I had an interesting conversation with a friend on Discord about Platonic realism. So we decided to dress it up as a Platonic dialogue.

DT Sheffler: Did I tell you, Philomathes, about the encounter I had the other day with a bright young philosopher?

Philomathes: No. I am glad, however, to hear that such encounters are still possible. Is he one of your students at the College?

D: No, I do not believe I have ever seen his face. That wasteland, the internet, among its many evils also makes possible this good, that philosophical dialogue can take place across great stretches of space.

P: Indeed it does, but I wonder whether that good is worth the cost.

D: Perhaps not, but let us savor the good at least. It happened like this: We were discussing the distinction between poetry and prose, and noticing the sometimes vague boundary between the two. In light of this vagueness, this philosopher Kincaed was skeptical that the distinction between the two kinds of language was real or meaningful. As always—you know well my inevitable bent of mind—I resisted the move to do away with, reduce, or subjectify the distinction, arguing that even in the case of a smooth spectrum, such as that between hot and cold, the spectrum itself could only exist if there were first a real distinction between the poles. I don’t think that poetry and prose have such a smooth spectrum between them, just a fuzzy boundary, so the necessity of a real formal distinction between them is all the stronger, a fortiori as they say.

P: And how did he respond?

D: Well, I’ll tell you. The conversation went like this..

Kincaed: Hot and cold as a spectrum is functionally useful for describing a physical phenomenon, but even temperature can be described non-categorically, as states in a single system, if we prefer that.

D: It’s not just functionally useful, the spectrum wouldn’t exist ontologically without the real difference in the poles. Lots of things in reality are like that.

There’s a general problem in philosophy known as the “vagueness” or “sorites” problem. It goes like this:

1. Suppose that one grain of sand does not constitute a “heap” (σωρός is Greek for “heap”).
2. Suppose further that there is not magic number n, such as sixty-seven, such that n grains of sand would constitute a heap, but n − 1 would not.
3. From (1) and (2) it follows that we can add grains of sand, one by one, to infinity and never get a “heap” of sand.

We have a classic paradox here because (1) and (2) seem intuitively plausible, but (3) seems absurd. And yet, (3) follows deductively from (1) and (2). The problem is that we know, intuitively, that a bunch of sand piled up together makes a heap of sand. The heap, considered as a whole, is a real collection and it has a formal arrangement—grains heaped together is a different structuring of reality than the same grains apart—yet at the edges, we find it impossible to state the exact number that draws a sharp line between a heap-arrangement and a non-heap-arrangement. We can do the same trick with many other formal realities: Exactly how many hairs can a man have and still be bald? Exactly what wavelength establishes the line between red light and orange light? Exactly how many people form a city?

In virtually any definite category, one can cherry pick edge cases with the goal of drawing the category itself into question. Such objections become very difficult to answer with a rigorous logic at a fine-grained level, but the difficulty drawing the line should not cause us to doubt the objective reality on either side of it. A man with no hairs is clearly bald. Light with a wavelength of 700 nanometers is clearly red. One hundred thousand people living together in civil society is clearly a city.

K: Mmm, this is why I said before that I’m tepid about metaphysical realism as usually described. I would agree that a spectrum is one way to class temperature, but I don’t think it’s ontologically more real than classing it another way. It isn’t particularly unreal, but its perception as a spectrum is reliant on a particular frame of reference, which can be shifted even within the bounds of human thought. The phenomenon exists as it is, but classification can be pluricentric.

D: Yes, reality is always more rich than one particular analysis of it. But that doesn’t mean that the reality to be analyzed doesn’t really have the features in question. Like the cliche example of the blind men and the elephant, there is more elephant than any one man realizes, but that doesn’t mean he hasn’t grasped a real feature of the elephant.

K: Sure.

I think the best analogy to use would be a kaleidoscope, for which you don’t perfectly know either the way the lens refracts, or the pattern of the objects inside. You can reliably perceive a certain feature, and the way the shapes move as you twist the kaleidoscope—so you can infer certain things, based on the way the shapes change.

D: I like that analogy, but whatever else you want to say about temperature, I think you’d be hard pressed to think that hot and cold are not real features of the universe.

