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In the paper Why There is Something Rather than Nothing, Peter Lynds presented a nice introduction to the question I asked in the title of this article, and since it is very well written I'll use it here.

Why does this universe exist rather than some other kind of universe or no universe at all? This question has been termed the "primordial existential question" (PEQ) by philosopher Adolf Grünbaum.

The implicit assumption underlying the PEQ is that the existence of the physical universe is contingent. Things may have been different and the universe not have existed. If one were able to reject this assumption, the conclusion that the universe must exist and could not have possibly done otherwise naturally follows; its existence would be necessary. Furthermore, because in order to answer the PEQ, it is said we need an explanation as to why the universe exists rather than not, and by its very nature, a contingent explanation already admits the possibility of the universe not existing, any such explanation must fall short for it cannot tell us why non-existence was indeed not the case. As such, only an appeal to the necessary and non-contingent nature of existence can potentially provide a satisfactory explanation.

From Parmenides onwards, denying that non-existence is possible has had a long and venerable history in philosophy, and in attempting to address the PEQ, and this is the approach that authors such as Armstrong (1989), Lowe (1996), and Rundle (2006) have taken. However, and while it is logically contradictory to deny the existence of something because that “something” must exist for its existence to be denied, this only applies to the abstract “idea” of that something. One can certainly assert without contradiction that a living unicorn does not actually exist, but that the idea of it exists in a non-physical, timeless, platonic sense.

Contrast to Leibniz (Principles of Nature and Grace), who argued that non-existence was more simple and natural, and so required the existence of a necessary God to create a hugely complex and unlikely contingent physical existence, Van Inwagen (1996) has attempted to explain why there is something rather than nothing by showing not that non-existence is impossible, but existence far more probable. Because there are so many ways in which there could have been something, but only one in which there is nothing, something is more probable. Indeed, given there is an infinite number of ways there could have been something, but only one in which there is nothing, nothing, while not strictly impossible, is maximally improbable.

A third approach, such as that of Max Tegmark (2007) and Dean Rickles (2009), is to argue that mathematical structures exist necessarily, and given that theoretical physics represents the physical universe as a mathematical structure, the physical universe exists necessarily as a consequence of mathematical structures necessarily existing. As Rickles argues:

"Either existence is contingent or it is necessary. If it is contingent then there is no complete coherent account of existence. If it is necessary then we need a necessary structure to ground this fact. Mathematical structures are of this kind. If reality is mathematical then it must exist. Reality is mathematical (as evidenced by the effectiveness of mathematics in the sciences)."

However, and while it is arguably a different case for a non-physical, platonic reality, the idea that physical reality is mathematical is extremely difficult, if not impossible to justify. While many would accept that mathematical structures exist necessarily in a platonic sense, and very few would deny the effectiveness of mathematical structures in describing and mapping the world, it can be argued that this is so simply because the world naturally has quantities, and mathematics is, by its nature, quantitative. Geometry corresponds so well to the world because the world has extent, and by default, is geometric and has dimensions. Indeed, the only way in which the world wouldn’t be geometric is if it didn’t exist. Given this, it should then be no surprise that mathematics and mathematical structures correspond so well to Nature. (For further reading about the ontology of math, see Carrier, 2017BuilesSmolin, 2015; Lakoff, 2000; Balaguer, 2001; Hartry, 1980/2016)

A fourth approach is to say that there are some concrete things because there is some necessary abstract principle that entails the existence of concrete things. John Leslie proposes that abstract goodness itself is ontologically productive. It is good that some concrete things exist; therefore, they do. (Steinhart, 2010) Leslie briefly discussed his idea here.

