We here allow ourselves ‘The Raphael License’, copying Raphael’s deliberate time-distortions, by inserting portraits and images of post-Renaissance Italian men in his Scuola d’Atene. Raphael retrojected his own contemporaries — men of distinction of the Italy of his own time — placing these alongside Plato, Aristotle and their contemporaries of the Early Academy (=the Scuola). Here we allow a depiction of a young Theaetetus figure, industriously constructing the Fifth of Plato’s regular solids, his personal then-dodahedron [this coinage is not without ancient evidence: likely it is Philip behind the dismissive phrase ‘tote trigwnon’ in Scholion 18 to Euclid I, 1, constructing that particular triangle] This expression is clearly meant to demean the mere product, as it later gets called, a poiesis-fabrication. But the personalised and temporalised ‘product’ makes its collision with that special a-temporal elevation of Plato’s exemplar. It is exclusively this latter, Philip never relented from warning the world, satisfactorily underlying all references by the mathematician in his purity — his pure form so to speak.
Yet there is value in such imaging, even if it indulges in anachronisms. It allows us to respond more empatheticaly to (for example) the young Theaetetus, — working ingeniously at his mathematics at a time earlier than Plato’s dialogue Theaetetus. This will likely have been a time even early enough that the Academy itself was still so to speak ‘under construction’ ? Our imaginations can benefit today from a similar projecting backwards of the work even today underway in Pisa and Rome. I refer to constructions — as we may call them — of the platonic Scholia. This allows us to decipher Plato more fully, more vividly. On the basis of such empathetic reconstructions, we may make further reasonable inferences about Plato. These will help us decipher nearby figures of these exact particulars of Plato’s own time and place. This licenses us to fasten our eyes on a Theaetetus-like industrious American workman, got up in our present-day clothing, here in Boston at a date after 1973 A.D. Or to get a vivid image of a Plato-like figure pointing upward from the Rome of today. Today such an image on the Internet is called a Gravatar. What would Plato’s academic colleagues make of today’s Vatican, or its library ? It might be heavenward of our Plato figure’s gesturing hand. Your imagination is invited, dear e-reader, to construct such a thing:
Is the Greek word ‘sunstEsasthai’ special ? Yes, it can be so special as to qualify as a “PAWAG”, a “PoorlyAttestedWordinAncientGreek “. Its rarity is due to its curious mid-word string -nst- which makes it a difficulty phonologically, being difficult to pronounce. Yet one of our best mss. from ancient mathematicians has words from this family. — three examples are manifested in one excellent ms. now in Florence, all from the Platonic polyhedra chapter in Book XIII. Further, an example of similar rarity comes down to us via an ancient papyrus. This strong basis makes it worth emphasising this point. It is a PAWAG of precisely of this -nst- form which is attested by a parallel in a 3d cent. BC Menander papyrus : ‘sunstomoteron’. Despite the difficulty — or in part because of it — this difficult word is accepted by the Oxford editors of Sikyonioi. A striking parallel to the mid-word -nsp- occurs in a disputed reading in the text of Symp. 206d6. Two good mss. and a papyrus reading there have the phonologically difficult string ‘ksu[n]sper-‘. Now a mid-word string -nsp- is rather like the -nst- we are examining. An additional minor feature of the papyrus is its ‘ks-‘ opening letters, which follows the model of Thucydides as Marcellinus confirms that Plato prefers to do. The late Plato was known for experimenting with his diction, and we may be seeing such special diction here. Lewis Campbell was good at pointing the way to connecting the archaisms in Plato He did this with particular pointedness and skill in his ‘Vol II’ (Oxford U Press) essays on Plato. The initial edition was printed in 1894, a volume often since reprinted. He calls special attention to Diogenes of Halicarnassus, finding Plato and Thucydides similar in their archaising Attic diction.
The Venetian Plato ms. T has recently been put online :
We might paraphrase this biographer of Thucydides (from about the time of Boethius): in Thucidydes Plato finds a ‘consolation in the Archaic.’ and his Thucydides-like later style.
Please give close attention to this image of philosopher-astronomers, taken here at YoungerSocrates as the exemplary of those immediately around Plato. The annotations give pointers to the observational astronomy of the day. Plato, Aristotle, Eudoxus and Philip are all present, but the particular focus on astronomy is contained in the foreground. Plato and Aristotle (not in their summer-solstice clothing) are put into the mosaic’s background. By contrast, Raphael renaissance-era ‘Scuola’ depicts many of the same scientists, but gives Plato and Aristotle the central positions. Between the two epochs there falls of course a rich and lengthy pair of traditions, Academy and Lyceum , causing this understandable promotion of Plato and Aristotle. In that ancient scene and in the earliest years of the Early Academy it is fitting to have Eudoxus and Philip still the foreground and central figures.
The above mosaic may contain a better likeness of the face of Eudoxus — and also the face and attitudes of Philip of Opus, better than most other images now extant. He will have been a truculent ‘epanastander’, or uprising younger man, displaying his self-willed attitude by literally ‘turning-your-back-on-your-colleagues (i.e. being willfully determined to NOT SPEAK to them). Self-willed as in ‘authadEs’, means, among other things, being content to remain silent towards those with a claim to hear from you. That is the essential attribute of the authadEs man, wrapped in his own pleasure. Something akin to Narcissism, of the malignant variety.
