Previously, we have discussed the differences between sensibles and intelligibles, using the example of Bill Evans’ “Waltz for Debbie.” Individual performances of this song are “sensibles,” while the song itself, the deep structure that remains the same across multiple performances, is an “intelligible.” In the last essay, we examined the way that Plato uses the terms εἶδος and ἴδεα to refer to this shared structure or “character” that undergirds similarity across differences, and we ended by puzzling about the mode of existence that such structures might have if they are not physical objects that we can poke or kick. To answer this puzzle, let’s begin with the kind of geometric example that Plato uses in the Meno and the Phaedo, before attempting to tackle the thornier issues raised by “Waltz for Debbie.”

Suppose I see two sticks of equal length. As in the other cases of intelligibility that we have examined, when I see such sticks, I am doing something with my mind, not just with my eyeballs. I am recognizing a pattern, the deep structure that we call “Equality,” or if we are speaking Greeklish, “the Equal.” I look again at two baskets each containing five apples. Although this case is a little different, being an equal count rather than an equal length, I nevertheless recognize that one and the same deep structure has shown up again.

We can immediately realize that this Equality that we recognize exists in a wholly different way from the sticks and the apples. Both are “real” in the sense that they are objective features of the world rather than things we make up within our own minds, but we usually think that the sticks and the apples are more “real” than Equality in the sense that we can pick them up, handle them, use them as food to fill our bellies, as fuel to warm our hands, or as weapons that cause pain.

In yet another sense, however, Equality is something more real than the sticks and the apples. Equality has a kind of permanence and invariability that the sticks and the apples can never achieve. After its flower falls and the remaining bud swells, an apple comes into existence in the course of some particular spring. It slowly ripens, reaches a point of perfect maturity, and begins its decline into decay. Eventually, if it goes uneaten, it becomes the soil for future apples and no longer exists as an apple at all. Equality, by contrast, did not begin one day, it does not ripen or decay, and even in a billion years, it will be just the same as it ever was. Even saying “will be” and “was” are not quite the right words because the structure of Equality simply is what it is and past and future are simply irrelevant. Equality is incompatible with More and Less. Equality is quantitative. Equality is a reciprocal relation. The “is” in these statements is not the “is” of the present moment, but the “is” of timeless truth. It isn’t that Equality has always existed but rather that the very categories of before and after, creation and destruction, growth, change, and decay, simply do not apply.

To express the difference between these two totally distinct ways of existing, Plato used the terms “being” (εἶναι) and “becoming” (γίγνεσθαι). Equality simply “is” what it is, always expressed with the present tense of the verb “to be.” Apples, by contrast, must “become” what they are before passing away. In fact, even the expression, “what it is” does not really apply to the apple. As both Parmenides and Heraclitus observed from their opposite perspectives before Plato, there is never any single moment when the apple fully is what it is. For any given second, the apple only realizes a thin bit of its total life. You might catch it while still green, but at that moment, you would miss what it is to be a ripe apple or a decaying apple. You might catch it at the very moment of perfect ripeness, but even if this is the best moment, the fullest moment, in the life of an apple, you would be missing the stage of green growth which is also an essential part of what it means to be an apple. All these moments—and not just in the life of this one apple but in all the apples in all the world—are expressions of what it is to be an apple. From moment to moment it is “becoming” itself, rolling out its existence until there is nothing left to roll. And so it is with everything in time. Even the comparatively more sturdy life of mountains or glaciers cannot lay claim to the timeless present of the verb “to be.” Instead, they merely “become” themselves more slowly. Plato calls such things “the things that become” (τὰ γενόμενα) in contrast to “the things that are” (τὰ ὄντα). Again doing a little violence to English, we might translate these phrases as “becomings” and “beings.”

Granting the timelessness of mathematical structures like Equality, we might well ask whether the same things can be said about “Waltz for Debbie.” Clearly, the individual performance of the song, the sensible instance, has a momentary existence bound in time. Indeed, the performance of a song is a wonderfully illustrative example of becoming since a song cannot be a song if we freeze it at some particular moment or take only one chord. Try pressing pause on your stereo, and you will have no music at all. By it’s very nature, the performance can only exist as something unfolding. The very condition of its life is mortality, living precisely by dying in the act. By contrast, the song itself, the intelligible structure underlying all the performances, the thing that can be written down as notes on a page, lacks this momentary temporality. From Friday’s performance to Saturday’s performance, the song is just the same. Even in a thousand years, some archeological musician might dig up the tune and play it again. In this way, we might think of the song itself as a timeless intelligible structure in the same way as Equality.

