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It would be profoundly difficult to overstate the influence of Plato on the history of philosophy. From theology and metaphysics to politics, aesthetics, ethics, and on virtually every aspect of Western philosophy, there has been influence by or a reaction to that greatest student of Socrates. Perhaps Whitehead put it best when he described all of Western philosophy as consisting of, quote, "a series of footnotes to Plato."
Despite this enormous impact, Plato's actual inner teachings may remain hidden from us. There is good, though controversial, reason to believe that the inner core of Plato's teachings were never written down, and thus his famed dialogues actually contain exoteric teachings alone. The existence and nature of those inner, esoteric teachings remain the topic of active investigation and acrimonious debate among specialists.
Why do we think that such esoteric teachings did in fact exist? What of them might we be able to reconstruct? Further, might a brief digest written centuries after the death of Plato contain some of the mathematical esotericism downstream of this hidden Platonism? Here, the occult mathematics of Pythagoreanism and the metaphysics of Plato combined to perhaps form the core of an esoteric philosophy whose impact can still be felt as a deep undercurrent in contemporary philosophy, number theory, and even physics.
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Now, let's turn to the esoteric, unwritten doctrines of Plato and how they might echo in the *Theology of Arithmetic* attributed to Iamblichus. I'm Dr. Justin Sledge, and welcome to Esoterica, where we explore the arcane in history, philosophy, and religion.
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The surviving corpus of Plato's works is itself daunting, nearly 2,000 pages in a single volume. Generally speaking, scholars divide the dialogues into three groups, tracking mostly to the developing maturity of Plato's thought. The early dialogues are those more firmly in the orbit of his teacher, Socrates, often with that personage bringing these texts to a kind of conclusion in an aporia or puzzle. Socrates befuddling his interlocutors. Perhaps these, in fact, even echo memories of actual historical conversations.
The middle period is thought to include Plato's mature philosophical positions, rather than Socrates merely knowing that he knows not, which is a lot more than most of us. These dialogues contain sophisticated analyses of a wide range of philosophical positions, including the famed doctrine of the Forms, the notion of the tripartite soul, his theory of knowledge as anamnesis or recollection, the notion of the ideal state, like the one found in the *Republic*, his theory of virtue, and on and on. It's the foundation of all of Western philosophy. Indeed, these dialogues form the core of what we typically refer to when we discuss Platonism as such.
Finally, in the later dialogues, Socrates himself seems to fall virtually silent. In many central tenets from the middle dialogues come under sustained attack. Even the core doctrine of the Forms, one of the central tenets of Platonism, is viciously assaulted in the masterful but absolutely puzzling dialogue, the *Parmenides*. Without a doubt, the surviving corpus of Platonic works presents one of the most sophisticated literary and philosophical outputs in all of human history, and as I mentioned in the introduction, in some ways or another, these works underwrite almost the entire project of Western philosophy, either in their continuance or as a reaction against them.
Yet, there are reasons, good though controversial reasons, to believe that Plato actually taught a hidden, esoteric philosophy which was never committed to writing during his lifetime. The existence and nature of these *grapha dogmata* or unwritten doctrines, as Aristotle referred to them, are the subject of intense and sometimes acrimonious debate among specialists. Some schools of thought, especially the Tübingen school, have sought to actually reconstruct these *agrapha dogmata* as far as possible, while other camps are a bit more moderate, admitting that such teachings probably existed but also noting that we can probably reconstruct very little of them with accuracy. Of course, there are other folks who are totally skeptical and argue that Plato's extant dialogues alone represent the totality of his teachings, a completely reasonable position in its own right.
So, what reasons do we have to think that such unwritten, esoteric Platonic doctrines actually existed at all? Well, the first is that Aristotle, a student of Plato's for 20 years or so, just comes right out and he just comes right out and says they existed. Further, Aristotle even communicates Platonic doctrines which seem unusual compared to other known Platonic concepts found in the standard corpus of dialogues. Of course, Aristotle is also doing this polemically, so we have to, we have to be careful here. Though, to be honest, Aristotle tends to be rather intellectually sincere in representing his opponents fairly. In fact, many of the pre-Socratic philosophers are really only known through Aristotle's polemics, and he does seem to quote them word for word.