The yellow circles at the bottom of the compass-like pair of sticks here near the feet of Serpent-Bearer signify yet another instrument for observing the stars and their positions, here near summer solstice, when Serpent Bearer’s brightest star, Alpha-Ophiouchos will be culminating in Athens very near first twilight (8:25 PM local time). How can we calculate this particular star’s culminating there and then, near 104th Olympiad ?
Curtis Wilson, shortly before he died, did the calculation below, with the notes explaining his process. You may rightly find in its details something close to what Plato in Rep I calls the Real Calculator, as infallible as the Real Astronomer necessarily is. It is in any case my opinion that this internationally acknowledged expert on the moon’s motions was an exemplary soul whilst he was still with us sub luna. He loved learning, and his astronomer-colleague included a reference to this then-recent act of calculation, a reference he wrote in Curtis’s obituary. It seems we have rather few with much likeness to Curtis, still now sub luna. When I asked him directly — then in his 91st year — “how does the phrase ‘sub luna’ differ from the Greek ὑπὸ σεληνῆς ‘hypo selEnEs’ , he retorted at once “the two of them mean and are precisely the same thing”.
There are three main families of manuscripts, all from medieval times, which give us primary witness to what Plato actually wrote. The lead member of Family II is the so-called Marciana, housed in the San Marco Library in Venice. Efforts are now being made to improve scholarly access to this codex, now that a very high quality digital copy has been made of the entire book. A good copy has also been made accessible on-line , at This site aims to be part of this. It aims also to stimulate new lines of discussion about the Early Academy, especially the short period of time when, although Aristotle was present there, he had not written the bulk of his works, not even his Organon or Rhetoric.
It is a struggle to reconstruct some of the writing going on there — in science, mathematics and philosophy especially — at the period when Plato was near his time of flourishing. Or more precisely, when he was only a few Olympiads past this peak, say Olymp. 103 and 104 . This is the 8-year period overlapping with the final years of the so-called ‘Theban Hegemony’.
Various of the sciences, astronomy, stereometry, number theory, meteorology, mineral science were under rapid development at the time and in Plato’s immediate vicinity in Athens. We have evidence that Academic writers including the early Aristotle, were writing at a furious pace (as was Plato) in this peak period. The famous Seventh Letter, probably written by Plato himself, seems to be referring to just such lively writing activity, in context quite pointedly at 344 d4. His comments run: “. . .wrote something On Nature. . .not at all. . .[satisfactory] according to my own mind” [ ἔγραψσεν τι τῶν περὶ φύσεως. . .οὐδὲν. . .κατὰ τὸν ἐμὸν λόγον 344 d4-7]. Primary and ultimate things about nature, written about prematurely and before giving Plato himself frequent enough opportunities to clarify and discuss them — this could be a Dionysius II or some “somebody” ( τις : d5 ) — let him be of greater or lesser talent than Dionysius himself, this doesn’t matter — will almost inevitably result in a serious insult to Plato. All the more insulting if this ‘somebody’ was doing this writing, having been motivated by small personal ambitions. A further cause for alarm might have been some affinities with the writings, then still available, of Democritus. More on this topic below.
Assuming we here have an ‘unknown Socrates’, a man of blood and bone and no mere fictional character inside two of the dialogues, we have someone fitting quite closely various descriptions of Plato’s student and friend Philip of Opus. Seventh Letter complains about such a person: he ought to have allowed more frequent opportunities to get himself clear about central platonic teachings, teachings about ‘first and last things’ as the letter puts it. At a minimum, he ought to get himself clear before going public, in writing, about them. I will be bringing to bear evidence for my theory that at least some writings, alongside their authors, inside the Academy in the Olympiads between 103 and 105 will be in the target zone of Plato’s polemics, both in middle books of Rep. and in Symp.
The target zone both here in Seventh Letter and likely also in parts of Symposium and Republic, will be a man committing “allotriopragmosunE”, parallel to Elder Socrates’s committing (or anyhow allegedly committing) “polypragmosunE”. R.G. Bury puzzled over this very issue, in his Symposium edition of 1909: at whom does Plato aim his polemic of Symp. — if it truly has a polemical intent, as Bury strongly believed ? By 1932 Bury had been joined in this ‘polemical’ understanding of the dialogue, by his eminent rival L. Robin. Here the hypothesis will follow out that same joint line of interpretation. It will add supporting evidence from the history of early Greek mathematics and astronomy. The view here is: “the polemic is pointed chiefly at Younger Socrates, or the man bearing that academic nickname”. In one view of it at least, Younger Socrates stands in need of a ‘defense’. Something resembling a second Apology. But Athens — in the person of the Early Academy — may be now willing to take the risk, the legendary risk: “sinning a second time against Philosophy”. In ways to be explained here, the intra-academic proceeding is to be perjudicial rather than standardly judicial. This will have been a major shift between the times of Plato’s very early days, Elder Socrates still alive and no accumulation of ‘writings’ extant, and the two-generations later maturity of Younger Socrates, — Aristotle still a very young man. There are nuances here, to do with procedures of athenian courts. Some of these R.G. Bury had taken pains to spell out, in comments to his edition of Symposium (1909).
Did some of Plato’s companions identify themselves through homeric legend characters ?