A fifth response was presented by philosopher Quentin Smith in his article Internal and External Causal Explanations of the Universe. He argued it is logically impossible that there be an explanation of why any possible world is actual. Each possible world contains among its conjuncts both necessary propositions and contingent propositions. Take any contingent proposition T that belongs to any possible world W. Suppose W is actual and that T is true. T’s being true explains why W is true only if T explains why each conjunct in W is true. But no contingent truth T is such that T’s being true explains T’s being true. Since T’s being true cannot explain why T is true, T cannot explain why each conjunct in W is true. Therefore, T’s being true cannot explain why W is true. Nor can any necessary truth explain why W is true, since no necessary truth can explain why any contingent proposition is true and the maximal proposition W is contingently true. Consequently, it is logically impossible that there be an explanation of the truth of W. For any possible world W, if W is actual, it is logically impossible that there be an explanation of why W is actual.

In case Quentin's explanation is unclear, let me try simplify it.

According to Quentin, it is impossible to explain why the world exists the way it does. First he begins by pointing out that every possible way the world could be has some things that must be true (necessary) and some things that could be true or false (contingent).

Now, let's say there's a specific thing in the world that could either be true or false (he calls it "T"). If this thing is true, it can only explain why the world is true if it also explains why every other part of the world is true. But here's the problem: "T" being true can't explain why it itself is true. So, it can't explain why the whole world is true.

And even if we try to use something that must always be true (necessary truth) to explain why the world is the way it is, it won't work because necessary truths can't explain why things that could be true or false are actually true. And our world has some parts that could be true or false.

Ergo, there is no way to explain why our world exists the way it does. It's logically impossible to find an explanation for it because any explanation would run into these problems.

Finally, suppose no physical things exist. This does not mean that space is empty; there would be no space to be empty. Anyway, if no physical things exist, then the proposition “No physical things exist” is true. And, in order to be true, it has to exist (however, see Moore). So at least some abstract propositions exist. Logic now urges you to affirm that a very large system of platonic abstract objects exist – propositions, possible objects, logical truths (or laws) and mathematical objects. After all, it’s reasonable to think that if no physical things exist, then the number of existing physical things is equal to 0, less than 1, less than 2, etc. And to think that some physical things are possible. These abstract objects (propositions, possibilities, logical truths and mathematical objects) all exist necessarily. The problem is now how to explain the existence of concrete things, including physical things. The question “why is there something rather than nothing?” thus becomes “why are there some concrete things rather than no concrete things?” (Steinhart, 2010) Moreover, this only works if you're a realist about abstract objects. Nominalists do not accept that abstract objects (such as logical laws) exist in reality. As Richard Swinburne, the eminent philosopher of religion, explained:

"I think a lot of philosophers, particularly a number of recent philosophers, have given a status to these things that they don't really have, as it were. ... Principles of logic are, in my view, rules for which human sentences make sense. They are not eternal truths, and therefore, talk of possible worlds is just talk about which combinations of sentences are consistent with each other. So, they're all truths about human language that don't exist apart from humans." (For an exposition and defense of this view, see Swinburne, 2010Carrier, 20052004a, 2004b & 2022; Moore, 2019; Juhl & Loomis, 2009. And for alternative views, see Nagel, 1945Tahko, 2009Gila, 2011. I would also recommend Penelope Maddy's book A Naturalistic Method, pp. 200-302).

The Universe Could Be Necessary

In the book The Case Against Theism, Raphael Lataster explained that religious apologists, like William Lane Craig, merely and gratuitously assu
me that the existence of the universe is not ‘necessary’. They often attempt to shift the burden of proof. Despite the fact that they have made the argument, they feel no need to prove their assertions, based on assumptions alone, yet expect critics to prove the truth of their negations. But the onus is on the apologist to prove his claim, which may entail disproving all other possibilities.