Another reason is that Plato himself seems to hint at these unwritten doctrines from time to time in the dialogues. The most famous instance is when, toward the end of his life, he was to give a much-anticipated, quasi-public lecture on the good life. Well, people showed up to hear, you know, a lecture about ethics and virtue and how to live a good life. What they got was hours of dense mathematical and astronomical analysis of the One. Most left the lecture midway, completely baffled.
Further, Plato himself seems to have actually come under a kind of Pythagorean influence throughout the mature part of his life. That school, as you probably know, held that the *arche*, our fundamental substance of reality, was number or *arithmos*. Well, what is just is number, and elements of Pythagoreanism can be seen through Plato's mature dialogues, from his music theory in the *Republic* to the complex geometric ratios and entities which comprise all of reality, the elements and the soul in the *Timaeus*.
Further, Plato goes out of his way to express skepticism about the nature of the written word, especially for the ability of the written word to express fundamental philosophical truths. Such truth, it seems, must be experienced, often in profoundly altered states of consciousness, such as the various forms of divine-imbued madness that Plato talks about in places like the *Phaedrus* and the *Symposium*. In fact, in *Letter VII*, Plato makes this about as clear as he ever would. There, he argues that philosophy itself cannot truly be communicated through books at all, but only through a kind of communal striving towards the Good, which results in brief, ecstatic glimpses of the truth. Thus, no book, no book can truly teach philosophy. In fact, books can just result in progressive dogmatism, because philosophy for Plato is a way of life, so as to achieve its aim through kind of quasi-mystical insights.
Now, the authenticity of *Letter VII* is disputed, though very reputable Plato scholars accept it. And interestingly enough, computational analysis indicates that it is, in fact, very similar to the other dialogues that we all accept as Platonic. Further, if the dialogues themselves seem to hint at deeper teachings and often conveniently break off discussion just as one would expect such a discussion to begin, and it's worth mentioning that the exoteric-esoteric structure would have been absolutely common in Plato's day for everything from craft guilds to mystery religions. Given the deeply spiritual, for lack of a better word, the spiritual character of Plato's project, it would just be conspicuous, shocking even, if what was taught in his inner circle within the Academy itself was really completely echoed in the published dialogues meant for non-philosophers and certainly non-initiates into his philosophical circle.
Finally, the Old Academy, including Plato's self-appointed heir and nephew, Speusippus, seems to be wrestling with a set of philosophical and doctrinal issues which clearly they've learned from Plato, who else would they learn it from but which don't seem to appear in the dialogues as such. These are the same doctrines that Aristotle seems to take to task in his writings and probably over which he decisively broke with the Academy to found his own school, the Lyceum.
Now, all of this combined circumstantial evidence, a bit, but still something, it seems reasonable to hold that Plato taught specific unwritten and well, esoteric teachings to his own inner circle of students. It seems like the *agrapha dogmata* existed.
Now, what were these *agrapha dogmata*, these unwritten doctrines? Well, well, well, I'd like to welcome you to a part of the episode I like to call "Hold My Beer," where I enrage a bunch of academics by trying to take a moderate position on a complex matter for which there is only highly contested. Why do I do this to myself? Highly contested evidence. So, this is a lot of fun, and make sure that you bring your pitchforks to the comments.
From what we can tell, and I'm going to largely follow the lead here of John Dillon, who I respect a lot on this issue, Plato seems to have held, as I mentioned earlier, a kind of Pythagorean or mathematical approach to first principles, or what we now call metaphysics. In the later and more mature period of his philosophical speculation, he seems to have arrived at a system of an ontological primal set of opposed principles: the One and the indefinite Dyad, and a three-tiered system of reality, primarily based on an interlocking system of souls: the One, the World Soul, and the individual soul. The One is a kind of active principle which acts as a limit on the indefiniteness of the Dyad, thus rendering it a duality or continuum which structures reality as a continuity between two extremes. This is true for magnitudes like measurement or hot and cold, but also for ethics, in terms of things like, well, good and bad. It's a limit on extremes, a *peras*.
