Secret Teachings of Plato & Theology of Arithmetic - Pythagorean Origins of Sacred Geometry

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 has been influenced by or is a reaction to that greatest student of socrates perhaps whitehead put it best when he described all of western philosophy is 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 throw 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 contained 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 if you're interested in esoteric philosophy the academic study of the occult alchemy and kabbalah make sure to subscribe check out my other content on topics in esotericism and also if you want to support this kind of work of providing accessible scholarly and free content on topics and esotericism generally here on youtube for free i hope you consider supporting my work on patreon or with a one-time donation you can find those links below in the description and in the first pen comment and i really do appreciate your consideration of supporting the work of making esoterica widely available now let's turn to the esoteric unwritten doctrines of plato and how they might echo in the brief theology of arithmetic attributed to iambolikus i'm dr justin sledge and welcome to esoterica where we explore the arcane in history philosophy and religion [Music] [Music] 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 on thought the early dialogues of 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 anamisis 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 dialogue 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 demate among specialists some schools of thought especially the tubing in school has 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 rk 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 and 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 seven 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 seven is disputed though very reputable plato scholars accept it and interestingly enough computorial 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 it 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 spucipus seems to be wrestling with a set of philosophical and doctrinal issues which clearly they've learnt 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 the 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 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 dylan 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 daiab 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 aperon a limit on the limitness and that actually we see already in mature pythagorean teachings now by limiting the indefinite diad the one introduces the reality of division into what we call the mini that's a big problem in plato the mini 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 how somehow in here 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 in here 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 ekmageon as actually aristotle tells us by the way that word ekmageon 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 play-doh and 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 tetricus is said to combine this primal unity with the one plus two plus three plus four equals 10 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 arrhythmic progression point line shape surface solid can be found in the timaeus account of the genesis of the universe the four elements the soul dnd dice 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 a 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 dianoya 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 noesus 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 seven again legend has it that plato had let no one ignorant of geometry enter written over the gates of the academy itself 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 done written 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 quoi 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 specifics and xenocritis until the turn toward academic skepticism beginning in the 3rd century bce with our kessel house indeed this is probably why the old academy strikes modern students of philosophy is 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 and 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 pneumonias platinus are proclass though both pneumonias and yamblicus 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 nico marcus of garasa and a slightly later digest of pythagorean platonic arithmetological speculation in a work known as the theology of arithmetic sometimes attributed to yamblicus 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 yamblicus perhaps by probably by amplicus 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 weave between theological philosophical arithmetic and geometric properties of each of the ten numbers from the monad one through the decade 10. here we're treated to a fully neo-pythagorean 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 erythmological and 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 safer yetzera 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 paras the limits of spiritual and physical reality for instance why elements and directions both come in and fours there's a there's an erethymological 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 arithmeological 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 text 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 erythmological 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 yamblicus 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 alemba jiu 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 erythmology 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 d and cornelius agrippa cornelius agrippa's entire second book of the cult philosophy is just about a rhythmology in this way from philosophy to physics to magic the esoteric teachings of plato and the erythmological 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 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 a an excuse to start the process of introducing this topic here on the channel this idea of the other terror 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 hack it brill if i were you i'd start with the dimas 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 seven though of course it also shows up obliquely in other dialogues especially the republic and really in many ways as early as the amino where it famously illustrates plato's theory of knowledge as recollection there he teaches a slave geometry although the slaves really remembering jam whatever 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 and 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 you

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Length: 32min 17sec (1937 seconds)

Published: Fri Feb 04 2022