Reality has no fundamental level

What infinity can teach us about dependence

Most of us think that reality has a foundational level, perhaps in the form of ultimate particles. But Ross Cameron argues that this view is misguided and that the nature of reality might be turtles all the way down.

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Imagine you’re on the ground floor of an office building. You could go up the stairs, to an above-ground floor. Or you could go down the stairs, to the basement, and stand among the foundations of the building. Some buildings even have a sub-basement, so you can go down even further than the basement. Some even have multiple sub-basements: perhaps you have to go down three floors from the ground floor to reach the true foundations. You can easily imagine more and more extensive sub-basements: ten levels below ground, a hundred, a billion! We outstrip the bounds of architectural plausibility, but not the bounds of coherence. For any finite number, n, it’s at least conceivable to have n basement levels below the ground floor.

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But we can imagine even more elaborate possibilities. Imagine a building where you can keep descending, without ever reaching a bottom level. Where for every level of sub-basement you reach, there is yet another beneath it. No matter how far you descend, you will never reach the foundations of this building, for there are no foundations: every floor rests upon a lower floor. Perhaps even wilder still, imagine a building where you descend from the ground floor to the upper basement, and from here you descend to the lower basement, from which you descend to the second floor, from which you descend to the ground floor. In this building you keep going down and end up back where you started (likewise if you keep going up). And this isn’t because there is a teleporter in the lower basement that makes you think you’re going down but in fact it teleports you up – it’s the even stranger thought that immediately below the upper basement is the very same level of the building that is above the floor that is above the ground floor.

Both of these imagined buildings involve a type of infinite regress. The first building has infinitely many floors, and so you can descend and descend ad infinitum without ever reaching the end and without ever setting foot in the same floor twice. The second building has finitely many floors but they go in a circle, so you can descend and descend ad infinitum, finding yourself back where you started despite never retracing your steps. Neither building has a foundation: in each case, every floor rests upon another floor.


The claim that reality must have an ultimate level is often supported by little more than an appeal to intuition or incredulous bafflement at the alternative.


Must reality have a foundation, or might it be like one of our two strange buildings? Especially in Western thought, scientists, philosophers, and theologians alike have been attracted to the idea that there must be a fundamental level of reality that gives rise to everything else. Aquinas thought that the ultimate being was God. Thales thought that at the ultimate level, everything was water. Contemporary philosophers might be more inclined to defer to science and say that the ultimate level consists of fundamental particles, or fields, or the quantum wave function, although some more adventurous philosophers might defend a contemporary version of the idealism of Leibniz or Berkeley and hold that the ultimate level of reality consists of minds or consciousness. But while these theorists all disagree, sometimes vehemently, on what the ultimate layer of reality consists in, they are in agreement that there is a fundamental layer of reality. Even pure mathematicians, unconstrained by the nature of the physical world, have tended to think that there is a starting point to the mathematical realm, and so we have the iterative hierarchy of standard (Zermelo-Fraenkel) set theory, where every set is built out of the empty set, that lies at the bottom - arising out of nothing.

But perhaps reality has nofoundation. Atoms, it turned out, could be divided into protons, neutrons and electrons, which it turned out could be further divided into quarks. Maybe we can keep going, further dividing and further dividing without ever reaching an end. Perhaps, as Leibniz thought, our material world depends on an entirely mental realm. But perhaps, as Leibniz did not think, that mental realm depends on some other material world, which itself depends on yet another mental realm, and so on. Perhaps we will break open a quark to find something even smaller, and perhaps we will break that open to find . . . our entire universe! (Like Borges’ Aleph.) Why rule out the possibility of infinite regress in the composition of reality, whether that be infinitely many distinct layers, each more fundamental than the previous, or whether it be reality going in a circle, such that if you dig down far enough you discover the universe as a whole?

In the mathematical realm, there are perfectly coherent set theories where you can have sets with infinitely regressing membership chains, like a box that contains a smaller box that contains a yet smaller box, and so on without end. (Imagine a set of Russian dolls, but with no smallest doll: inside each doll there is yet another smaller doll.)  Or sets where if you follow the membership chain far enough you discover the set you started with, like a box that contains a smaller box that contains a yet smaller box that contains the very box you opened at the start.


Contemporary foundationalists might replace God with non-divine foundations, but they mimic Aquinas’s reasoning: some ultimate being or beings are needed to get everything off the ground.