A difficulty arises at this point, however, a difficulty about which the students of Platonism have debated and sometimes taken different views. “Waltz for Debbie” was written by Bill Evans, and we might plausibly think that it depends for its very existence on him. An enterprising biographer might even date the particular day and hour on which it was composed. Unlike a sensible object, this intelligible sequence of notes may not exist at any particular place and time and it certainly doesn’t exist only in Evans’ head since it continues on long after his death. Nevertheless, we might think that it only comes into existence through his creative effort. In the literature, such cases are known as “Forms of artifacts,” i.e. intelligible structures not found in nature that seem to depend on human creativity. In the Republic, Plato mentions Forms for beds and tables (596b), and this caused his students in later years much material for perplexity and ingenious commentary.

Putting to one side the scholarly question of what Plato really meant, I think we can, with a little nuance, give a solid answer to the underlying metaphysical question. I read somewhere that someone had written a little computer script to generate every possible eight-bar melody playable on a piano. They stored all these possible melodies as MIDI files on a single flash drive. Of course, the collection is rather useless since discovering the good melodies among all those myriad possibilities would take exactly the same kind of genius as composing them in the first place. As any mathematician or programmer can tell, the program has not really created anything. All it has done is make explicit for us the truth that the very structure of Western musical scales already contains within itself all the possible eight-bar melodies that there ever could be. In the same way, the pixels on your computer monitor already contain within their very structure all the possible images you will ever see on it. The composer does not so much create these melodies as find them and bring them to manifestation out of the great ocean of possibility contained in the scale itself.

The program only works, of course, by limiting the sequence of generated notes to eight bars and only allowing the notes playable on an ordinary piano. If we removed these constraints, allowing any note on any instrument, for any length, at any level of volume, the range of possibilities explodes to an uncountable infinity. Nevertheless, the uncountable infinity of possibility is precontained within the very structure of Western Music, from which the composer draws out this one particular arrangement.

One might object that I am still limiting the possibilities to “Western” music, which has a history, came into existence over the course of particular centuries, and is itself the product of human creativity even if it is the collective creativity of a whole civilization rather than that of a single composer. This objection, however, is just repeating at a higher level the same issues as those involved in the composition of a single song—and the answer is just the same. “Western Music” is itself an intelligible structure vastly more complex (and from another angle vastly more simple) than the structure of a single song, but it is one of the possible structures precontained in the very nature of Sound. Human creativity did not produce this whole system of music ex nihilo, but instead drew forth and made manifest one possible way of making music that has always existed latent in the very structure of Sound. And “Sound,” in turn, is simply one of the possibilities precontained in the very physics of waves.

This is not to slight the genuine creativity of human genius. The chords we hear at the beginning of “Waltz for Debbie” owe their manifestation entirely to Evans. Granting that “Waltz for Debbie” has a kind of latent timeless existence hidden within the very laws of physics, those particular chords would never have been played in that sequence if not for Evans. The bringing to manifestation, the actualization of this intelligible structure depends on the creative genius of Evans’ mind. Hence, mind plays a crucial bridge role in this whole picture. On the one hand, the mind of Evans apprehended one possible way of arranging sounds out of all the possible notes that he could play and saw that it was good. On the other hand, the mind of Evans directed the playing of that pattern on a concrete piano, drawing out into sensible space and time the intelligible structure that he had grasped.

This gives us some hint toward a solution to a key question in Platonism, the “problem of instantiation.” Why should some intelligible structures become instantiated in sensible, temporal reality rather than others? Why should this intelligible become instantiated here and now? This technical question is related to the broader philosophical questions, “Why should things be ordered? Why do we live in a cosmos rather than sheer chaos? Where did order come from?” The hint we have here is that Mind (Νοῦς) is responsible for bridging from intelligibility to sensibility. This is clearly true for the products of human creativity, but what of nature? Could there be non-human minds or a single Divine Mind responsible for the ordering that we see in the non-human world? The answers to those questions, however, will have to wait for another essay.