Our Unified Universe
Imagine a universe in which mind, matter and mathematics all exist but stand in no interesting relation with each other. Minds don’t know any mathematics, mathematics has no application to matter (or mind), and mind and matter have no causal interaction or even correlation with each other. The three merely coexist in this universe as separate realms with no connection. It is not a unified universe but simply a three-element universe—a mere list not an organic whole. The parts don’t interlock and function together but merely exist alongside each other. In particular, the minds in this universe don’t understand mathematics and apply it to reality; mathematics simply exists abstractly, not even being true of the rest of the universe. Think of it as an ontological trinity without connecting relations: each realm has a robust existence but they are totally cut off from each other. They are a Many that does not correspond to a One (except the set consisting of all three). It would be hard to think of any design to this universe; it seems gratuitous, random, and pointless—just three types of being idly sitting beside each other (and not even that, because “beside” expresses a spatial relation). They are non-communicating cohabitants not collaborating members of a team. They leave each other completely alone in splendid isolation. If a super-being had created this universe, you would wonder what its purpose was—a cosmic storeroom perhaps? Each component has its own reality and set of truths, but there is no inter-category impingement and hence no higher unity.
Our universe is not like this; indeed, the universe described is the negation of ours. We have the same set of basic categories, but our categories interact in substantial and meaningful ways. Our minds do grasp mathematics, mathematics does apply to the world, and mind and matter interact in manifold ways. We can picture our universe as a triangle with mathematics at the apex and mind and matter at the two base angles. A line connects mind to mathematics with an arrow pointing upwards (this is understanding mathematics); the opposite line connects mathematics to matter with an arrow pointing downwards (this is mathematics applying to the world); and the two base angles are connected by arrows pointing both ways representing causal interaction. This last involves perception of matter by mind, dependence of mind on brain, and possibly the origin of mind in matter. In virtue of these relations the three-part structure functions in a certain way: mind and matter enjoy causal commerce and are deeply connected, while mind uses mathematics to describe and explain the world by exploiting the fact that mathematics applies to the world. It might be said that matter causes mind, which understands mathematics, which applies to matter. Mathematics is not cut off from mind and matter at all, as in the previous universe, and mind and matter are closely intertwined. This is not mere cohabitation but close collaboration.
None of the relations I have described is philosophically unproblematic; in fact, they constitute some of the deepest problems of philosophy. How does the mind come to grasp and know mathematical truth, especially given a Platonist understanding of it? This can’t be a causal relation, but then how does the mind make the connection? Similarly, why is mathematics applicable to the world? If mathematical truth concerns an autonomous abstract world, why is there an uncanny fit between it and empirical reality? How is mathematical physics even possible? And the mind-body problem is too well known to need exposition: how does psychophysical interaction occur? Is the mind the same as the body or separate from it? Nevertheless, these relations evidently exist, puzzling and mysterious as they are. They lead to a variety of familiar theories: materialism declares all three realms to be variations on matter, so that all the inter-category relations reduce to physical relations; idealism makes all three mental, thus eliminating ontological gulfs (matter and numbers being mental constructions); and dualism (or pluralism) affirms the reality of all three and lives with the accompanying mysteries, maybe invoking divine assistance (pre-established harmony and so on). These problems don’t arise for the list-like universe, because the problematic relations don’t even obtain there; but that is not our universe. Our universe consists of interlocking parts in which ontological chasms are routinely crossed: we do know mathematics, mathematics applies to extra-mathematical reality, and mind and matter are on intimate terms. Our universe is structured by these relations: psychophysical causation, mathematical knowledge, mathematical application. The first relation has received much attention, but the other two should not be neglected.