Athens in Olympiad 103 is still in ferment, so still suffering from Athenian litigiousness reminiscent of the Ἀιξωνέα (Aixwnea), mentioned in Lysis, Chapt. 1. Young pupils in the lineage of socratic elenctic — vexatiously exhibiting the extreme ‘parrhsia’ of the times, will have been experimenting and pushing the boundaries of civil discourse at the early Academy. These encounters are represented in Lysis, but represented even more vividly in the ferocious sophistic battles in Euthydemus. In Republic for the most part the tone is not that of shrill or extreme disputatiousness, a manner which risks descending into low comedy. Such a risk is however, always on the horizon in democratic Athens, and with skilled comedians such as Eubulus knocking on the door, academic disputation will have had avenues for expression other than Plato’s writing, dramatic stages for them to be represented. Stallbaum’s notes to Rep. VI, 489 c bring this out forcefully. There is comic potential in the seemingly anti-socratic humiliation of ‘the Sage’, — Eubulus seems to have had his so-called Sage debasing himself by his readiness to ‘bargain away’ his wisdom, in exchange for any of the world’s known ‘profits’, ‘fruits’ or ‘kerda’. Wealth may be preferable to wisdom. Here in the Eubulus play echoed and cited by Stallbaum we have the Sage throwing his wisdom aside (comically) asking a ‘Socrates’ if the wise man or the wealthy is superior ! Twice more in Plato’s corpus do we find an echo of this “whether to go to the door of the wealthy man, or the wise man” story: a second instance in Rep. 2 the Republic and one striking instance instance reappears in LAWS XII.
Campbell is endorsed by E.B. England as to the frequency of this topic in Plato — throwing oneself at the door, either of the ruling and knowledgeable, — or perhas the the door of the wealthy ! But the proverb will have shone more brightly after Eubulus had a ‘Socrates’ commit a major “Anakronismus” (so Stallbaum denominates it). He is conversing with comic playwright Eubulus, some generation after Socrates had died, in this anachronistic episode much noted by Stallbaum. , including the anachronism of a playwright of Olymp. 101 presenting live exchanges with “Socrates”: this is at the peak of Republic, Bk. VI , Ch4. The occurrence in Republic is also of interest historically. It falls in Bk 2, where our Ephraim ms. has some extra items of lexical particularity to offer. Perhaps our Plato texts are perturbed on account of their simultaneously representing different controversial facets of Academic dispute ? [Brandwood and Denniston had begun work on the truly special piece of wording ‘Ti dai’ in Rep., but this work has been remained regrettably incomplete, even for the 3-book portion of that masterwork in the Marciana text.]
This specimen from Eubulus remains, echoed at Rep VI, Ch4, has to do with the ‘this-worldly’ realities and ways of reacting to these stories. There will be an occasion to return to a similar topic, but elevated from the plane of history to that of mathematics and the more abstruse facets of Platonic teaching. I refer to school teachings which (some of which may be more fully recoverable by careful study of these intra-Academy echoes. I refer especially from the book of lemmas to the final book of Euclid’s Elements, h.e. Bk XIII. These lemmas are contained in Euclid’s Book IV, which a fragment of Polyaenus refers to. the Polyaenus who, contemporary with Epicurus, wrote mathematics and philosophy both). This will have been the era when of Plato and Younger Socrates had been both writing at the Academy, young Aristotle’s work not yet far advanced there. This is the Polyaenus of Lampsacus, learned in mathematics but subject to disillusionment, seemingly due to paradoxes about physical minima and paradoxes about fitting lines between a curve and a tangent line. [the Horn Angle may be at issue both here and at Plato’s Theaetetus 155, what Cornford called the ‘paradoxes of number’. Some of the barriers to Polyaenus’s pushing forward his ‘Definitions’ and ‘Aporiai’ will have grown up at the very early Academy, likely when some reports have Epicurus listening to young Aristotle there. A linkage is formed by the technical phrase of mathematico-physical discourse κατὰ παρέγκλισιν , coming to us — not directly via Epicurus or Lucretius — but via Scholion #3 to Euclid’s Book I, its ‘Definitions’.
Yes, it is difficult to show that we are justified in tracing this scholion all the way back to an original author in 4th cent. BC, contemporary with Younger Socrates and Aristotle. It is a help, however, that we have reports of Epicurus himself hearing Aristotle in Athens. But a fragment of Polyaenus refers to ‘comments’ apparently applied to works of ‘elements’ (hypomnemata of Stoicheiai, a phrase from Frag. 38). Is the compounded prefix deployed by Epicurus as ‘pareg-klisis’ (or ‘parem-‘ or ‘paren-‘ these are all essentially the same compound of ‘par-‘ and ‘en’. Interesting to note that there are two clear cases of this very prefix (and one unclear case) in Fragment 38 relayed by Demetrius. Easily the most striking case from our point of view is the one appearing in item #18 (Frammenti, p. 101). This is a definite ‘parem-‘, made more striking by the fact that the name of Epicurus appears just a few lines below, in the same fragment (38,18). It may or may not be a valid example, in item #14, where we have extant just ‘-arem- (Frammenti, p. 100). We may rightly put alongside these Epicurus-era men those editing and revising such works at Timaeus, Symposium and Charmides. In his corpus there are only a handful of this compound, one each from LAWS, Timaeus and Charmides — and a fourth (somewhat textually soft) Theaetetus 199c passage, on elements, where B and T have stoutly variant wordings, staying away from the precise form ‘parem-‘ in the remaining three.