Now, that *peras*, or limiting process, is actually otherwise really known from Pythagorean teachings already. It's a *peras* on an *apeiron*, a limit on the limitlessness, and that actually we see already in mature Pythagorean teachings. Now, by limiting the indefinite Dyad, the One introduces the reality of division into what we call the "many." That's a big problem in Plato, the many and the One. This generates a series of primal numbers, probably the integers one through four, but perhaps the entire decade of one through ten. At least one through four seem to somehow inhere with it, the One with five through ten, and all other numbers as a kind of extension or emanation of those more primal numbers.
It's key to recall that most of what we've been raised with actually in our lifetime is a kind of quasi-set-theoretical version of number theory, where we imagine one, two, three, etc., as sort of containers holding discrete abstract values or entities. What I call the "apples in a bucket" theory of numbers. That's just not how the ancient Greek philosophers conceived of numbers generally speaking. For them, geometry was really primal, with arithmetic's authenticity and mathematical rigor anchored in that discipline, in geometry, much in the same way that there are all those heroic efforts to anchor arithmetic and logic in the early 20th century, rest in peace. That project.
Thus, Plato probably imagines the One, or the Monad, that's something much more akin to a geometric point. The indefinite Dyad as line itself. Thus, numbers outside of the primal numbers, which somehow inhere in the Monad, it's not clear how that works, are the very process of segmentation of the indefinite by the One itself, and not as sets. This is not a set theory of number theory, this geometry-first number theory, which is a bit odd considering how much ancient Greek geometry was done completely without reference to arithmetic in most ways.
Might also help to grasp the next move in Plato's *agrapha dogmata*, his unwritten doctrines. These emergent numerals are, unsurprisingly, from my Plato people out there, also identified, at least the primal numbers, with the Forms or Ideas, made super famous by Plato as the ideal entities through which all other becomings, well, come to be. Thus, all instances of goodness, beauty, and justice are so, insofar as they participate in the eternal, unchanging Forms of goodness, beauty, and justice itself. In the unwritten doctrine, these Forms are mostly fundamentally numerals. Thus, the first 10 numbers somehow capture all the ideal Forms, with those from 11 to, I guess, infinity being themselves mutations of the primal numbers, as if made in a mold or *ekmageion*, as actually Aristotle tells us. By the way, that word *ekmageion* is the exact same word for the famed receptacle in the *Timaeus*, the fundamental substratum of all being.
Though there's some evidence that all natural objects have corresponding Forms, this is something that deeply puzzled Plato in the *Parmenides*, whether it's a form of hair and dirt and mud, with the combination of the primal numbers generating that infinity of Forms. However, the first four numbers held for Plato, like they did for the Pythagoreans, a more fundamental ontological status. In fact, the Pythagorean holy symbol, the *tetractys*, is said to combine this primal unity with the One plus two plus three plus four equals ten. It generates the decade, the decade itself producing all other finite integers. In fact, Plato has something similar in the *Timaeus*, although in a lambda form, not a triangle, of course. This geometric-arithmetic progression: point, line, shape, surface, solid, can be found in the *Timaeus*' account of the genesis of the universe, the four elements, the soul, and the Dyad, everything that matters. Not only the elements, but also the soul is a system of geometric proportions, a topology of ideas, from the circular totality of all being to the World Soul, of which the individual soul, our souls, are actually a regional microcosm.
Here again, soul is an onto-geometric relation of proportion rather than a substance in itself, no matter how ethereal it appears in classical Greek mythology or even the ghost-like conception of the soul that I think many contemporary people still have. Thus, our soul receives glimpses of the upper, perfect harmony, all the while converting sense data into the pure mathematics which allows for justified true belief, or what we just call knowledge. Thus, fitting this highly mathematical ontology with the epistemology of the analogy of the divided line that Plato lays out in, surprise, surprise, his most famous work, the *Republic*.
But note here, though, that even mathematical knowledge or *dianoia*, again, over there in the *Republic*, which can be written down in textbooks, I mean, Euclid's textbook is the longest continuously used textbook in human history, I think, is still not the peak or true knowledge of *noesis*, knowledge of the pure Good for Plato, again, knowledge that can be experienced but not taught from books. If we return to the sentiment of *Letter VII*, again, legend has it that Plato had "Let no one ignorant of geometry enter" written over the gates of the Academy. Though this story is admittedly somewhat late, it certainly wouldn't be out of place given our discussion so far, where metaphysics and mathematics are basically the same thing.