The universe or some Aristotelian substratum underlying it, which itself could be described as ‘the universe’, could be necessary. Craig does acknowledge that the “atheist or agnostic” could simply claim that the “universe exists necessarily” and displays an unorthodox style in addressing it:

"We have, one can safely say, a strong sense of the universe’s contingency. A possible world in which no concrete objects exist certainly seems conceivable. We generally trust our modal intuitions on other familiar matters (for example, our sense that the planet earth exists contingently, not necessarily, even though we have no experience of its non-existence). If we are to do otherwise with respect to the universe’s contingency, then the non-theist needs to provide some reason for his skepticism other than his desire to avoid theism." (Reasonable Faith, 2008, Third Edition, p.109)

Craig is somehow overlooking that not everyone shares his intuitions, and it is precisely those that do not that Craig is supposed to convince. Already his dialectical opponents may wonder why their own intuitions about the universe’s being necessary and/or eternal should be so easily dismissed. It also goes without saying that intuitions are not necessarily truth-conducive, perhaps especially with discussions of cosmology where quantum mechanics makes a mockery of the far more intuitive – to us – general relativity.

Craig further argues that a stronger argument for the universe’s contingency would be desirable, rather than mere intuition, and thinks he has good grounds for assuming such: his imagination. He constantly refers to the ease of conceiving the contingency of this universe and its components. Seemingly overlooking the obvious conceivability of a Godless universe, Craig implies that the universe not existing is conceivable, and that this somehow makes its contingency more plausible. However, conceivability does not necessarily entail metaphysical possibility, and the assumption that it does has been recently criticised (see: David Chalmers, Does Conceivability Entail Metaphysical Possibility? & Howard Sobel, But that – that conceivability entails possibility – is simply not true!). Furthermore, just because the logical necessity of something is not obvious, doesn't mean it is not there. For instance, we also have no problem imagining a world without God, but if the Ontological argument is true (an argument that Craig defends, by the way), then God is logically necessary  the fact that we can imagine its negation would be irrelevant after all. Additionally, when defending his Kalam fallacy, Craig "argues that Hume’s attempt to show that the universe could have come from nothing fails to show this to be a real possibility [because] it is a mistake to suppose that imaginability entails real possibility. ‘We can, in our mind’s eye, picture the universe springing into existence uncaused; but the fact that we can construct and label such a mental picture does not mean that the origin of the universe could really have come about in this way.'" (Graham, Oppy, "Divine Causation"). Finally, philosopher Quentin Smith argued that "when [apologists] say that you need a disembodied mind to cause the universe, the problem is that the concept of a disembodied mind is inconceivable; it's words. You can't really conceive anything when you're saying them." If it is the case that conceiving or not of something informs us of its (im)possibility, then shouldn't the theistic concept be rejected as impossible?

The great philosopher David Hume also presented a robust response to this kind of reasoning, which is sufficient to cast doubt on Craig's argument:

"But farther; why may not the material universe be the necessarily existent being, according to this pretended explication of necessity? We dare not affirm that we know all the qualities of matter; and for aught we can determine, it may contain some qualities, which, were they known, would make its non-existence appear as great a contradiction as that twice two is five. I find only one argument employed to prove, that the material world is not the necessarily existent being; and this argument is derived from the contingency both of the matter and the form of the world. “Any particle of matter,” it is said, “may be conceived to be annihilated; and any form may be conceived to be altered. Such an annihilation or alteration, therefore, is not impossible.” But it seems a great partiality not to perceive, that the same argument extends equally to the deity, so far as we have any conception of him; and that the mind can at least imagine him to be non-existent, or his attributes to be altered. It must be some unknown, inconceivable qualities, which can make his non-existence appear impossible, or his attributes unalterable: And no reason can be assigned, why these qualities may not belong to matter. As they are altogether unknown and inconceivable, they can never be proved incompatible with it." (Dialogues Concerning Natural Religion, p.65; edited by Dorothy Coleman)

Or as philosopher Felipe Leon explained in his book: "For then one can likewise say that it seems that I can imagine a world at which no concrete objects exist at all, whether contingent or necessary. But if that’s right, then if we stick with an unqualified or unrestricted version of the imaginability-possibility principle, then it seems that we should conclude that there is at least one metaphysically possible world at which no concrete objects exist at all, in which case necessary concrete objects are impossible. Thus, for these and related reasons, I am skeptical of putting much weight on imagined scenarios involving the possible non-existence of material objects." (Is God the Best Explanation of Things, pp. 28-29)

