 I've become persuaded by a version of Platonism. The universe seems to be composed of concrete and abstract things, and the abstract things seem to exist separate from our individual minds. For years, I've been making anti-Platonist arguments. One of my most popular articles, No Chairs Do Not Exist, sketches out a conceptualist position, which claims that the famous chair-ness of Plato isn't an ethereal platonic form, but rather its conceptual criteria situated within our own minds. It seemed to me that all abstract stuff was situated within the mind. But now I think conceptualism is incorrect, or at least incomplete. This change of mind happens since coming up with my theory of indirect interaction, which allows objects in multiple ontological categories to effectively interact with each other. If there is a distinct mental and physical realm, then perhaps there's a platonic one as well. So, for the past couple of years, I've been playing Devil's Advocate with myself. And to my horror, the Devil eventually persuaded me I now think some kind of Platonism is a better theory to explain how the universe operates. Abstract things seem to be as fundamental as concrete things. Not only might chairs exist, but chair-ness probably does as well. Let's begin by calling abstract things abstracta for simplicity. First of all, it's hard to understand what abstracta are, because you can't point to them. They're hard to clearly reference since they don't look like anything. They don't take up space, so we have to be content understanding this concept without directly observing what it references. I'll try to illustrate the idea, then rephrase it several ways from several different angles. Abstracta are things like patterns, connections, and most importantly, relations. Any metaphysical theory needs to explain the existence of objects and their behavior across time, and it turns out, relations are essential to explaining the behavior of objects. Note for idealists reading or listening to this article, you can substitute the word object for, quote, areas of experience, and the argument still holds. The general idea is this. The universe comes bundled together. There are individual objects and concrete things, and there are relations among them. These relations are abstract and independent from our minds. Concrete objects in the world are not isolated from one another. Their states affect each other. Their states are related, and these relationships have a real metaphysical existence. Individual objects by themselves are not sufficient to explain their own behavior across time. Their behavior is determined in relation to other objects. Were concrete objects completely isolated from one another, then their behavior would be different. Therefore we have to posit the existence of the concrete objects and their abstract relations. We observe that the fundamental building blocks of the physical world, let's call them atoms, get unified into larger objects, meaning their behavior is different than if those individual atoms existed without any relation to each other. I've previously argued that this unification is done by the mind. Now I believe the unification is also done by the universe. You can think of relationships like glue. Fundamental units of matter are glued together, their states are interrelated, and this relationship exists in addition to the fundamental units. To grasp these abstract relations, it's helpful to break apart the physical world down to its most fundamental components. Take any physical object, break it apart, and you'll end up with smaller pieces. Break those pieces apart and you'll end up with even smaller pieces. Keep breaking things down and eventually you'll end up with atoms and molecules, which you can break apart into subatomic particles and so on. The key question is this, at some point do you ever reach indivisible units? Or can you keep breaking things down ad infinitum? For purposes of this article, let's say that there are indeed fundamental indivisible units at the bottom of everything. Let's say we can completely reduce the physical world down to different arrangements of these indivisible units. At this base level of analysis, there's a further interesting question here. What is the difference between these individual units and the space that they occupy? What is space at this fundamental level? For purposes of this article, let's posit the following. The most fundamental units of the physical world are identical with units of space. They are atoms of space. They don't occupy space. They are space. You can call this theory geometric atomism. At the bottom of everything, there are only units of geometric space in particular states. You can think of it like an extremely fine resolution Minecraft world where indivisible blocks form all other complex structures. So regular, large-scale atoms like helium would be ultimately reducible to a pattern of units in space in a particular state. To keep this model simple, let's say that the geometric atoms can be on only one of two states, on or off, empty or full, zero or one. This allows us to represent patterns of atoms as sequences of zeros and ones. For example, empty space might be represented as just a bunch of zeros, zero, zero, zero, zero, zero, zero, zero, zero, while an atom of helium might look like zero, zero, zero, zero, zero, zero, zero, one, one, one, one, zero, zero, etc., or a chair might be something more complex like zero, one, one, zero, one, one, one, zero, one, one, one, one, one, zero, one. Lots more ones. You get the idea. Different objects are different patterns of geometric atoms, but since the