Now, this is a very rough outline of what might have been some of the unwritten doctrines. It's a pretty good disclaimer, you should get that disclaimer business again. One of the reasons we think this is that Aristotle, when he really wants to take on Plato, *quâ* Plato, he seems to be arguing primarily with these kinds of ideas rather than those published in the dialogues as we have them, especially in the *Physics*. Further complications that seem to logically flow from teachings like these are exactly what seemed to occupy the early Academy, the Old Academy, especially Speusippus and Xenocrates, until the turn toward Academic Skepticism beginning in the 3rd century BCE with Arcesilaus. Indeed, this is probably why the Old Academy strikes modern students of philosophy as so profoundly foreign, even students with advanced knowledge of the Platonic corpus. That's probably also why the Old Academy just doesn't get studied in graduate school. Sadly, most of the writings of the Old Academy are also lost.
And by the time that this Platonism thread gets picked up again, it's with pretty different philosophical concerns in mind. That's especially true of Middle Platonism, with its highly syncretistic approach, which is especially cozy with Stoicism, of all things. And the later Platonists, who seemed both interested in other problems and were perhaps just actually unaware that there really ever were these unwritten doctrines. For instance, not much in the way of these kinds of philosophical concerns of the Old Academy seem to be taken up by folks like Nummius, Plotinus, or Proclus. Though both Nummius and Iamblichus might, even if kinda accidentally, have actually been closer to the *agrapha dogmata* because of their recognition and the emphasis they put upon Plato's Pythagorean inheritance. Thus, these doctrines might have survived, though not under the aegis of Platonism, but through a parallel track of Neopythagoreanism. Neopythagoreanism, specifically in the works of folks like Nicomachus of Gerasa, and a slightly later digest of Pythagorean-Platonic arithmetological speculation in a work known as the *Theology of Arithmetic*, sometimes attributed to Iamblichus.
And I want to conclude by turning to this small, though terribly fascinating, little volume, which gives us, again, perhaps a glimpse into some of the nature of these lost mathematical-metaphysical teachings. The *Theology of Arithmetic* is a compact handbook of arithmology, that is, a specific intersection of numerology, geometry, and philosophy. The text itself is somewhat haphazardly composed and edited. It is either a digest, largely of older material, lecture notes, either extracted from or prepared by somebody, probably in the circle of Iamblichus, perhaps by, probably by Iamblichus himself, sometime in the third or early fourth century of the Common Era. The text itself is a series of ten brief essays dedicated to each number of the decade, with special attention paid to the first four numbers, what we might call the primal ontological numbers. The text weaves between theological, philosophical, arithmetic, and geometric properties of each of the ten numbers, from the Monad, one, through the Decade, ten.
Here, we're treated to a fully Neopythagorean exegesis of the primal numbers, which, and I think this is pretty conspicuous actually, leans quite heavily on the sections of the Platonic corpus which are arithmetological in character, really thinking here of the *Timaeus*. In fact, the *Theology of Arithmetic* may be the best surviving text of an entire sub-discipline of the metaphysics of mathematics that actually proved popular for nearly a millennium, a millennium in the ancient world, and probably served as the philosophical foundations for the earliest Kabbalistic speculations and things like the *Sefer Yetzirah*. Yeah, we think, I think one can draw a line between these forms of mysticism. Here, we're giving glimpses into the development of the emanations of reality, how the cosmos, the soul, and the human body are structured, the origins of various limits, remember the *peras*, the limits of spiritual and physical reality, for instance, why elements and directions both come in fours. There's an arithmetological reason for that. There are digressions into musical theory, why fevers come and go in rhythmic cycles, the scope of cosmic justice, and and more, all set within the scope of the mathematical analysis of the classical and late classical Greek world.
While the exact unwritten doctrines of Plato may be lost, the arithmetological tradition he developed and seemed to have prioritized in his own hidden teachings seems to have survived, at least in some form, into documents like the *Theology of Arithmetic*. In fact, the whole field of sacred geometry, that certain geometric shapes bear metaphysical or spiritual truths through them, is clearly grounded in texts such as the *Theology of Arithmetic*. Indeed, much of the numerological symbolism that will inform later magical theories is found in this text. In this way, the text really punches way above its weight in terms of influence, despite its relative obscurity these days.