The naturalist philosopher Graham Oppy mentioned (and rebutted) a somewhat similar argument for the contingency of the physical universe: “According to Kenny, any explanation of [the universe] that respects current physics must be a non-necessitating explanation. Why? Because in the decades since the discovery of Einstein’s Field Equations, physicists and philosophers of physics have debated the physical significance of exotic solutions to those equations, premised on the assumption that a significant number of non-exotic solutions to those equations describe physical possibilities. According to Kenny, if we take our cues from current physics, we should endorse the principle that solutions to Einstein’s Field Equations describe physical possibilities unless there are compelling reasons to the contrary. [However], I am saying that only one of the solutions to Einstein’s Field Equations describes a physical possibility. ... Of course, this is not to say that there was no point in History at which it was an open question which of the solutions to the Einstein Field Equations provided an accurate description of our universe... All that is required for open questions is something like epistemic possibility; but our present question concerns ontological or metaphysical possibility.” (Is There a God? A Debate)

There is another, more complex, argument that tries (but ultimately fails) to prove only God could be this necessary being. It is the argument from limits. As Joseph Schimd explained:

"The Argument from Limits [basically says that] "a property P is a limit" means that, necessarily, whatever that has P is limited in some positive respect. So, the way the argument goes is that limits are possibly explained  and by 'explanation' we mean a non-circular explanation (an explanation can't presuppose that which it is just meant to explain in the first place). 

Now, what justifies this claim that limits are possibly explained? Well, first of all, we can certainly conceive of an explanation for any particular limit; we can conceive of something that explains it. For instance, a water bottle is limited in a variety of respects and it's certainly conceivable that something could produce this water bottle and its various limits. And given that conceivability is sort of prima facie defeasible evidence for possibility, it seems as though we can say that limits are at least possibly explained. And again, you can say, "isn't there the conceivability in the other direction? We can conceive that this water bottle doesn't have an explanation and so we have evidence that it's possible that it doesn't." Sure. That's compatible with limits being possibly explained. All we're saying is that limits are possibly explained and something can be both possibly explained and possibly not explained, so that's actually compatible with the evidential bearing of conceivability on the principle that limits are possibly explained non-circularly.

Another another piece of evidence that we can bring to bear for this principle of explanation is that it certainly seems coherent for a limit to be explained. It's certainly coherent for there to be an explanation of the limits of a chair. There's nothing that seems to contravene reason itself; there doesn't seem to be anything that engenders incoherence when we say a limit has an explanation. There are lots of other reasons that we can cite in support of this principle, so it certainly seems to be the case that, for any limit, it at least could be explained. That just seems kind of intuitive. What's stopping there from being an explanation? It certainly seems intuitive, so there's that epistemic seeming that provides some sort of prima facie defeasible evidence for it. There's also abduction; the fact that when we look around us all sorts of limited things have explanations: what best explains that? Well, perhaps what best explains it is that limits are just the sorts of things that can have explanations and so it's no surprise that in our experience we see limits that have explanations. It would be strange if we came across some limit and we just found out that it just couldn't be explained whatsoever in no possible way. So perhaps our experience in the world is best explained by this principle of explanation. You can also use induction: all around the world we look in our empirical experience and every limited thing we've come across is such that not only it can have an explanation but it does have an explanation. So, it seems that we can just do a straightforward induction to justify this another reason in support of this. Is just that for any given fact F an explanation of F is more probable than none. That seems to be just a sort of foundational principle of reason (it's presupposed by science). So, absent special reasons to think otherwise, there's a sort of defeasible presumption in favor of there being an explanation or at least possibly being an explanation.

