we can understand this as asserting that the universe has no bumps or hairs, no outstanding inexplicable features. The properties of all substantial entities, like the properties of the totality of the positive and negative numbers, are all different and related to each other in a complex manner, but in the end they are so perfectly balanced that they wipe each other out. Thus we end up with Zero.

It could be argued that really it is the notion of symmetry that does all of the work here. We have a profound intuition, expressed again and again in science and art and in everything else, that symmetry needs no explanation. It is already perfect, and perfectly in accord with itself. Asymmetrical structures and facts, on the other hand, are "odd". They have to be woven into an explanatory story that squashes the bumps and shaves off the hairs. When we originally consider the question "Why is there something instead of nothing?" it seems that we are confronting a massive and terrifying asymmetrical fact. It is asymmetrical because there is apparently no fuzziness or in-between state when we are dealing with being and nothingness. Either there is something, which is the case, or there is nothing, which is not the case, but there is no intelligible compromise between them (or so it seems). Furthermore, there is no reason for one instead of the other. Our minds are immediately stalemated by the question. Nothing compels us towards thinking that there must be something, or that there must be nothing. We are also stalemated by the fact that any particular thing that explains why something exists will itself be something, which rules out our standard explanations - for example, it rules out causal explanations (unless there is a self-caused entity, a conjecture few are prepared to make).

The Zero ontology restores the symmetry to this situation, so that instead of thinking only that there is something, we may also think that there is nothing, although in a different way. The exact sense in which this is so cannot be envisaged until the details of the ultimate (grand, unified, and true) theory of the physical world are available. However, if we are to imagine it, we may imagine the position of 0 in the series of numbers. It is the summation of them all, yet they are distinct from it and have complex relationships with each other. Better still, in the structure of the numbers both being and nothingness have been included in a single structure, for Zero includes both the absolute void and all of the numbers within itself, that is within its arithmetical structure. Zero is only meaningful in the context of the other numbers and their mathematical relationships. Thus it must "include" them all in some sense. Pearce's proposal is that the totality of physical entities and their properties adds up to 0, and is in this logico-mathematical-theoretical way "identical" with total nothingness. Nevertheless, at the same time he does not wish to deny that there are lots of distinct things in the world. As he puts it:

"In a (as yet cognitively inaccessible) rigorous, technically defined sense, nihilism and plenism, it is here proposed, are to be taken as physically and logico-mathematically equivalent."
In this way, it seems to me, he defends a restoration of the symmetry of being and non-being. He does so by claiming that there is some sense to actually equating them, but he does not say what kind of theory will be able to establish that this equation holds. Perhaps this is a pipe-dream approach to the problem, but it does not seem that way. For one thing, there are measurements of physical quantities, cited earlier, which suggest otherwise.

The void and the world of existents are both abstract totalities. They do not belong to the world we experience, but somehow they act as "boundaries" around which we can make sense of things. To unite them into one boundary by claiming that Zero has rich properties that allow it to be at once "empty" and yet "full of infinite possibilities" [as in the Tao Te Ching] is to make sense of the two together, working as a single totality which requires no explanation. However, when one of the derived properties of Zero is considered in isolation from the whole system, then it does demand explanation, for it must then be seen as something "independent". In truth there is no independence, but it is a necessary fiction used for dealing with the deceptive appearance of hairs and bumps. As Pearce says, 42 would demand an explanation, but 0 does not. The explanation of isolated objects, or the realisation of quantities other than 0 emerges in showing how a derived property of 0 (ie. a thing or property) is related to the rest of the cosmos, and thus how it too cancels out in the process to express the ultimate 0 of reality. To actually show this may involve an enormous calculation, if it is feasible at all. All that we can do is marvel at the idea of it, yet this marvelling is important.