K: Hmm. Hot and cold are harder to argue because there is an absolute zero.

D: And hot is just the infinite upper end.

K: Yes. So there is at least “hotter” and “colder.”

D: Yes, as Plato points out in the Philebus, all such terms must be analyzed as relations.

K: Right, exactly.

I think the sorites paradox comes down to heaps being a construction. Or at least, a snapshot of a moving system, and there is no “heap” as an object.

It’s a problem of treating definitions as objects.

D: I disagree.

I think it’s ok for real things to be fuzzy at the edges.

K: I didn’t say it doesn’t describe something real, just that it’s not an object.

D: What distinction would you make between “something real” and “an object”?

K: I’m not sure there really is such a thing as an object. I think that you can accurately express reality as a system of systems—no part of it is static as an object, with each system composed of systems, and composing systems, except at the very highest. The “object” is the focus of the frame of reference. The systems viewed statically, frozen by this or that definition. But that doesn’t mean that what we’d call individual isn’t ontologically real. It’s just that the reality of things is more complicated than static being. I’d be comfortable saying that there is no real distinction between “Action” and “Being,” and that the perceived difference is a matter of light refracting through a lens.

D: So far we are saying things that Plato and Aristotle said, provided that we are just talking about spatiotemporal reality. Both Plato and Aristotle think of “existing,” at least when it comes to “those things that become” (τὰ γενόμενα), being in action, a dynamic system. When Aristotle uses the word “substance,” he doesn’t mean something in contrast to this. A “substance” (again limiting our current conversation to spatiotemporal substance) is just what you are calling a “system,” with the caveat that the substance has a particular dynamic arrangement or structure such that it has enough integrity to qualify as a “this” (τόδε τι). It’s ok for this arrangement or structure to be constantly in motion; It’s ok for it to be extremely complex; It’s ok that we imperfectly grasp such systems; And it’s ok that our definitions inevitably fall short. (Incidentally, I shifted from “object” to “substance” on purpose, since I don’t think the subject–object distinction is really what we are talking about.)

Here’s a way to put it to you as a question: do you think we could just drop the word “object” or “substance” and replace it with “dynamic system”? When I refer to “this chair,” could I just acknowledge that the referent is not a static thing, but a highly complex always being-in-act dynamic system?

K: For sure.

D: In that case, we just have a semantic dispute, because that’s exactly what Plato or Aristotle (or Aquinas etc.) would acknowledge vis-a-vis the chair.

When we take something like “Justice” or “Three,” however, the story will necessarily be different. But I suspect you would not want to say that “Three” is an ever-changing dynamic system.

K: Mmm.

I would be more comfortable saying so of Three than Justice. Though not the concept of Three. Rather, its expression. I don’t think it’s very accurate to say that objects participate in quantity.

D: Keep in mind that we are not talking about what we say justice is, or what any human being understands justice to be, but what Justice is in itself.

K: I think that quantity is more a quality of the system itself, than a thing that exists.

D: Well it’s certainly not a “thing” in the sense that spatiotemporal systems (as you call them) are things. But it is a “thing” insofar as it is a real ontological feature of being.

So far the Platonists and the Peripatetics can agree, but here we come to the question of whether the quantity Three is “separable,” from the systems that exemplify it.

K: Right. I think not.

D: I say yes, and I also think Aristotle says yes by the end of the Metaphysics too, despite what he says at the beginning.

K: It’s been a while, to tell the truth, since I read the Metaphysics.

D: Here’s a basic argument just for the case of number, but I think you can transfer it to other forms:

1. We know that the series of integers is potentially infinite.
2. The highest number exemplified by particulars is certainly very large, but finite.
3. Therefore, there is some number that is potentially exemplified, but is not actually exemplified.

Similarly, we could do a thought experiment: Could there possibly be a universe in which there are no blue objects, yet structured in such a way that there could be blue objects? The intuitive answer is, yes of course, and there are strong reasons to suspect that this intuition is supported. For this to be possible, the intelligible structure of Blue, must be a real structuring feature without actually being instantiated in the system.