Brandwood groups the Venetus T variant with the other ‘parem- examples, following the ‘Y’ manuscript, but also citing both B and T as part of a minority view. The singular example of Tim 50e4, sharing both compound prefix and the balance of the word ‘fainesthai’ deserves very close attention, and not just for reasons of textual scholarship. [The 1995- new edition of the OCT will have an opportunity at Tim 50e4 and 55a to put the textual matters right. History of mathematics and physics may be needed to get the Polyaenus/Epicurus part of this right. If it helps clarify the roles of Younger Socrates, this would only be to the good. It is only 5 Stephanus pages distant from a a geometrical puzzle which tormented A.E. Taylor, and which may possibly incorporate a no-parenklisis measure “4 right angles”, this being a size differing ‘not even by the most mimimal of deficiencies’ from 4 right angles proper.
This line of speculation asks us to keep Parenkliseis excluded as strenuously as Scholion #3 to Euclid does from the concept of RightAngle. There is a logical similarity to the atomists excluding parts less than their minima. Between Democritus’s playful concepts ‘ou-‘ and ‘-den’ we must leave no room for even a ‘lightly weighted’ infinitesimal part of a regular minimum. There is another similarity in evidence here, this one on the side of the Academy, and
Is Aristotle’s work on continuity relevant here ? Yes, but we would be ‘putting the later in front of the earlier’ unless we adhere strictly to history of science and mathematics. And much work remains to be done here, especially under the guidance of Heiberg’s collection of the Scholia to Euclid’s elements. This rich source of further clarifying the very early Academy (and Younger Socrates) still has drawn little scholarly attention It is now largely digitised, and searchable under ‘TLG5022). More of the material may soon be added by the work of Italian textual specialists such as D. Cufalo.
Theaetetus’s work is very likely echoed at Tim. 55A. If there were in fact a ‘door of the wise’ for someone to make a plea in front of, where better than the door of Theaetetus’s ? But this means paying close attention to Chapters 1 and 4 of the scholia to Book X, and getting guidance from this in piecing together the series of ‘ancestors’ to the final chapter — the one usually called the Platonic Solids chapter — of Euclid Book XIII. It was precisely men such as Menaechmus (from ‘within’ the Academy) and Polyaenus (from Athens and Lampsacus). Some light touches of literary mannerism, are likely to help. They must be teased out. Sometimes, on the side of the Academy, this textual work will make progress only by a higher-criticism approach to recognising nuances within Plato’s chronology. Leon Robin, R.G. Bury and Leonard Brandwood have already done such explorations inside Plato. They carefully traced textual nuances such as diphthongal variants of αἰεὶ of δαὶ and of εἴς . This needs further interpreting, and needs applying to works whose place within the orthodox chronology may need clarifying. These would include notably, closer study of Euthydemus, Republic 1-3, Symposium and Alcibiades I.
On the side of geometry — of which Polyaenus became deeply dismissive — we have the work(s) of Euclid, which Polyaenus suggests that he wrote commentary upon. What we now have, other than writings of parallel authors such as Archimedes and Apollonius, is more accessible in the JLH compendium of scholia. This can count as an entire separate ‘author’ (it does in fact count — TLG gave this compendium the author-number 5022). It has the further claim of containing mutually cross-referring “chapters”. That is to say, its Chapter markers are not merely added from outside, but come down to us embedded within the scholia themselves. This makes of them a more secure part, and better articulated, of these old materials. ‘Hebdomon’ is a kephalion, according to a scholion now included in a later Chapter.
As a sample of the internal criticism of Plato, please see this folio in Venetus T. So far from being just a routine part of our Venetus’s text, it gives evidence on which Brandwood made a decision, at a textual crux, namely Theaetetus 199 c8 :
It increases the likelihood that there is a true connection, likely via mathematics, in that Polyaenus’s fragments include a reference to the name ‘Philip’. Scholars have wanted to make this refer to the ‘Philip’ who was an archon in 292-291; reasons can be given, however, for keeping the reference closer to home — not to any extra-academic figure of political standing, but to geometry and astronomy within the Academy when Plato (or Philip) is constituting, and even populating, the ‘Nocturnal Council’. Very likely with help from Philip, a hopeful.
There are references to names which point to that same very early point, Epicurus and Polyaenus still alive and giving the epicurean school its start. ‘Neocles’ ‘Dionysius’ and ‘Leon’. The name ‘Neocles’ [an echo of the Epicurus family ?] surfaces mysteriously in the ps-Aristotle work Problems (sc. 6,30). The question there — an answer appears ‘demanded’ by some Neocles, from Plato ! how to account for loyalties and ‘obedience’ in the animal kingdom, forms of behavior which appear to belong distinctively to humans? Our ways of affiliating in schools where there are leaders and obedient followers is part of this characteristic. ‘DiadochotEs’ one might rename it, or ‘the status of Successor’ [in a line of succession]. The name “Dionysius” is admittedly very common, as is the name (present in one of Polyaenus’s fragments), “Philip”. Scholars have taken this Philip to be an archon of 292-291. But there are significant reasons for keeping this reference aligned more with the known scientific interests of Polyaenus and his generation. Our less politically prominent astronomer and theorist of the heavens Philip of Opus is a candidate here. He too sometimes went by the name ‘Philip’. will have been more vulnerable than most to having his writings ‘re-attributed’, the less prominent man’s work to the politically prominent Archon. Philip wrote on eclipses of sun and moon, and Polyaenus wrote a De Luna. Each wrote material about the proto-Euclidean geometrical Elements.