metaphysics of space is not the subject of this article, just treat geometric atomism as the model for the physical world that will help illustrate the point about abstract things. So in this model, what is a chair? Well, at first glance, it appears that a chair is just some pattern of atoms, it's not something in addition to the atoms. The whole chair is not greater than the sum of the parts of the chair. The whole is the parts, it's just a shorthand way to reference all the parts. I like the way that myriological nihilists like to phrase it. A chair is just atoms arranged chair-wise. In this theory, the word chair merely references some patch of space which contains a pattern that meets our own conceptual criteria for being labeled as a chair and nothing more. My personal favorite example of this that I've used in my previous writing is constellations. Without any humans, would there be constellations of stars, would there be a big dipper that exists in addition to the individual stars that compose it? It seems unlikely, while individual stars might have some mind-independent existence, their unification into the big dipper is something that minds do. I've previously claimed that this unification of parts into holes is always a mental function, and in the mind-independent world there would be no such unification, but now I see this argument is incomplete, it misses something very important. The behavior of those atoms across time. The real-world behavior of composite objects implies that the universe unifies parts into holes too. Abstract relations are not all created by the mind, some of them are actually discovered in the universe. Consider a metal spring. Let's reduce it down to a purely geometric form, a pattern of ones and zeros. As the spring is compressed, that pattern of ones and zeros changes, and as the spring returns to its original position, that pattern also returns. Notice, when the spring is compressed, it doesn't fracture into a trillion isolated atoms. The atoms instead have a particular behavior, and their positions are determined in relation to each other. The ones and zeros change across time, depending on the neighboring ones and zeros. The individual atoms alone do not determine their own behavior, they're stuck together in a kind of composite system with many interrelated parts. Now, critically, these relations are not like the relations of stars and constellation. Distant individual stars do not seem to affect one another's states, but the atoms of a spring do affect each other's states. So the universe, not our minds, seem to unify the atoms of a spring into some composite object whose behavior is different than if the individual atoms weren't unified. You could say it this way, a hundred ones next to each other behave differently than a hundred isolated ones that are unrelated, therefore the fundamental units themselves are not sufficient to explain their own behavior. While our minds do glue seemingly unrelated things together, like the stars and the constellation, the universe also seems to glue things together, and this glue is a bunch of abstract relationships that exist independent from our individual minds and take up no physical space themselves. In fact, there seem to be many relations and connections in the world. A tree's top and bottom, for example, are related. When the state of the roots changes, the state of the leaves change. Two ends of a stick are related. When one gets pushed down, the other rises up. Families too act like composite objects. The state of the husband affects the state of the wife. Where they isolated individuals without relations, their states wouldn't affect each other. So whether or not some set of individuals qualifies as a, quote, family might actually be a metaphysical question. Do the states of the individuals in question affect the states of the others according to our abstract criteria of family-ness? Do they behave like a family? If not, then regardless of the last names of those individuals, they are not unified into the composite object known as a family. There are in fact billions of people on earth whose states don't affect me so I'm not unified into some composite object with them. Through this lens, even nations seem to behave like composite objects. The atom of society, if you will, the individual human, is affected by the state of others who are glued together into a nation. These humans' lives would be different, for better or worse, if they weren't glued to each other. Though this doesn't square too nicely with my current libertarian philosophy, factually speaking my state is affected by the state of other people who consider themselves part of the same nation. I find myself part of a larger system, whether I like it or not. The universe seems to be a relational system and this applies both to physical objects and to humans. Let's return to the metal spring example and compare these two statements. Statement number one, springs are just atoms arranged spring-wise. Statement number two, springs are just atoms, period. Now there's clearly a difference between these two statements. What is it? What does the first statement convey that the second does not? The concept of arrangement or you could say structure, form or shape, the pattern of atoms. Their states and relationships analyze together rather than individually. A spring actually cannot be described by simply stating X number of atoms existing. That's not enough information. Springs are X number of atoms arranged in a particular way. To use more traditional language, this is like the difference between matter and form. Well actually in the context