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, it’s conceptual criteria situated in our own minds. It seemed to me that all abstract stuff was situated in the mind. But now I think conceptualism is incorrect – or at least incomplete.
This change of mind happened 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.
Seeing What You Can’t See
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 the concept without directly observing what it references. I’ll try to illustrate the idea, then re-phrase it several different 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 this article, you can substitute the word “objects” for “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 have previously argued that this unification is done by the mind. Now, I believe the unification is also done by the universe.
You can think about 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 the physical world down to its most fundamental parts.
Reducing the Physical World
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 you’ll eventually 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 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: what is the difference between these indivisible units and the space they occupy? What is space, at this 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. Regular, large-scale atoms like “helium” would be ultimately reducible to a pattern of units of space in a particular state.
To keep this model simple, let’s say the geometric atoms can be in only one of two states – on or off, empty or full, 0 or 1. This allows us to represent patterns of atoms as sequences of 0’s and 1’s. For example, empty space might be represented as:
While an atom of helium might look like:
Or, a chair might be:
You get the idea. Different objects are different patterns of geometric atoms. Since the metaphysics of space is not the subject of this article, we’ll just treat geometric atomism as the model for the physical world that will help illustrate the point about abstracta.
Parts and Wholes
In this model, what is a chair? Well at first glance, it appears that a chair is just a pattern of atoms. It isn’t 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 a shorthand way to reference all the parts. I like the way “mereological nihilists” 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 favorite example of this is constellations. Without any humans, would there be constellations of stars? Would there be a “Big Dipper” that exists in addition to individual stars that compose it? It seems unlikely. While the individual stars have a mind-independent existence, their unification into “The Big Dipper” is something humans do.
I’ve previously claimed this unification of parts into wholes is always a mental function, and in the mind-independent world, there would be no unification. But I now see this argument is incomplete. It misses something important: the behavior of atoms across time. The real-world behavior of composite objects implies that the universe unifies parts into wholes, too. Abstract relationships are not all created by the mind; some of them are discovered in the universe.
Composite Objects and Their Behavior
Consider a metal spring. Let’s reduce it down to a purely geometric form – a pattern of 1’s and 0’s. As the spring is compressed, the pattern of 1’s and 0’s changes. As the spring returns to its original position, the pattern also returns.
Notice, when the spring is compressed, it doesn’t fracture into a trillion isolated atoms. The atoms have a particular behavior, and their positions are determined in relation to each other. The 1’s and 0’s change across time depending on the neighboring 1’s and 0’s. The individual atoms alone do not determine their own behavior. They are stuck together in some kind of composite system, with many interrelated parts.
Critically, these relations are not like the relations of the stars in a constellation. Distant, individual stars do not seem to affect one another’s states. However, the atoms of a spring do affect each others’ states. The universe – not our minds – seems to unify the atoms of a spring into a composite object whose behavior is different than if the individual atoms weren’t unified.
A hundred 1’s next to each other behave differently than a hundred isolated 1’s that are unrelated. Therefore, the fundamental units themselves are not sufficient to explain their own behavior.
While our minds do glue seemingly-unrelated objects together – like the stars in a constellation – the universe also seems to glue things together. This “glue” is a bunch of abstract relationships that exist independent from our minds and take up no physical space themselves.
Trees, Sticks, Families, Nations
There seem to be many relationships 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; were they isolated individuals without relations, their states wouldn’t affect each other.
Whether or not a set of individuals qualifies as a “family” might be a real metaphysical question: do the states of the individuals affect the states of the others according to the abstract criteria of “family-ness”? 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 billions of people on Earth whose states don’t affect me; I’m not unified into any composite object with them.
Through this lens, even nations seem to behave like composite objects. The atom of society – 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 it doesn’t square 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 to both physical objects and humans.
Matter, Form, and Arrangement
Here’s another way to grasp the abstract. Let’s return to the metal spring example and compare these two statements:
(1) Springs are just atoms arranged spring-wise.
(2) Springs are just atoms.
There’s clearly a difference between these two statements. What is it? What does the first statement convey that the second does not?
Arrangement. Or, you could say structure, form, or shape. The pattern of atoms. Their states and relationships analyzed together, rather than individually. A spring cannot be described by simply “X number of atoms.” That’s not enough information. Springs are “X number of atoms arranged in a particular way.”
To use more traditional language, this is the difference between matter and form. (Well, actually in the context of historical philosophy, “matter” and “form” meant something different, but in contemporary English, these two words convey the correct concepts.) “Matter” is the atoms; “form” is their arrangement. Form is a bundle of abstract relations. We can distinctly reference both matter and form.