Consider this page of discussion:
Are there echoes of Polyaenus of Lampsacus, or other ‘allotrioi’ to whom Plato may be planning — in LAWS XII,6 — to ‘send a mission’ from the Academy ?
The famous ‘catalogue of geometers’, probably originating in Aristotle’s immediate vicinity, the author of the p. Gwnias (as we will see, the idea of a ‘parenklisis’ is intimately linked to angles and their definitions). Eudemus’s report on Philip has Philip an immediate student of Plato pursuing mathematical inquiries, following Plato’s lead. Thus if Philip’s understanding of Plato is reliable (the report implies a doubt) there will be a kind of ‘successor’ relationship, linking Plato to this Philip.
The name Dionysius may possibly refer to the co-author of early scientific treatises on stones. In ancient evidences traced out by French scholar Halieux in 1985, Dionysius is so close enough to his coauthor as to have provoked the akronym ‘SD’ to name the pair of them. So Halieux. The other author goes by the name ‘[young] Socrates’. Dionysius II seems to have been a follower, only intermittently and haltingly obedient to be sure, of Plato’s, and is said to have had Plato in mind when he named his own son ‘Apollokrates’. (It could well be within such a group that Polyaenus intends us to find the man he names ‘Apollonides’. Son of Apollo is after all one way of pointing to Plato himself).
In any case it would be of interest to trace the famous Lucretian concept of ‘clinamen’ back as far as possible in the direction of Epicurus, in whose work the term appears repeatedly. Perhaps, if Polyaenus were the technical geometer of the group, this would get us even a short step earlier than Epicurus, on the road back to Democritus ? In any case the context of geometrical puzzles over the Horn Angle (a peculiar hybrid angle, heterogeneous to all the genus ‘rectilineal angle’ family, was famous at and near Eudemus’s time, in generating some tormenting logical and mathematical puzzles. Aporiai, to use one of Polyaenus’s titles — and Definitions, to use another. The Horn Angle fail to be exempt aporiai about to ‘clinamen’ or ‘secundum climaminem’: κατὰ παρέγλισιν. It is worth paying close attention even to the small particular of the ‘kata’ in our text of Scholion 3 to Euclid. It suggests a habit or manner of being rather than a self-standing thing: not a substantive ‘swerving motion’, but rather ‘the manner of the swerve ( perhaps purely theoretical and geometrical, thus not at all dynamic) . Similarly to the common phrase ‘secundum [a man’s] mentem‘ or its primitive, the phrase ‘kata ton [tou Platonos] noun’. Here in Scholion 3 it is as if an angle of otherwise unchallengeable ‘rectitude’ were to be found habitually executing a a tiny ‘curtsy’ or ‘bow’. Our English phrase ‘bowing [down before someone]’ seems rooted in the bow-shaped curvature ‘curvature of its otherwise erect spine’.
The Eighteenth Chapter of Timaeus ends with a puzzling segment on a certain ‘hybrid reasoning’ (logismos nothos: ‘bastard reasoning’). Hardly believable, says of it, relying as it does on a kind of contact ‘helped by insensibility’ (met’ anaisthEsias: 52 b3 Some useful speculation can be brought to bear here from the Epicurean school, and its leaving a door open to a kind of parenklisis measure. We need only do for these parem-Euclidean authors what some clearly did for Eudoxus and Menaechmus: create a ‘weak’ standard, one that barely achieves believability (to compare also: A Robinson’s followers and their ‘weighted’ infinitesimals, leaving room for ‘non-standard equality). In Polyaenus’s case, the Right Angle, by whose ‘rectitude’ so much else is kept strictly upright — can be weakened, just by dropping the stricture ”no parenklisis allowed”. More needs to be done here, but certain of Polyaenus’s fragments relating to inserting a line ‘between’ some others in a complex figure together with the idea that we get ‘the same Absurdity’ (Euclid only once uses ‘to atopon’ as a more colloquial variant on the more formally technical ‘to adunaton’. Amongst the motivations may well be to allow, as our colloquial “atopon” (Socrates calls himself this) one of these to be a matter of degree. Thus ‘adunatoteron’ has the air of paradox, like ‘athanatoteron’ — whereas ‘more odd’ varies a term weaker and more flexible than its fellow. Here in Tim. Chapt 18 we see Plato calling ‘Earth’ and ‘Heaven’ siblings, thus hinting that Friends of Earth and Friends of Forms or Heaven, might reconcile their differences. So with other ‘allotrioi’, like Epucureans (when they come to formulate this name for the ‘DiadochE’). More exploration needed here, Polyaenus’s texts and the scholia to Euclid the main guides.
The name ‘polyaenus’ has a more common meaning when deployed by Homer, one of his standard epithets for Odysseus (including Od. 12, 184) ‘the much-praised’. Polyaenus has a fragment in which he warns of the danger in ‘ep-ainein’, or ‘praising’: you may make an associate into a flatterer. Both the words ‘ainein’ and ‘epainein’ are in LAWS XII, 6, alongside a repeated word ‘poly’, — arranged in a usage that is conspicuously pleonastic.