The unwritten and likely esoteric doctrines of Plato very likely depended on a highly Pythagoreanized mode of framing questions of the origins of reality in terms of classical Greek mathematics, really specifically geometry. This arithmetological metaphysics, however, did not go extinct with Plato, by no means. It survived, at least in the first generations of the Old Academy, and probably at least in parallel developments in ongoing Pythagorean speculations, which can be found as late as this document, this wonderful *Theology of Arithmetic*, still under discussion in the school of Iamblichus.
Of course, this Pythagorean impulse, as I would call it, that not only can reality be described by mathematics, but reality fundamentally *is* mathematical, still survives today in both physics and metaphysics. In fact, in a recent poll taken of professional philosophers, in fact, many of which are actually analytic in their disposition, 39.3 percent of the respondents voiced support for Platonism in regards to abstract objects, including mathematicals. On the continental side of that debate, the influential French philosopher Alain Badiou is a professed Platonist, arguing that set theory is simply ontology. Of course, an entire generation of physicists have been taken with string theory, for better or worse, at least in substantial part because of the elegance of the mathematics and the seeming a priori commitment to naturalness dispositions, far more on the Pythagorean side of things than the "follow the experimental evidence" of a couple generations prior.
In fact, one of the more curious places where arithmology seems to actually play its most meager role is in modern and especially postmodern theories of magic, despite being of central importance to Renaissance figures like John Dee and Cornelius Agrippa. Cornelius Agrippa's entire second book of *Occult Philosophy* is just about arithmology. In this way, from philosophy to physics to magic, the esoteric teachings of Plato and the arithmetological metaphysics of the ancient world may still prove interesting and perhaps even illuminating.
The debate over Plato's *agrapha dogmata*, the unwritten doctrines, and general Platonic esoterica cover a veritable pile, a mountain of monographs, all of which require specialized knowledge of both Plato and ancient philosophy. They require that you have serious command of ancient Greek. In fact, this episode was kind of just me using the *Theology of Arithmetic* as an excuse to start the process of introducing this topic here on the channel. This idea of the other, hidden teachings of Plato are decisively important in many ways, I think. Of course, I'll be circling back to it at some point soon. Regardless, I'll include some of the more accessible volumes on the question of Platonic esoterica in the description below. I'm thinking of "accessible" here in a very broad sense. The volumes, like I said, are highly specialized and pretty pricey, but the topic is, it's really fascinating.
The best edition of Plato, if you're curious and want to really get into Plato, is the Cooper edition, published by the wonderful folks over at Hackett. You hear that, Brill? You need to learn from Hackett. You need to channel your inner Hackett. Brill, if I were you, I'd start with the *Timaeus*. If all this mathematical metaphysics stuff interests you, that's where Plato really explores it in the most sustained fashion. Then, of course, flip back to *Letter VII*, though of course, it also shows up obliquely in other dialogues, especially the *Republic*, and really, in many ways, as early as the *Meno*, where it famously illustrates Plato's theory of knowledge as recollection. There he teaches a slave geometry, although the slave is really remembering geometry.
The *Theology of Arithmetic* is available in a really nice English translation by Robin Waterfield, though I have to say that I wish the introduction were a bit more substantial. The notes, however, especially explaining the language of classical Greek mathematics, are invaluable. The text is indecipherable without the notes, at least for me, as a non-ancient Greek mathematics specialist. Much of the technical language just doesn't survive into modern mathematics or requires acquiring a kind of specific arithmetological jargon that was unique, in many ways, to the ancient Greek world. It's certainly worth having for anyone interested in the intersection of mathematics and metaphysics, or the origins of numerology, or really the origins of sacred geometry more generally.
Again, make sure to subscribe. Check out my other numerous contents on topics in esotericism. I have a lot of curated playlists about specific topics in esotericism. And again, I hope you consider supporting my work of making scholarly and free content on topics like this by checking out my Patreon or maybe considering a one-time donation. Again, you can find those links below.
Until next time, I'm Dr. Justin Sledge, and thank you for watching Esoterica, where we explore the arcane in history, philosophy, religion, and apparently, mathematics.