The universe treats form as something in addition to the matter. It’s a unique, relevant feature of the universe that 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 arrangement. Geometric structures are the fundamental objects of the physical world.
Why should units of matter behave differently when they are 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 it has an “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. 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 says, “When atoms are arranged this way, then render out this state, and when atoms are arranged that way, render out that state.”
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 that “relative position” and “relative arrangement” are not themselves concrete objects. They aren’t atoms; they aren’t composed of atoms. They don’t weigh anything or look like anything. They are abstract. Yet, since they seem to be an integral part of the universe’s operation, I think they are both abstract and mind-independent – a metaphysical status I’m calling “Platonic.”
Chair-ness as Universal Criteria
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.
Let’s start with what we know. Before theorizing about the Platonic realm, we can say 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 doesn’t qualify as a “chair” to you, but it would qualify as a “chair” to me.
However, “chair-ness” might also reference something else – universal criteria. Just like we have abstract criteria that determines whether something gets the label of “chair”, the universe seems to have some criteria for determining the behavior of the things we call “chairs.” 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 a structure that we call a “chair”) then the universe will output a unique state, keeping those atoms glued together in a specific way.
The best analogy is to computer code.
Dinosaur Code and 3d Printing
You can imagine universal criteria is 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.”
This is how “chair-ness” might exist completely separate from any chairs. The code can still exist – “If A, then B” – but since there might not be any A, there might not be any B.
Let’s say a “dinosaur” is a particular structure and pattern of behavior of atoms across time. When dinosaurs exist, the universe is running the “dinosaur program.”
If in 2020, atoms were arranged in a way that constituted a “live dinosaur,” then would we see those atoms behave like a dinosaur? If so, then we can say 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 “dinosaur-ness”, and suddenly Platonism makes sense. What is the Platonic dinosaur-ness? It’s that part of the universe’s code which determines when some arrangement of atoms is to behave like a dinosaur. Notably, there don’t need to be any actual dinosaurs in order for this Platonic form to exist.
In fact, if we understand Platonism this way, the contrary position 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 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 is 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 1’s and 0’s. Well actually, to be precise, it’s not just 1’s and 0’s; it’s 1’s and 0’s in a particular arrangement. In this case, the arrangement is the whole point.
You won’t find a physical object inside the code. And yet, it contains enough abstract information to be able to construct a physical object. Like Platonic forms, the code exists separately from any printed structures. Even if the code is never instantiated into a physical object, the abstract information – the form, the structure, the pattern – still exists.
The Special Composition Problem
Let’s say that fundamental units can indeed get unified into composite objects. We run into a famous problem 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. It’s precisely the universe doing this unification, not our minds, which means we don’t know beforehand exactly what structures will yield unique behavior. I can’t tell you a simple rule. It’s a matter of empirical inquiry. Whether X and Y are related is not discovered by examining X or Y in isolation. X and Y’s state-changes are observed together across time to see if there are discoverable patterns.
For example, a tiny asteroid trillions of lightyears away probably doesn’t form an object with my thumb; their states appear to be unrelated. The asteroid can do anything, move anywhere, and change its structure, but it won’t affect my thumb. However, my fingers and thumb do appear related. The states of my fingers affect the state of my thumb. There are a large bundle of relations between them, such that the universe outputs their behavior as a composite object I label “my hand.” My hand shares many further relations with my arm, which shares relations with the rest of my body. The universe treats the parts of my body as tightly bundled and not isolated from each other. Hence, my body also qualifies as a composite object.
Prosthetics are an interesting case. Is a prosthetic a true part of the body? Well, it depends on the tightness of its relations. 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. It does not 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 say that while the arm is attached, it acts like part of the body, but when it’s removed, it becomes a separate object. Our own conceptual criteria for saying “X is a part of the body while Y is not” might actually correspond to universal criteria.
Divine Conceptualism vs Platonism
As the above has demonstrated, there seems 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 are abstract. But what exactly are abstract things? I see two possibilities. Abstract things are either mental or Platonic in nature.
Thought it might sound odd, some mental things could be mind-independent, within the framework of “divine conceptualism.” Abstracta might exist separate from our own personal minds, but still within the mind of God. In the same way that “chair-ness” is conceptual criteria inside of our minds, the universal “chair-ness” 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, and they 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 reside 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 that we can’t say much about it, since our minds aren’t in that realm and behave according to different rules. By calling abstract stuff “Platonic”, it might just be a placeholder word that means, “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 abstracta are 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.