What precisely is this riddle of the “Silent” Socrates ? A tradition in the later Academy has it that Socrates “remained silent at his trial”. It is shocking, of course, in that this completely mismatches both Plato’s and Xenophon’s reporting — where we have a characteristically talkative Socrates, not silent in the least. The “irony” for which Socrates was famous derives its name quite directly from one who is ‘eirwn’ must be talkative, even what one can rightly call double-talkative. Doubles entendres are understandings we get from listening to the man speaking ‘with forked tongue’, or in a double mode. It is a noteworthy fact that the adjectival and adverbial forms ‘eironikos’ and ‘eironikws’ are both present in Plato, but only rather rarely. The second of these, the adverbial form, occurs but once — and has Socrates reporting on the speaking ‘ironically’ of the young sophistic verbal gymnast Dionysiodorus (in Chapt 28 of Euthydemus, a chapter very near the end of this 31-chapter work). More needs to be done to clarify this singular outcropping of this word ‘ironically’. Other ancient authorities point the same way, to an extremely talkative Socrates, speaking to a largish audience in his Apology, not at all silent. Yet Maximus of Tyre, squarely in the Socratic-Platonic tradition, takes pains to explain and justify Socrates’s alleged silence at his trial: he had good reason to maintain this silence, Maximus argues in a little essay on this subject. A whole scholarly book has been assembled in very recent years, “The Unknown Socrates”, which tries to solve this riddle.
Two possible explanations are available, based upon research in the vicinity of Younger Socrates. One is based on a suggestion in Plato’s Symposium, one based on a set of suggestions in Euthydemus. R.G. Bury brings up the the specialist language from Athenian lawcourt jargon, to comment on the particular term: diadikasometha . Here in the opening chapters of Symp. much is said about various social protocols for this highly ritualised and ceremonious ‘banquet’ about to happen. Also about how Socrates’s standard behavior is odd, mismatching what Athenians expect in the way of ceremonious behavior. This introductory material is not without comic touches: shoelessness is an issue, and whether or not one has been directly invited to the party, or whether this is something we party-goers are entitled to ‘pass along’.
There is an extra nuance, that goes a good bit deeper than all this bantering preliminary talk. The particular term Bury focuses on, and wants the reader to be clear about is a non-standard use of the idea of lawcourts. The text in fact does not have the standard word (like our words ‘judiciary’ or ‘judicial’). It says rather — we should think of a judgment of a ‘perjudicial’ nature. The Greek has the prefix ‘dia-‘ in front of its standard word for ‘judiciary’, and Bury makes a point of explaining this nuance. The Greek reads: διαδικασόμεθα . . . [175e] ‘perjudicial’ . The verbs and nouns derived from this root word were written by Plato [and/or Philip] in a strikingly skewed pattern. Of the 17 total cases, 13 occur in the second half of LAWS, and something still more pointed occurs with the noun-form derived: διαδικασία [diadikasia, a perjudicial place]. Cicero standardly renders this Greek prefix into Latin with his own ‘per-‘ — in such terminology we have a ‘perjudicial’ proceeding. This identical term reappears in LAWS XII, ch6. This passage [952d4] is not only late in LAWS, it falls just a few chapters short of the works final words. That is, it falls just 8 chapters short of Philip’s taking on full authorship of the work, h.e. ‘Bk XIII’). Does it occur elsewhere in the Corpus Platonicum, perhaps remotely from any signs of Philip’s presence ? The answer is “not at all frequently elsewhere, except two cases in Phdo and one case in Republic Bk X. One of the 3 latest in LAWS occurs in the final chapter (i.e. 14) of Bk XI — thus the ultimate chapter of the works penultimate book. Just by itself (independently of signal further evidences, of which however there are many), this specialist term’s chosen locations is plenty worth notice. We will later be giving close attention to LAWS Bk XII,6. Some refinements of rhetorical figures and Euthydemus-style playing on the ending of names will turn out to make serious pointers toward Polyaenus of Lampsacus, Epicurus’s close associate. Many of the clues will turn out to be from the history of mathematics at Plato’s time (and very shortly after), and will turn on a scholion to Euclid using rare locutions, such as
The text’s more complete statement proceeds to add a serious note by bringing in the topic of ‘wisdom’ and putting the event’s judgment under the judgment of the god Dionysus. The Dionysus part is of course easy to explain — drinking wine is the basic social activity of the day, and when wisdom (about Love) is the topic for the required speeches, a judgment is fittingly put under the the wine-god.
Here in Plato’s more nuanced description he backs off to the standard term for an Athenian ‘court’, the unprefixed ‘δικασ-‘ with various endings. The contrast stands out, in that the same 175e sentence includes both standard and nuanced words: . . . . διαδικασόμεθα ἐγώ τε καὶ σὺ περὶ τῆς σοφίας, δικαστῇ χρώμενοι τῷ Διονύσῳ [175e] The subspecies is distinct in its that there will standardly be — its format being preserved, — an absence of any Apologia. This means the non-speaking of the defence party. This in turn translates into a court scene in which our Socrates remains silent. Which was to be found (Q.E.I.).