K: My gut response to that would be that all numbers are simply an expression of “quality,” a descriptive feature of a system of systems. To reify particular integers is only sensible when speaking from a very particular frame of reference. Insofar as they might exist, they only exist like the chair from before.

“Structuring feature,” however, is a sensible term to me, in that context.

D: Yes, I too think that all numbers are simply an expression of “quality.” But that just means that “Quality” is the deeper structuring reality, and all the numbers are (some of) the possible shapes that it could take. (I am understanding “Quality” as being such which includes “Quantity” rather than “Quality” in contrast to “Quantity.”) This means, however, that all the numbers are still real and further that they are ontologically grounded in Quality itself rather than the instantiations.

K: I think that my reaction to whether or not more abstract things are “separable” might come from a misunderstanding of what is meant by “separable.”

D: “Separable” (χωριστός) means “real independent of X,” so when we say, “Three is separable from instances of Three,” we mean that “Three would be real independent of whether or not there are any instances of Three.”

K: I would say that it’s fair to say that color is resultant from colored things, but they are only colored insofar as color is a feature of the system of things.

D: This is true for the material cause of a particular case of a color, but what it means for something to be blue is what we are talking about when we identify the Blue itself, which is not, itself something blue, cannot be seen, has no material cause, because it is just an intelligible structure.

K: In color, though, we can say with some certainty that it is purely experienced. The categorization of wavelengths is a subjective one. It cannot exist independently of the viewer. The system that we experience as color may exist independently of the viewer, but its categorization cannot.

D: No, that’s describing the qualia of blue. By “blue” I mean to identify the disposition of the system such that it is the sort of thing that gives rise to such qualia in observers. Hence, a blue ball would still be blue even in an empty dark room. (At one level this is just a semantic distinction we need to make, since we do use the English word “blue” in a number of ambiguous senses.)

K: In this case, you’d call “blue” the traits of the ball that make it reflect light in a certain way when experienced by a viewer?

D: Exactly.

And the intelligible pattern of such traits is “the Blue itself,” which is not, itself, a blue thing.

There’s also a relevant distinction between the intelligible pattern of traits in all blue systems (“the Blue itself” or “the transcendent Form of Blue”) and the particular intelligible pattern of traits in this blue ball such that it is disposed to reflect light in such-and-such a way (“the blueness of the ball” or “the immanent form of blue”). The former is “separable”; the latter is not.

K: Well, I’d say that “the Blue itself” also should not purely be treated as a static thing, being a “highly complex always being-in-act dynamic system,” as said of an individual chair. It may not include change like other systems do, but it is still only meaningful insofar as it relates to a complex set of characteristics of other things…Though I suppose it is not directly “dynamic” as actualized in the world. But it could be hypothetically dynamic, were the parameters surrounding it to change.

D: Well, it certainly only is insofar as it is in act (ἐνέργεια), but it does not change or move in the way that spatiotemporal systems do. We also want to be careful with what we mean by “meaningful.” It may only be meaningful to us insofar as it comes into manifestation in our experience of changing things, but it may have a meaning in itself that we know nothing about.

K: I have a vague notion of reality “moving” in a dual kind of way. The Hermetic formulation from the Emerald Tablet expresses this, I think, in saying, “That which is above is from that which is below, and that which is below is from that which is above, working the miracles of one.” I think it applies to discussions like this, in that it can be said that the more immaterial relies on the more concrete, but the more concrete also relies on the more immaterial. So in a way they are “inseparable,” though distinct. I think this becomes much more sensible when considering “systems” rather than “objects,” and considering all thought in terms of frames of reference. “Maleness” does not exist without the granular expression of males. But it could be framed in the opposite way, that males are males because they participate in maleness. I think those two things might be reconcilable, if they are expressions of the same thing, from different frames of reference.

D: Yes, I think all of that is compatible with classical metaphysics, and understanding material “substances” as “systems” rather than static “objects” is certainly a helpful suggestion. A lot hangs in your above statement on what is meant by “relies on.” I would argue that “maleness” is already inherent in the very structure of Being prior to there being any biological males. So it doesn’t “rely on” the concrete males ontologically, although the maleness of this particular male (what I earlier called “immanent form”) does. Maleness, however, does “rely on” particular males for us epistemologically. We come to learn of the intelligible pattern Maleness only through encountering that pattern played out in many concrete particulars. Only then are we capable of seeing analogues in other systems, and finally come to understand that it was a structuring principle of Being all along. Traditionally, we call this the “order of knowing” as opposed to the “order of being.”

