Why is there something rather than nothing?

 

This was the question at our Cambridge philosophy café on 22 January 2023. The first impression is that it is both a question that demands a decent answer, and a question that cannot have one. This post does not provide an answer. Instead, it sketches some of the territory.

Why is an answer demanded?

There are items of many types in the world (meaning not just the world as it is today, but the world with all its history). There are physical objects, events, relationships of space and time (or of spacetime when we focus on physics), laws of nature, mathematical results,  thoughts, feelings, and so on. We may be more or less generous in what we regard as an item in the world. But whenever we admit something as an item, we can ask why it is in the world. And we tend to think either that an answer will already be known, or that the discovery of an answer would be perfectly conceivable. Even if we do not have much hope that an answer will in fact emerge, for example where historical records have been lost, we still think that an answer could have been found if things had been different in perfectly identifiable ways. At the extreme, we might forgo even that hope and say that no answer could be found, but even then, we would think that there was some unknowable reason for the presence of the item in the world. 

To put all this in traditional philosophical terms, we have a strong inclination to subscribe to the principle of sufficient reason. And we are disturbed when quantum mechanics suggests that there may be no reason why some observations rather than others come to be made. We are left hoping that physics will advance to restore compliance with the principle. The hope may be forlorn, but it is there.

If we routinely find reasons for the presence of items in the world, and if we can put quantum mechanical worries to one side by noting that they do not extend to everyday items when characterized in the macroscopic terms we in fact use to individuate and describe those items, it would seem reasonable to ask why the whole ensemble is present (not present in the world, for the ensemble is the world, but simply present). And the question of why is there something rather than nothing is a less demanding question than that of why the particular ensemble we find is present, in that an answer to the latter question would automatically be an answer to the former one but not vice versa. Moreover, not only would the question seem reasonable. A response that it should not be asked, or could not be answered, would seem to be unreasonable.

Types of explanans

Our explanandum is the existence of some non-empty world or other (we do not need to explain its actual make-up). Our explanans could be causal and within the world, causal and external to the world, or non-causal.

By way of background, we shall make some remarks on ways to explain the existence of items within the world. Then we shall consider causal options, followed by non-causal options. Finally, we shall look at the option of dismissing the question.

Ways to explain the existence of items within the world

We can find reasons why individual items are in the world.

Sometimes reasons are directly causal, as when stresses between continental plates cause earthquakes, or the values of certain physical constants together with some conditions in the early universe determine which forms of matter have come into being.

Sometimes reasons are indirectly causal. We may for example say that a particular taxonomy of animals has been created because of the causal influences that have produced the actual variety of animals. Or we may say that a thought exists because of causal influences on neurons. Or we may say that an emotion in general (as distinct from individual instances) exists because causal patterns in the world are such as to generate particular types of human reaction in particular circumstances, where those reactions are reasonably systematic.

Sometimes reasons are not causal at all, as when we identify the reason why some mathematical statement is a theorem. 

There are also items that would be amenable both to non-causal explanation and to indirectly causal explanation. For example, the existence of Mannerism as an item in the history of European art could be explained non-causally by the presence of distinctive formal features in the relevant paintings and sculptures. And it could also be explained causally, albeit in an indirect way, by an analysis of the thoughts in the minds of artists and their patrons, in turn explained by a causal history of their neurons and of preceding developments which created the artistic context.

Internal causes of the whole

Now let us consider the whole universe, in all its history. The prospects for a causal explanation that relies on causes within the world are not bright.

Causes generally precede their effects. A cause might arise at the same time as its effect, but even then we require a direction of causation. If one thing caused another, it was in fact the case that the second thing did not cause the first one, even if in other circumstances the second thing could have caused the first one.

Moreover, we do not expect A to cause B to cause C to cause A. In mathematical terms, we want the causal connections between things to form a directed acyclic graph. In particular, cycles directly from something to itself are ruled out. No self-caused things are permitted.  We can however allow that A might cause B on some small scale, which then caused A to grow, which caused B to grow, and so on. Causal feedback is allowed.

(As usual, quantum mechanics complicates things. See for example the analysis and the references to earlier work in Barrett, Lorenz and Oreshkov, "Cyclic Quantum Causal Models", at https://doi.org/10.1038/s41467-020-20456-x.)

As soon as we have a direction of causation, we get causal chains to trace backward. We would expect to find something at the head of a chain into which all chains merged as we worked backward, or maybe several things at the heads of various chains which did not merge. A head item would explain everything that followed in its chain, so if it went unexplained, we would still not have explained why there was something rather than nothing because explanations for the existence of other things would be contingent on its existence. And everything that was not at the head of a chain would have to stand in some chain or other, so its existence would only have such a contingent explanation.