of historical philosophy, matter and form probably meant something different but in contemporary English these two words convey the correct concepts. Matter is the atoms and form is their arrangement. Form is a bundle of abstract relations and we can distinctly reference both matter and form. The universe apparently treats form as something in addition to the matter. It's a unique, relevant feature of the universe that actually affects how things behave. If the form of the matter changes, its behavior changes. Thus, there is a real metaphysical difference between a trillion atoms arranged this way and a trillion atoms arranged that way. In fact, the difference between physical objects is precisely their atomic arrangements, geometric structures of the fundamental objects in the physical world. But why should units of matter behave differently when they're in different arrangements? I don't know but that's the way the universe seems to operate. We might consider physics then, the study of exactly which geometric structures yield which behaviors. Consider the position of an individual atom. We can imagine that it might have some absolute position in space, perhaps identifiable by X, Y, and Z coordinates, but the universe doesn't seem to care too much about absolute position if such a thing exists. Relative position seems to be what matters, an atom's position in relation to other nearby atoms. It's changes in relative position that yield different behavior. It's as if the universe is saying, when atoms are arranged this way, then render out this state. And when atoms are arranged that way, render out that state. So it is a mistake to consider objects in the universe as being in a state of radical metaphysical independence. They are not. They are glued together. Their states are unified. And unless solipsism is true, it's not our own minds doing the unification. Notice, when we talk about relative position and relative arrangement, these aren't concrete objects themselves. They aren't atoms. They're not composed of atoms. They don't weigh anything or look like anything. These are abstract, and yet they seem to be some integral part of the universe's operation. Because I think they're both abstract and mind independent, I'm calling this metaphysical status platonic. Part of the reason I've been so skeptical of Platonism is because I've never been able to fully make sense of the concept of platonic forms, the infamous chair-ness that Platonists like to talk about. I also couldn't understand how our human minds might interact with these ethereal platonic forms since they're supposed to be explicitly non-mental. But now, thanks to my theory of indirect interaction, I have a workable analogy. But let's start with what we know. Before theorizing about the platonic realm, we can say this, that at the very least, chair-ness can reference our own conceptual criteria for determining whether we label something a chair. That criteria does exist, and it's unique to each of our minds. We can imagine edge cases where something that doesn't qualify to a chair to you might qualify as a chair to me. However, chair-ness might also reference something else. Let's call it universal criteria. Just like we have abstract criteria that determines whether or not something gets the label of chair, the universe seems to have some criteria for determining the behavior of things that we call chairs. So in that sense, the chair-ness in our minds might actually correspond to chair-ness in the universe. A chair is simply an object, a unique pattern of behavior, a particular output state or pattern of outputs across time. If the atoms of the universe stand in particular relation to each other to form the structure that we call a chair, then the universe will output a unique state, keeping those atoms glued together in a very specific way. The best analogy, I think, is to computer code. You can imagine universal criteria as like computer code, which says if criteria A is met, then output state B. So chair-ness would be that part of the universe's code that determines when atoms behave like chairs or when atoms are unified in a unique way that we reference as chairs. And this is how chair-ness might exist completely separate from any actual chairs. The code can still exist if A even B, but since there might not be any A, there might not be any B. Consider the dinosaurs. Let's say that a dinosaur is a particular structure and pattern of behavior of atoms across time. So when dinosaurs exist, it's as if the universe is running the dinosaur program. If in 2020, atoms were arranged in that way that constituted a live dinosaur, then would we see those atoms behave like a dinosaur? If so, then we could say that the universe's code for dinosaurs still exists even though there are presently no dinosaurs. The program is still out there even if it isn't running. Now let's call the code for dinosaurs, quote, dinosaur-ness, and suddenly, Platonism makes sense. What is the Platonic dinosaur-ness? Well it's that part of the universe's code, which determines when some arrangement of atoms is to behave like a dinosaur. And notably, there don't need to be any actual dinosaurs in order for this Platonic form to exist. If we understand Platonism this way, the contrary position actually seems bizarre. Anti-Platonism would imply that the universe could no longer produce dinosaurs. So even if atoms were arranged exactly like they were back when dinosaurs existed, those atoms wouldn't act like dinosaurs. The universe somehow couldn't run the dinosaur program or output any dinosaur states. To me it seems more reasonable to think that even