Another support for this principle comes from categorical uniformity: all the limits around us have a variety of explanations. [For example, a water bottle] was produced by a factory, and so this category of limited things seems to be at least uniform. In our experience, it seems to be such that there are explanations of those limits. If we want to break categorical uniformity and say that all these limits in our experience have explanations but there's this one special one or the special kind of limits that couldn't have explanations, we're breaking categorical uniformity and these sort of breaks in uniformity in modal continuity or modal uniformity seem to add an improbability. All else being equal, we would expect a sort of categorical simple uniformity across a given type or category precisely because it's unified in virtue of being within a category. Therefore, it seems less probable that there would be these sort of seemingly arbitrary breaks in uniformity; we would need some sort of special reason to think that there's a break in uniformity and absence such a special reason there's a sort of defeasible presumption in favor of adhering to this categorical uniformity. So, again, this is further evidence that limits are categorically uniform with respect to possibly being explained.

Finally, we could cite the Principle of Relevant Differences to justify it. That is, it seems to be the case that, if you pick any two limits, what's gonna be a relevant difference between those limits that could account for why one does or can't have an explanation and the other one literally cannot have an explanation. What's gonna be that difference? You can't just say "It's just not possible for this to have an explanation" because it's precisely the question at issue as to why it can't have an explanation whereas this one does, since they're both limited. What's the relevant difference between the limits here that could account for why one of them literally is impossible for it to have an explanation and the other one it's not impossible. Just intuitively, it seems as though we won't be able to pinpoint a sort of relevant difference between limits. So, that's just a further piece of evidence in favor of this principle.

[Conclusion of the Argument]

The property "having limits" is itself a limit. Whatever instantiates the property "having limits" is itself limited precisely because it instantiates that property; it is limited in some positive respect. In which case, whatever has this property, namely, the property of having limits, is limited in some positive respect and that's precisely what we defined limit as. So, it follows that "having limits" is itself a limit and hence by our principle of explanation, the property of having limits is possibly explained. But the only possible explanation of the property of having limits is an unlimited being  you can't cite a limited something that already instantiates the property of having limits to explain why that property is instantiated in the first place; it already presupposes the instantiation of the property. If you're trying to explain the instantiation of property by means of something that already instantiates that property, it's just sort of viciously circular. Therefore, possibly, there's an unlimited being because we just found out that the property of having limits is possibly explained but the only explanation is in terms of an unlimited being and hence it's possible that there's an unlimited being. But whatever is unlimited is a necessary perfect being since whatever is less than perfect is limited in some positive respect, and so if it's not limited in some positive respect, namely, if it's unlimited, it must be perfect. So, it's going to be a perfect being. Also, whatever is contingent is limited in respect of sort of the robustness of its existence; its grip on reality, its liability to corruption or cessation and that seems to be a sort of limit. In which case, whatever is unlimited is necessary and so what we get is that it's possible that there is a necessary perfect being. 

By the S5 axiom of modal logic, whatever is possibly necessarily the case is just necessarily the case simpliciter. It follows that there actually is, and there necessarily is, a necessarily existent perfect being and this, all men call "God". Something is possible if it obtains (viz., exists in or is true) in some possible world. Something is necessary if it obtains in all possible worlds. Now, if something is possibly necessary, that just means that something which is of its nature necessarily existent is in some possible world but, by the definition of necessity, whatever is necessary obtains in all possible worlds if it obtains in any world. If it's the kind of thing which is such that it exists in all possible worlds and you're saying that this kind of thing is instantiated in one of those possible worlds, then we can zoom into that possible world and ask how could this necessary thing be instantiated in this world. It's precisely because it's necessary that it must be instantiated in all worlds  that's just what its essence is; its essence couldn't obtain in a particular world if its essence didn't obtain in all worlds. That's just what it means to be necessary. Hence, if something necessary obtains in any world, it obtains in all worlds including the actual world, and whatever is possibly necessary is necessary simpliciter and whatever is necessary is, of course, actual, then we get that whatever is possibly necessary is actually existent. Of course, this assumes the symmetry of the Accessability Relation, the Transitivity of the Accessability Relation and the reflexivity of the Accessability Relation. But there are some plausible defenses of S5 and it is, sort of, majority view in contemporary modal metaphysics to accept the S5 axioms."