The claim that reality must have an ultimate level is often supported by little more than an appeal to intuition or incredulous bafflement at the alternative. If an argument is given, it is usually that reality must have foundations if anything else is to get off the ground. To go back to our analogy of the buildings, we might argue that there needs to be a foundational level for every other level to ultimately rest upon. If there is an infinite regress of distinct levels of reality, more and more fundamental but never ultimately fundamental, then (it is argued) there is nothing whose existence can account for the existence of everything else. A circular regression might seem even worse, from this perspective, since then every level of reality ultimately depends on itself, metaphysically bootstrapping itself into existence. The foundationalist, by contrast, can offer a picture whereby everything non-foundational ultimately inherits its existence from reality’s foundations. This echoes Aquinas’s second and third ways of demonstrating the existence of God: there must be a God, the prime mover, the sole necessary being, to account for the existence of every dependent or contingent being.

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Contemporary foundationalists might replace God with non-divine foundations, but they mimic Aquinas’s reasoning: some ultimate being or beings are needed to get everything off the ground. But in that case they are no less vulnerable to David Hume’s critique of Aquinas. Foundationalists take the ultimate beings - whether they be God, minds, quarks, quantum fields, or something else - for granted; there is no deeper explanation of where they come from. Why is an unexplained Prime Mover okay when an infinite regress of greater and greater movers is not, or a circle of things each moving each other? In fact, why isn’t it worse? The foundationalist posits some things that are, by definition, unaccounted for. In an infinitely descending or circular reality, at least everything is accounted for.

A demand for reality to have foundations, without some compelling reason, risks being an article of faith, even if it is a secular faith that invokes quarks instead of God. And as intuitive as foundationalism seems – as outlandish as infinite regression and circularity may strike us – we must remember that what we find intuitive and familiar is shaped by our intellectual traditions. Eastern thought has historically found regress and circularity more amenable than the Western tradition. Buddhist metaphysics has traditions in which every thing is thought to be dependent on some other entities, leading to infinite regression, and indeed traditions in which every thing is thought to be dependent on every other thing, and so reality consists of a vast web of interconnected entities. These views might turn out to be wrong, but to simply rule them out as an article of faith is to risk ignoring exploring reality’s possibilities to the fullest.

Of course, it’s one thing to say we should not rule out the possibility of a foundationless reality, and another to argue that there in fact are infinite regresses and circles of dependence in reality. I won’t attempt to survey reasons you might have for thinking that reality is actually lacking a foundation. One could write a whole book about that. (And I did, Chains of Being.) But I will close with one argument for circularity that I am fond of.

What makes you you, the very person that you are? Many philosophers think it’s not a matter of the particular body you have, for we can imagine science-fiction scenarios where we are uploaded into a computer and survive as software, not tied to any biological body. Why would that still be us? Because the essence of us – what makes us who we are – seems to be tied not to our bodily or biological features, but to our psychological ones. What makes me me are my beliefs, memories, desires, hopes, dreams, projects, etc. If those are preserved by some software program running on a computer, then I have survived the digital upload.

This thought, that our essence is tied to our psychological features, not our biological or bodily features, goes back at least to the 17th-century giants of modern philosophy, Descartes and Locke. But I think it has implications for the structure of reality that have often gone unnoticed. Many of my core psychological features involve other people. My hopes and dreams and projects, e.g., are intimately tied to my wife’s hopes and dreams and projects. To fully love someone in the way that romantic love demands is to, at least to some extent, take on their hopes and dreams and projects as your own, not because you find yourself coming to also value those projects etc. for their own sake, but simply because they are your beloved’s projects and you value them because they are your beloved’s projects. As such, your psychology – what makes you you – can intimately involve this connection to your beloved. In a perfectly real and literal way, you wouldn’t be you without them. But (in the good cases, at least, ignoring sad cases of unrequited love) this connection goes both ways: the exact same reasoning suggests your beloved would not be them without you. And so there is a metaphysical interdependence between the two lovers. Love can go so deeply that it literally creates circles of metaphysical dependency between us. And this is not restricted to romantic lovers: it could hold between siblings, between parents and children, between particularly close friends. These metaphysical connections are created when we open ourselves to one another in such a way that our essence – what makes us the person we are – is shaped by our relationship with the other. As this process spirals out, webs of mutual dependence are created among us.

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Mainstream Western metaphysics has long tended to see the self as a substance. Unlike metaphysically sub-par entities like shadows or holes that depend on the things that cast them or their surrounding matter, the self is capable of independent existence. But Eastern metaphysics, and indeed contemporary feminist metaphysics, has instead emphasized the connections between us that very literally make us who we are.

“All the women who are independent, throw your hands up at me”, sang Destiny’s Child ("Independent Women, Part 1". Then again, in the same song Beyonce sings “I depend on me”, thereby embracing a very small circle of dependence). Our culture teaches us that ‘being independent’ is good, and being dependent, especially co-dependent, is bad. While I do not of course deny that certain kinds of independence are good and that co-dependent relationships can be bad, I think it’s important to appreciate that metaphysical co-dependency can be beautiful.

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dolo pem 18 January 2024

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