At this point we may remark that telling us that empty space has non-zero energy does not answer the question, at least not in the obsessive form in which philosophers are apt to pose it. Empty space with its scientifically determinable properties is not nothing, but a something that could have led in a causal way to what we see today. It has been said that when Lawrence Krauss published A Universe from Nothing, it should have been entitled A Universe from Not Very Much. And to a philosopher, that criticism has bite. (Krauss is however fully aware of the issue. He discusses it in chapter 9. On page 149, he acknowledges that he takes empty space and the laws of physics to exist within his "nothing".)

We must tread carefully here. It would be possible for everything to be caused without there being anything uncaused, in the way that every positive real number has a predecessor positive real number (in fact, infinitely many of them) without there being any first one.

More interestingly, we may need to be careful because temporal precedence relies on there being time, and strange things may have happened with spacetime at the very beginning. Temporal precedence may not be the only type of precedence to give a direction of causation, if we allow for causes to be simultaneous with their effects. But it is the prevalent type. If the notion of temporal precedence were to get into difficulties in the context of the early universe, cosmologists of that early stage might be able to offer us a loophole that would allow a cause of things which was within the universe to be fully explanatory.

There would also be an argument to be had over whether one should see the quest for a causal reason for there being things in general in the same terms as the quest for a causal reason for there being some particular thing or other, even an unspecified thing that would stand as a representative member of things in general.

While one might raise such doubts about the easy argument that there cannot be, within the universe, a cause of the collectivity of things, there is enough room for worry that we should not expect to find such a cause.

External causes of the whole

Perhaps there could be a causal explanation which would be saved by not being within the world, so that it did not itself stand in need of a worldly causal explanation.

Sadly, this idea looks like a non-starter. Something that was causally effective but outside the world would look suspiciously like a god. And what could reasonably be substantiated about a supposed god would be so little as to make the supposition of one nothing more than a place-holder for an answer. Theists may rely on holy texts to describe their gods, but those texts are claims, not evidence. And in the absence of substantiated properties of a god or gods, the assertion of their existence does no more to answer our question as to why there is something rather than nothing than to say "If we had an answer, it would go here". Leibniz, who made an explicit connection with the principle of sufficient reason, may have thought he had done more (Principles of Nature and of Grace, 7-9; Monadology, 36-39). But he had not.

Non-causal options

It is time to look at explanations which would avoid the requirement to respect a unidirectional relation from each specific explanans to its specific explanandum. They would be non-causal explanations.

Such explanations would comprise facts about the world, or facts about the abstract realm independently of any connection it might have to the world, rather than comprising things within or outside the world. The facts might mention things, but they would not be those things. Given the difficulty of conceiving of facts about things outside the world, aside from unsubstantiated and possibly incoherent claims about supposed gods, we need not distinguish between internal and external facts in the way that we distinguished between internal and external causes. But we must recognize that facts may be about abstract entities, any relationship or lack of relationship of which to the world is not given and is not to be presumed (beyond the observation that logic and mathematics are readily applicable to the world). Such abstract facts may include structures of relationships in which the specific relata are unimportant.

We seek facts that would make the existence of something rather than nothing unsurprising. There are options.

Many possible universes

One option is the claim that there are a great many possible universes. An easy argument would be that since there would be only one possible empty universe and a vast number of possible non-empty universes, it is no surprise that a non-empty universe should turn up. All that would then be lacking would be an explanation of why any possible universe at all was actual. If some random one were actual, it would probably be a non-empty one.

This argument would rely on the claim that there was only one empty possible universe (or at least, not many of them). Fortunately, within the realm of the merely possible, the claim of a single empty universe could be made just as, in mathematics, there is only one empty set. It is only in the concrete world that there are many empty boxes.

Many actual universes

Another option is the multiverse claim that there are in fact a great many universes, all but one of them beyond our ken. It would not be necessary to argue that most of them would be non-empty. Any one non-empty universe would suffice. But this argument would only give a route from there being many universes to there being something rather than nothing. It would leave unanswered the question of why there actually were many universes.

Either this option or the option of many possible universes could be backed up by a weak anthropic principle to the effect that whatever we observe will be a universe sufficiently complex to support conscious life, and therefore not empty. An empty universe might be a possibility, or there might be one or more empty universes among a number of actual universes, but we could not be in an empty universe.