Joseph, then, went on to sum up some of the problems with this argument:

"I find such reasoning deeply implausible. First, even granting that the entity is unbounded, we can only get to immateriality/non-physicality if we assume that every physical thing is bounded. But why assume that? Why couldn't there be a foundational, unbounded quantum field (say)? Second, by their very own lights, God is bounded in a whole host of ways. For instance, God is limited or bounded in terms of the number of divine persons he is (3 as opposed to 4 or 1 or 12 or 77 or infinitely many). Third, I don't see why limits or bounds would or even could compromise something's necessity, which is a function of whether it exists in all possible worlds, not about whether or not it has demarcated limits. (Consider that, plausibly, the number 2 necessarily exists, but it certainly isn't unbounded/unlimited.)"

Elsewhere, he expanded on his points:

"One [problem for this argument] is just that [1] it seems entirely possible for there to be necessary unexplained limits. For instance, it seems entirely possible that there could be just a tiny particle that is such that it has its spatial dimensions and causal powers necessarily and there doesn't seem to be any contradiction in that. Or you could imagine a sort of quantum field which could be such that it necessarily exists and it necessarily has its limited structure and limited causal powers. There just doesn't seem to be anything incoherent about that. 

Another thing that we can bring to bear with respect to this objection is that [2] it seems as though this Argument from Limits might not be compatible with trinitarianism. When we have trinitarianism we have 3 persons; not four, not 20, not 365 and not 7512. So, there is a limit with respect to the number of divine beings, namely, 3. But there couldn't be other than 3 divine persons if trinitarianism is true. So, it seems as though there's just no explanation as to why there are 3 divine persons as opposed to two or one or ten or 365. And if there could be an explanation for our principle of limits, then it seems as though it couldn't be in terms of those very persons, so we'd have to cite some additional god that's accounting for why there is this Trinitarian God and that's not gonna be palatable. Now, one might [argue] it's just necessarily the case that there are 3 persons in the Trinity and that explains why there are 3 persons. But now there's a difficulty because now we can just say [that if the theist can invoke] these necessary limits with respect to God, then the Naturalist can bring in necessary limits with respect to the fundamental nature or the fundamental portion of natural reality. It's going to be, for instance, a necessarily existent quantum field and it is such that it's going to have its limits obtaining of metaphysical necessity. Why are those limits obtaining? Well, because they're metaphysically necessary. So, if we're going to cite metaphysical necessity as the explanation of why there is a limited number of Trinitarian persons, then it seems as though the naturalist is perfectly within his or her epistemic rights to reject this argument by means of pointing to necessarily obtaining limits in the natural foundation of things, [and as a consequence, it] undercuts the step to God.

A third [3] and final problem stems from desires. Desires seem to come in degrees; I desire water more than I desire to kick a puppy... Saying that this being is such that all of its desires have an unlimited force or unlimited strength engenders a lot of problems. For instance, we're not going to be able to mount any probabilistic arguments about what this being would do because when we're mounting such probabilistic arguments, there are going to be a range of different alternatives each of which has some value to it and hence some desirability to it. But we have to be able to say we would expect at least this outcome more than the others in order to predict what this being would do or even make sort of Bayesian arguments like the fine-tuning argument about what this being would do. [After all], if it's such that all of its desires  even for these incompatible states of affairs  are completely unlimited, then not only does it seem completely inexplicable as to which one does it choose, if the being is such that it has unlimited desires about all of these, then it seems that we're not going to be able to predict which one we should expect it to bring about precisely because its desire is such that it is unlimited to bring each one of them about; they're all equal in cardinality, namely, being beyond cardinality itself precisely because they're unlimited. So, it seems as though we're just gonna collapse so many different natural theological arguments because those rely on things that we would expect a perfect being to do. [Therefore], it seems as though we're going to have to get rid of a lot of natural theological arguments if we have this being which is such that all desires are unlimited."