[ see The Fundamental Question" ]

Following on from the previous point, these two totalities (the void and the world) share a further feature. When they are considered in isolation, each appears transcendent, in that it goes beyond what we can feel or imagine, and possibly unintelligible (at least by the lights of present-day conceptual resources). The totality of the world is beyond our experience, beyond our epistemic access, and beyond our wildest dreams. It is larger and more complex than we could possibly think. It is an absolute, and perhaps the concept of the world-as-a-whole is something like Kant's concept of "noumena", in that it is used only to curb the pretensions of our sensibility and not to describe anything. In any case, we do not have any ordinary descriptions of the totality of the world other than descriptions of our feelings about it [cf. Quentin Smith], and it is difficult to find a descriptive phrase synonymous with "the world as a whole". It just isn't an ordinary thing, like the sort of thing you would meet on the street. It is a transcendent thing; it transcends our experiences even though it encompasses them. Likewise with 0, or absolute nothingness. This too, considered by itself, is unimaginable and indescribable, though it does not appear immediately as incoherent or inconsistent. We cannot "decide" between these two totalities on purely intellectual grounds, nor explain why there should be one rather than the other. If we know that something substantial exists, it is because we think that we see and feel substantial things, not because we can analytically extract this information from the concept of "the world-as-a-whole" (which is one of the themes of Kant's philosophy).

The Zero ontology gratuitously helps itself to both totalities, both absolute nothingness and substantial somethingness. But then, either one on its own is just as gratuitous as both together. Neither seems to explain the other unless they are both taken to be aspects of some third thing. Pearce suggests, without a hint of Hegel, that this "third thing" is what we have previously called the number 0. We had thought that 0 was a simple thing, but it is not. It is highly complex, and includes all of mathematics and all of the physical world. Pearce also claims that it includes the whole of the phenomenal world, but this is not well defended (he uses the example of the colours "adding up" to white, a non-colour, but this does quite fit). In my view, the world of phenomenal feelings and mental states cannot be absorbed into the zero ontology unless there is a comprehensive identity between minds and all forms of physical stuff. That is, unless we adopt a version of panpsychism. Pearce employs this panpsychist identity, again highly speculative, into his sketch of an explanation space for existence, but of course it needs a full-scale philosophical defence of its own.

[ See Cosmic Consciousness For Tough Minds ]

How does the Zero Ontology Explain Why Anything Exists?

Even if we can make sense of the idea that Zero is the case, or that Zero lies in the centre of symmetry for the universe, the question of whether this actually explains anything, and in particular whether it can answer the question of why anything exists, is yet to be properly considered. What then is the explanation-space for existence? How would existence get "explained" within this kind of picture?

The answer is that there are several ways in which one might explain (or "explain away") the existence of "something instead of nothing" using the Zero ontology. Perhaps the most obvious is to discard the question itself as illegitimate, but to do so on solid grounds rather than positivist waffle. That is, one can argue that the question presupposes that there cannot be BOTH something and nothing, which is what the Zero ontology asserts. Hence it is already prejudiced against the truth, or uses a false dichotomy, and can be laid aside as ill-formed. The question presumes that there is an asymmetry to explain, whereas the explanation is that there is no asymmetry in the first place. It follows from this position, however, that the original question can be replaced by the equally perplexing problem of "Why is there both-something-and-nothing-together?". However, this question cannot be answered by the Zero ontology unless it turns out to be a self-supporting theory or it can explain its own truth in demonstrating that the substances of the world cancel themselves out. Before we can determine how this matter proceeds, we will need to have an actual theory to deal with, instead of conjectures and possibilities.

Pearce himself makes at least two distinct suggestions as to the way in which existence is to be explained by the Zero ontology. The first is implicit in a statement I paraphrased earlier, when he compares the cancellation of physical properties like mass-energy to the self-cancellation of the number series:

"[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.]"
A curt summation of this idea is that the existence of things is explained by a demonstration that nothing really exists. All of the things we thought were there are in fact mere appearances, whose apparently substantive features are all derivable from the properties of Zero. This must include ourselves, and thus the "mere appearances" that constitute the world are not just appearances in our own minds. They are appearances that necessarily flow from the central reality of Zero. Our minds are also appearances, and also derive from the properties of Zero. In fact, Zero becomes a sort of First Cause, given this sort of explanation. But if the demonstration that nothing exists works, then it really does account for the existence of each particular thing. Thus the "why" question is given an answer.