K: What do you think of the idea that those qualities that compose maleness exist eternally in Being, but undifferentiated in that context? Those become differentiated granular parts of maleness through the temporal lens.

D: Yes, by analogy all the colors already exist in the white light but are then differentiated through the prism.

K: Aha, that’s one of my favorite analogies.

D: It’s a fundamental axiom of any Platonism worthy of the name that it is all already “in” the One.

K: In that sense, I think it’s fair to say that “Maleness” exists in Being like “Justice” and any other immaterial, but creation is necessary for it to exist intelligibly. Which I suppose may be what is meant by the “order of knowing.”

D: I agree fully with the substance of what you are saying but let me quibble over one point:

When we say “intelligible” we don’t mean “intelligible to us humans.” We mean “intrinsically intelligible, that which mind (νοῦς) as such grasps.” So we need to carefully distinguish things “becoming intelligible” to us in our limited process of knowing (the “order of knowing”) from their simply being intelligible from the beginning in themselves.

K: I would tend towards thinking that “intrinsically intelligible” with that kind of definition isn’t very meaningful to consider, because any infinite permutation of things seems as though it could be “intelligible” to an infinite, timeless being.

D: Yes.

And what’s the problem with that?

K: With that in mind, what is the meaningfulness to us of “intrinsically intelligible”?

D: Just because there are an infinite number of integers, it doesn’t follow that the number Three is meaningless to us. Neither does it follow that, recognizing the limitations of our mind and our inability to form adequate concepts of all the numbers, we cannot come to see the intrinsic intelligibility of Three. In other words, we may come to see this one structural permutation out of all others that we have yet to see, and recognize that this particular permutation has indeed been there all along, that we are not simply projecting it onto reality, but rather discovering it. Just because there is always more intelligible structures—what you called “permutations”—for our puny minds to discover we shouldn’t cast into doubt the few that we have come to know.

K: I’m struggling to put this in a way that doesn’t sound questionable, but I think you’ll get what I mean; I don’t think we can very well consider Being as existing separately from Creation, regardless of the actual facts of that relationship, since “before” only exists once time does. Which is another component to what I am thinking.

D: Yes, for us, in our epistemic situation, our only way to think about Being is through Becoming. That doesn’t mean we can’t discover Being’s manifestations in Becoming or that those manifestations are wholly illusory even though we recognize that they are always incomplete.

As to “before,” there are two senses:

1. “Before” in time = X is before Y iff X is at time t₁ and Y is at time t₂ and t₁ < t₂.
2. “Before” in logical priority = X is before Y iff Y is ontologically grounded in X.

In the second sense we can say “before” atemporally. For example, “Number” is before “Three.”

K: I think this has been helpful in aligning the way I’ve been thinking more with metaphysical realism. Because as I’d mentioned before, at one point I was staunchly there, and then very much not there, and now I’m trying to integrate my older thoughts with newer ones.

D: Well it’s a worthy project to undertake for your intellectual life.

K: Since I mostly read Plato as a teenager, I think I still have an incredibly over-simplified view of him.

D: I don’t see how people can have any opinions about anything at all with a good conscience without first asking themselves these kinds of questions about the very nature of truth, reality, and our knowledge of it.

K:For sure.

In that sense my major reaction is against overly-categorical thinking, especially concerning social topics. I think it’s a major force in polarization, for instance.

D: I think that’s really what Socrates is driving at in most of the early dialogues: How are you all so confident in your ethical, political, or religious claims if you can’t even answer my basic questions about the nature of truth and reality?

K: Definitely.

D: So you see, Philomathes, this Glaucon was asking all the right questions and putting his finger on just those issues that one must face if he is to give a realist account of things.

P: Indeed he did, and I pray he continues along this line with many more fruitful discussions to come.