Bury’s note to 175e explains all of this. The roles of Plaintiff and Defendant are not ranged (in the perjudicial subspecial case) into the standard plaintiff-defendant stand-off. Co-ordinate suitors are here bringing the action to adjudicate their respective claims, for example to a piece of property. The goal is not to achieve a judgment against the defendant (or an exoneration), though it remains similar in being a court case. Thus a Socrates (or a ‘Younger Socrates’) need not play the role of defendant. A ‘silent’ Socrates is therefore quite in order, and in our case still more so, the immediate background not being the ‘older accuser’ Aristophanes and his Clouds, but rather a judicious resolution of a more localised ‘Battle of Titans versus Younger Gods’, or Friends of Forms and Friends of Earth. Back in the time of Elder Socrates and the then-performances of Clouds the issues are more akin to those surrounding Gorgias, Protagoras, Hippias and Prodicus; now with the Academy as background, we need a per-judicial settlement, not a judicial one. There might be various local reasons why (including the absence of the ‘defendant’ role) one or another of the Friends of Earth would be kept silent. This Symposium-based silence remains at the cultural and social (or rhetorical) surface of things. A somewhat deeper explanation can be presented, however, which drills down to the logic of ‘not-saying’, in the way it associates itself with the logically contradictory. He whose own speech refutes itself, is a manner self-silenced. This explanation can be derived from Chapt. 28 of the Euthydemus. Socrates is made to say of himself, I am a-phonwn (no speech, no sound from me, so fully have I been refuted: [᾿Εγὼ]. . . ἐκείμην ἄφωνος Euthyd. 303 a5).
This deeper level involves the more Academy-tinged feature, the ‘peirastic’ exercises that leave themselves open to logical hazards of a more perplexing sort. Again comedians can make sport of academicians, whom they picture as unreasonably busy about their seemingly ‘trivial’ or ‘academic’ topics. Say struggling to sort out pumpkins so they achieve logical distinctness from cucumbers. But these same peirastic exercises are soon to get major attention from young. Aristotle is soon to clarify how syllogisms more naturally move forward, when our academic debaters have finished their methodical pro-syllogistic ‘tentative explorations’, probing for just the right middle terms, or causes . In both directions, this will have been the robust exercising of what academicians will certainly have called ‘dialectic’ — likely echoing all three of the pre-Aristotle debaters, h.e. both Young and Elder Socrates and also the aging Plato himself. Will this not have been standard usage, for all 3 of these, and likely for Menaechmus, Eudoxus, Theophrastus and Dikaiarchus ? Likely so.
The subject of self-silencing may seem distant from that of ‘doing nuanced distinctions’ amongst garden products — but what of the deeper and universal topics, where the terms under debate are ‘Same’ or ‘Other’? ‘Yours’ and ‘mine’ ? Euthydemus presents an exercise by young peirastic dialecticians (significantly named Dionysodorus and Ctesippus; the latter may be suggestive of the Suitor of Penelope named Ctesippus). Like the nuanced debates over ‘One’ and ‘Many’ in the exercises of Parmenides (we are here premissing a chronology which puts ‘Late Theban Hegemony’ as the right time for both Parmenides and Euthyd. This premiss is plausible for various reasons, [incidentally we ought to include the Symposium — especially its ‘Alcibiades’ chapters (Chs. 32-28 of this 29-chapter work]. These late chapters of Symp. will likely have undergone Plato’s “comb and curl” form of editing, likely at precisely this period of the Academy’s early days, when Dodds has him rewriting Gorgias, and Owen has Plato drafting or finishing Timaeus. These scholars had the required intimacy with Plato’s manners and mannerisms as a writer. and his manner(s) of writing. Further writings which may well belong to this Olymp 102-104 period are Micro-Timaeus (=Tim. Locrus), De Mundo ( π. κοσμοῦ) and early drafts of De Caelo .are being composed. Bravo Owen, pace Cherniss. ]
Our special ‘Ephraim’ ms. of Symp. and Alcibiades I adds one more motivation for holding that this pair of works stem from the same time and place (Academy-Athens, Olymp. 103). It is hard to imagine a more striking mismatch between the Ephraim ms. (Venetus T) orthography in this pair of dialogues — mismatch Venetus T and the standard OCT text, which carries not a single example of the older form αἰεὶ. As against the 42 consecutive openings in this dialogue-pair, all are filled in OCT with the standardised form ἀεὶ Ephraim writes 42 consecutive tokens in a row. [there are a number of style-statistic curiosities here. If we take the long speculative look, and ask that each of these 42 decisions in Ephraim’s part had an antecedent probability of 50%, treating the two variant possibility with pure mathematical disinterestedness — it will have been more than a million times less likely to find 42 cases all falling in the same one of the to directions. Equally curiously, Burnet relented at Alc II 144 and accepted a single token of the 4-letter variety into his OCT text.] However we may end up explaining this (if we don’t simply decline to try any explanation), Ephraim’s preference is truly striking. Leon Robin’s editions of Symp. and Phdr. manfully preserved the 4-letter variants, mostly due to Ephraim, but Burnet resolutely resisted them in his OCT, not so much as registering the variations in his notes. The forthcoming edition of OCT’s Symp. will likely do better. Which means showing due respect to Family II of our ms. evidence. (Venetus T may come into its own in the course of this new round of OCT editing, the old-attic αἰεὶ Thucydides spelling holding its own and LRobin’s Presses de France being vindicated against OUP) TLG has Thucycides favoring this older spelling by a 128:0 ratio. Our obstreperous young dialectic explorers here long after the time of Thucycides and the historical Alcibiades in any case press the Euthydemus figure of the academicised Socrates hard: this ‘Same’, is it [or is it not?] always Same? And ‘Other’ is [or is it not?] always Other? As if they had both read Plato’s Sophist.