The second suggestion that Pearce makes is less decisive, and clearly allies him with the necessitarian approach. He says:

"Indeed an implication of the position to be argued here is that anything else other than what exists is, were what exists 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 lapsing into incoherence. In the case of the notion of nothing 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."
There may be a confusion here if Pearce means that we cannot imagine that nothing exists. For he is himself asserting that this may be the case, at least under a particular interpretation in which it is also true that something exists. But it seems plausible to assert that the kind of explanation offered by the Zero ontology will turn out to be a necessitarian one. The explanation will show that the existence of the world, in the only way that it could intelligibly exist (ie. as a world of apparent substances which are themselves ultimately intelligible as derivations of Zero), is necessary given the postulate that "Zero is the case". Even when this is demonstrated, of course, we are left with the question of why we should assume that Zero is the case, the answer to which must lie beyond the resources of any explanation which proceeds on the assumption that it is the case.

We are on uncertain but well-trod ground in contemplating the question of why anything exists. There are already well developed metaphysical systems which reduce the contingency of existence to some kind of necessity in an attempt to answer this question, among them the philosophies of Leibniz and Spinoza. However, in the case of these thinkers, it is arguable that they are not quite "smooth" enough. They insist that one being - God - exists without requiring explanation. But this being is a substantial being, a substance with distinctive features. As such, it stands out (the original meaning of "exists" comes from the Latin "ex-sistere" which means "to stand out") as a distinctive thing, and thus it becomes difficult to see why its existence does not need to be explained. The Zero ontology, on the other hand, is a purer system. It removes every last trace of substance from the world by cancelling it out in the context of the whole. There are no bumps and hairs, no gods, no substances, no things that are just there without explanation. The universe swallows itself up in the same act by which it releases itself into being.

This "explanation space" for existence is really a space in which theories, such as those of mathematics, physics, and philosophy, come together and show, in conjunction with each other, that no explanation is needed for the fact that the world exists. The only sense in which this constitutes an explanation is that in which a simple hypothesis (that Zero is the case) replaces a hopeless conundrum, which means that it is explanation by simplicity. We can always be left in doubt that the explanation actually works, at least until the combination of theories is devised which demonstrates that everything adds up to 0. Before this comes about, we are left with the perplexity of the fact "something exists rather than nothing", and only a sketch, a vague picture, of how this might not be perplexing (ie. if Zero is the case). So in this way, were there to be the right combination of 0-entailing theories, it would constitute a removal of perplexity, and in this minimal sense, an explanation.

I like to think of the Zero ontology in a slightly different way, as a perfect combination of rationalism and mysticism. Zero in this case is the greatest and most perfect whole, for it wraps up all of the substances of the world and reveals that they were never truly substances, never truly independent entities at all. But they had to appear in the world, in the guise of substances, for otherwise there would be no "adding-up" procedure, and thus no realisation of Zero. Without this realisation of Zero as the summation of things, the substances of the world would not be effectively combined with nothingness. They would then always remain problematic, for we could always say "well why not nothingness?" instead of "ah, clearly there is nothingness within the heart of the world".

Rationalism is involved here in relying upon the process of calculation. In order to believe in the Zero ontology as a possibility, we have to believe that mathematical physics, at least, accurately describes reality. Thus reality must have a rational, mathematical structure. Rationalists have always maintained this to be true. Mysticism is involved here in the final step, the step which claims that when everything gets wrapped up and added up, it is all tantamount to Nothingness. It plays no part in the theoretical structure used to make the calculation, but it is expressed by the final result of the calculation, and by the way that we interpret this result. The variety of mysticism which is particularly appropriate here is atheistic Taoism, which explicitly claims that there is a profound relationship, even an identity between being and non-being. The Tao Te Ching expresses this wisdom in poems rather than calculations:

We join spokes together in a wheel,
but it is the centre hole
that makes the wagon move.

We shape clay into a pot,
but it is the emptiness inside
that holds whatever we want.

We hammer wood for a house,
but it is the inner space
that makes it livable.

We work with being,
but non-being is what we use.

[Tao Te Ching, Chapter 11]

There are other religions which endorse similar ideas, but it is reasonably clear that western thought has been absorbed in the notion of substance, without being able to see how substantial things can dissolve into nothingness. This makes it particularly difficult for western philosophers to find the Zero ontology meaningful. In my view, there is a real and tantalising possibility that western physicists, if not western philosophers, will be able to show us the errors of treating substance so seriously.

Arthur Witherall
Canberra ACT


The Fundamental Question