I submit that our universe qualifies as an organic unity, unlike the unstructured universe. I don’t mean that it is literally a living thing, only that it works as a unified whole (as a machine does): it has parts that work together. One might venture to suggest that mathematics exists in order to be known and applied to the empirical world, while mind owes its efficacy (and maybe its existence) to the material world. In the other universe each category is irrelevant to its companions, but in our universe each category feeds off the others in a kind of cosmic dance (we might picture mathematics as being rather pleased that it is known by minds and applicable to matter). Our universe is unified, a One that encompasses a Many. It is not a mere random set but a functioning totality. An animal body consists of an interacting assemblage of organs not merely a collection of them, so that it constitutes a higher unity; the universe is similar in that its parts do not sit idly by content with their own internal reality but feed into each other to produce results not obtainable otherwise. Physics is one such result, as is science generally (psychology too has its mathematical side). Material civilization is another. These are not possible in the list-like universe, because the requisite relations don’t obtain. This universe seems logically possible, but it is a far cry from our universe with its rich internal structure. If it had been designed by a super-being, one could see the point: the whole arrangement was set up to exploit the relations between the different parts, not as a mere exercise in ontological fecundity. If you wanted to produce beings like us, such a universe would be necessary—not the universe in which disunity reigns. We are psychophysical beings who know and apply mathematics, but this human nature requires the existence of the relations I have been harping on. The mental beings in the alternative universe would have a very different nature, having no commerce with matter and no inkling of the mathematical realm. They would be vastly inferior to us in both power and knowledge, knowing only their own mind and being incapable of shaping the material world (or being shaped by it). The architecture of our universe, by contrast, delivers real dividends and does not provoke the reaction “What is the point?” If you were a god with a strong interest in mathematics and science (but not much concerned with morality), this would be an interesting project to undertake–while the unstructured universe would seem an exercise in futility.
These reflections edge us in a theistic direction, but not of the traditional Judeo-Christian kind. The emissaries of the god who created our unified universe are not Jeremiah, John the Baptist and Jesus, but Euclid, Pythagoras and Plato. This god has little discernible interest in sin, suffering, and salvation, but it evidently has a strong interest in mathematical knowledge and its applications. Its proudest products are Cantor, Godel, Gauss, Newton, et al. It also apparently believes that the psychophysical nexus is the beating heart of things—seeing, acting, feeling—not disembodied contemplation and self-directed introspection. Thus this super-being (let’s not call it “God” or “a god”) created a universe in which these ideals could be realized: a world of embodied minds and knowable mathematical order. And who is to say that these are not worthwhile aims? So we might try to convert the considerations of this essay into an argument for the existence of such a being—only a designer like this can account for the organic structure present in our universe. The disparate parts had to be brought coherently together, which was no easy feat, and is not built into the very ideas of mind, matter and mathematics. On the evidence, this being is not keen to reveal its existence, being more like a scientist conducting experiments than a caring father figure interested in our moral condition (perhaps at this moment the being is saying to itself, “Rumbled at last!”). At any rate, there is a challenge here to explain why the universe in which we live isn’t of the unconnected variety—why it seems so well designed for knitting the separate parts together. There is nothing random or pointless about it. The parts fit harmoniously together, nicely enabling certain things not possible otherwise, such as science and civilization. Even morality finds a place, given the need for concrete moral action and the possibility of a utilitarian calculus (though no doubt our super-being prefers actual calculus). Pythagoras was the true prophet, though (temporarily?) eclipsed by religions of a more worldly and practical bent.
There are two ways to render the universe metaphysically unified. One is to claim that everything is made of the same stuff—hence materialism and idealism. The other is to claim that the various parts of the universe, whether of the same stuff or not, are interrelated in such a way that an organic whole is the outcome. It appears that our universe is of the latter kind, unlike other universes that may be conceived. Perhaps in the logical space of possible universes ours stands out for its organic unity, fortunately for us.
 This isn’t to say that there are no areas of disconnect: we may not understand all of mathematics, some of it may have no application to the world, and mind and matter may harbor aspects that have no bearing on each other. So the links are partial not total; still they exist and are significant.
 As an exercise read Paul Benacerraf’s “Mathematical Truth” and Thomas Nagel’s “What is it Like to be a Bat?” in tandem—the structural parallels should stand out. The best conceptions of mind and mathematics leave their relation to the human organism deeply problematic.
 There is a question about other animals—do they know mathematics too? You might be tempted to say no, but that would be rash: animals live in a mathematically describable world and must be sensitive to mathematical facts. Animals need to be aware of amounts, plurality, size, distance, speed, and so on in order to function successfully (consider migrating birds). True, they are not taught arithmetic at school, but their brains must be capable of elaborate calculations. So let’s not exclude them from the realm of the cognitively mathematical; there can be many ways of “knowing” mathematics.