The universe as an abstract structure

A third option would be to say that the universe was itself some abstract structure, not dependent on anything for its existence.

The leading example is the mathematical universe hypothesis that Max Tegmark has set out in Our Mathematical Universe (2014), but that is better and more briefly explained in his paper "The Mathematical Universe" from 2007, available at https://arxiv.org/abs/0704.0646 (take care to obtain version 2, dated 8 October 2007).

In Tegmark's view, the universe actually is a mathematical structure. This claim goes beyond the observation that the universe is amenable to mathematical characterization. Moreover, we are substructures within that structure who are conscious and self-conscious by virtue of the complexity of those substructures.

Tegmark's approach has the advantage that it is plausible, although not uncontentious, to think that mathematical structures simply exist, independently of anything else's existence. In particular, and importantly for him, they can be seen as existing independently of any human predisposition to think in particular ways (for example to think in terms of objects and causation). They are all form, definable in strictly mathematical terms, and no non-formal content. And this is argued to be enough to characterize any universe. As physics digs deeper and deeper into the nature of reality, it identifies symmetries and conservation laws which say everything that physicists feel the need to say. The need for a separate stage of explaining how the mathematical structures identified give rise to what we perceive does not detract from the sufficiency of physics without that extra stage.

Tegmark's approach can however be challenged.

An apparent difficulty is that we need to explain how it is that the particular mathematical structures we find here are instantiated, rather than all possible structures being instantiated to form each and every possible universe. (He does posit a multiverse.) The problem is that once mathematics gets going, even with an empty set and minimal set theory, there is nothing within itself to stop its expansion. We would get all of mathematics everywhere, subject to a few large-scale decision points such as whether to adopt classical or constructivist mathematics or whether to adopt the axiom of choice.

This apparent difficulty is easily addressed. Tegmark thinks that what comprises any given universe is not a theory but a model of a theory. That allows for variation between universes, especially if we allow universes to comprise models of parts of theories.

This does not however leave an entirely satisfactory picture. A clue to the difficulty lies in Tegmark's invocation of the mathematical principle that "same up to isomorphism" amounts to "same" (the 2007 paper, section II.D). If our universe is isomorphic to a mathematical structure, then in his view it is that structure.

The problem is that "same up to isomorphism" does not amount to "same" in the everyday sense of "same". When we think in physical terms, we are happy with the idea of several distinct but isomorphic things. We could even imagine several isomorphic universes within a multiverse, so long as the multiverse was realised in a physical or quasi-physical way and not in a purely mathematical way. We would have to presuppose Tegmark's conclusion that we should think of the universe as a mathematical object in order to require ourselves to think of sameness in the mathematical way. 

Dismissing the question

The option of dismissing the question of why there is something rather than nothing remains.

One could simply take the existence of something rather than nothing as a brute fact.

One could add that the principle of sufficient reason did not have to be accepted. There are after all things in the quantum world which, so far as we can tell, simply happen. More precisely, there are observations which are such that we cannot currently give any sufficient reason why a specific observation was made rather than an alternative.

One could dismiss all questions as to why things were as they were and and simply ask how things came to be as they were. An argument for doing so, given by Lawrence Krauss, is that why-questions assume that there is some purpose to be found, and that there is no sign of any such purpose at the level of the universe (A Universe from Nothing, page 143). But it is not clear that this is so. A why-question need not assume purpose. It may be a rephrased how-question which, in the context of asking why there is something rather than nothing, carries the implication that one is going to go on asking how-questions until one reaches something that plainly has to be the case so that the stream of how-questions can come to a stop.

One could challenge the formulation of the question, on the ground that it was not possible to talk about nothing. But that argument might easily not succeed. While there might be nothing to which to refer, one could talk about the falsity of every proposition of first-order predicate logic which started with an existential quantifier, the variable of which actually bound an occurrence later in the proposition. (This is only a sketch of a solution. It would need to be worked out in detail.) Or one could point out that we have no difficulty in thinking mathematically of the contents of the empty set, even if philosophers have found that natural languages run into difficulties over such notions.

Finally, one could treat the existence of something rather than nothing as a mystery. In the words of Wittgenstein (Tractatus 6.44), "Nicht wie die Welt ist, ist das Mystische, sondern daß sie ist". But that would seem to amount to no more than accepting the existence of something rather than nothing as a brute fact and taking up a particular emotional attitude to the fact, unless one had good grounds to think that the mystical was itself a repository of information that was so far inaccessible and might eternally remain so. That would be a hope without justification.