if all the dinosaurs go extinct, the code for dinosaurs would still remain. Another intuitive example is 3D printing. There's a clear difference between a computer file, which contains information about how to build a physical object, and the physical object itself. The file is just a bunch of ones and zeros. Well actually to be precise, it's not just ones and zeros. It's ones and zeros in a particular arrangement, in this case that arrangement is the whole point. But you won't find a physical object inside the code. And yet somehow it contains enough abstract information to be able to construct a physical object from it. Like Platonic forms, this code exists separately from any printed structures. Even if the code is never instantiated into a physical object, that abstract information, the form, the structure, the pattern, it still exists. Let's entertain the idea that fundamental units can indeed get unified into composite objects. We run into a famous problem, it's called the special composition problem. Exactly when does this unification occur? Under what circumstances do fundamental units suddenly get treated as a whole thing? I think the easiest resolution to the special composition problem is this. New objects are composed whenever the universe treats fundamental parts as interrelated. Since it's precisely the universe doing this unification, it's not our minds doing it, which means we don't know beforehand exactly what structures will yield unique behavior. I can't tell you some simple rule, it's a matter of empirical inquiry. Whether or not X and Y are related is not discoverable by examining X or examining Y in isolation. Has to be X and Y's state changes that are observed together across time to see if there are any discoverable patterns. For example, a tiny asteroid trillions of light years away probably doesn't form an object with my thumb. Their states appear to be unrelated. The asteroid can do anything, move anywhere, change its structure, but it won't affect my thumb. However, my fingers and thumb do appear related, the states of my fingers affect states of my thumb. There are quite a large bundle of relations between them, such that the universe outputs their behavior as a composite object that I reference as my hand. My hand shares many further relations with my arm, which shares many relations with the rest of my body. Hence, the universe treats the parts of my body as very tightly bundled and not isolated from each other, so my body might also qualify as a composite object. Prosthetics are actually an interesting example here. Is a prosthetic a true part of the body? Well, in this model it depends on the tightness of its relations, so a removable prosthetic arm has far fewer relations to the body than a hip transplant. The universe treats the hip transplant as an integrated part of the body as a whole, but it doesn't treat the removable arm the same way. Thus it seems reasonable to say the hip transplant is a true part of the body, while the removable arm is not. We could even say, while the arm is attached, yes it acts like a part of the body, but when it's removed it becomes a separate object. So our own conceptual criteria to say, well X is a part of the body and Y is not might actually correspond to universal criteria. As this article has demonstrated, there seem to be mind-independent relationships that are discoverable in the world. They are a distinct feature of the universe that can be referenced separately from any concrete objects. They aren't physical things, they don't weigh anything, you can't see them. They're abstract. But what exactly are abstract things? I see two possibilities. Abstract things could either be mental or platonic in nature. That might initially seem odd to say that mental things could be mind-independent, but within the framework of divine conceptualism it actually makes sense. Abstracta might exist separate from our own personal minds. But still exist within the mind of God. In the same way that chairness is our own conceptual criteria inside of our minds, the universal chairness is also conceptual criteria, but it resides inside the mind of God. The abstract categories, forms, patterns, and relations that we have direct access to are all mental objects. They might correspond to the abstract categories, forms, patterns, and relations that are mental objects inside the mind of God. Within the divine conceptualist paradigm, we don't even need to posit that this mind of God is personal. We might simply define the mind of God as all of the human mind-independent abstract stuff. It's the universe's categories. The mind of God is what glues individuals into groups. This fits rather nicely into the pantheist worldview I explained in my article, Understanding God as Nature or the Universe. The other option is if abstract things are platonic, explicitly non-physical and non-mental. They would resign in their own unique ontological realm, the realm of forms. Perhaps this is where information and the laws of physics reside as well. The trouble with the realm of forms is we can't say too much about it, since our minds aren't in that realm by definition, and they must behave according to different rules. By labeling abstract stuff platonic, that might just be a placeholder word that means it's in another realm that we don't have access to. To the extent we have direct access to it, it's mental, not platonic. I don't know whether abstract or platonic or mental, both theories seem beautiful to me. Regardless, I have become persuaded that my previous position was incorrect and that abstract relationships are a real feature of the universe.