This is the same encounter, we are approaching the moment where Socrates falls silent. It is perhaps not a sheer co-incidence that in this dialogue, the name of young Ctesippus might suggest an implicit reference to Homer, and more pointedly to that little band of obstreperous suitors, the theme something of a ‘diadikastic’ sorting out of inheritances and wealths of one sort or another. One of our young dialecticians bears the name Ctesippus (associated in Plato’s time with riches), another Amphinomus (associated with moderation and justice, h.e. wanting the inheritance to flow to the rightful heir, not to some impostor. This is also where a sacrilegious set of thoughts surfaces and is (perhaps playfully only) evaluated. Sophistic arguments can explore an ‘academic’ theoretical point about gods, more radical than anything countenanced in Euthyphro. It is the following sequence: being ‘ensouled’ and thus ‘animals’ gods might conceivably be ‘owned’ by a human owner ‘like other animals’. Inside such perverse or playful exercises in logic, we may even conceive a god’s being sold, — or sacrificed to some [other?!] god of our citizen’s choosing ! Passing over the point that gods are here called the ‘despots’ or ‘lords’ of a given human, the status of these individual gods as ‘animal’ and even ‘your animal’ leads to such dumbfounding, or mouth-stopping conclusions. As if an academician had turned the tables on Socrates, playing the ‘sting-ray’ and forcing him to close his mouth. Socrates the Silent ! Which was to be found (QuemEratInveniendum).
These mind-numbing and mouth-stopping conclusions (Stallbaum’s discussion disparages them as conlusiacula) are more deeply dumbfounding (silencing) than a formal rule in a quasi-judicial proceeding. Such sophisticated theodicy can be traced to an Early Academy, replacing a naive Euthyphro with an academicised young jester — call him ‘gift of Dionysus’ or Dionysodorus, we move from the pre-Academy scene to the one very near in date of composition Aristotle’s De Sophisticis Elenchis. Recall: Euthyphro had not been allowed to reach any real result in the eponymous dialogue with Elder Socrates. He was stymied by a series of ‘aporiai’. Here in Euthydemus the tone is diametrically opposite. A confidently asserted theological doctrine is put forward, someone other than Socrates doing the analogy or ‘parabolE’ by an elenctic that is ‘poristic’ or ‘finding an opening, or finding a way’.
Porismata is what academic mathematicians called these (we have good scholia to Euclid to add detail to our explanation here). Such inventively discovered truths are rightly put midway between mathematical ‘theorem’ and ‘construction’. Philip of Opus and Amphinomus (assuming he was someone other than Philip himself) debated the topic of theorems, problems and porisms.
Much more work needs to be done on the 1991 edition ‘I Frammenti di Polieno’, especially fragments from Polyaenus’s book of Aporiai. Striking that Euclid’s standard word ‘eutheia’ is only used in a variant spelling ‘euthEa’, striking also that a key conception inside Eudoxus’s Definition of ‘logos’, “non-homogeneous” is also there in Polyaenus. The motivation in Eudoxus (we are allowing ourselves to believe that Euclid has not yet edited his work or assembled it into his own work at Book V) is exactly that of excluding ‘infinitesimals’. We are in the immediate vicinity of another of the giants of early Greek mathematics, Archimedes, after whom the ‘Archimedean axiom’ is named. Our argument can so-to-speak get ‘leverage’ from Archimedes and his father, and their immediate awareness of Euclid-independent editions the work of Eudoxus.
These recently published ‘frammenti’ of Polyaenus can cast more light on what is at issue in our commentator’s definition of Right Angle, precisely where it has the clause designed to exclude ‘swerve’ As can be seen directly from the the word ‘euodia’ would surface in this work — that, in Polyaenus’s work entitled ‘Aporiai’ (much of our Polyaenus text alas illegible !) we have the word ‘hypomnemata’. We also have references to Polyaenus writing comments on what will soon become Euclid Book IV, Prop. 12. This part of Book IV (it would be aptly entitled, with the Five Platonic Solids in mind, a Euclideo-Platonic ‘book of lemmas’. Given what we know of Eudoxus, Philip, Leodamas and Leon, this location inside Euclid is precisely where we would expect to find input from a good contemporary mathematician. It is just the right place (lemmas doing preparatory constructions for Theaetetus’s co-constructions of the Five Regular Solids. Just conceivably this will prove to be part of Plato’s democritean’ heritage, now in the 21st century being researched by some scholars in northern Italy and in Cambridge, England. Wherever it originally was written, the phrase now in Scholion #3 ” οὐ κατὰ παρέγκισιν” serves as a limitative clause. True rectitude in the Right Angle excludes any ‘bowing’ or ‘bending over alongside’ what was then often standard. That is, taking a kind of converse of “tangent to circle at right angles to circle’s diameter” and clarifying how this ‘rightness’ excludes any manner of declination or bending or bowing, no matter how slight be the manner of its Parengklisis. Was this a way deployed by atomists at and before Polyaenus’ time, thus early enough to alarm Plato and his academic adherents ? This would likely predate Plato’s seeming to sponsor ‘atomic lines’ and predate the academic treatise De Lineis insecabilibus, so harshly refuted by Aristotle. It is not so much later than all this — perhaps only a few Olympiads — that Aristotle’s ‘didaskalia-writer’ Eudemus will have assembled his tract περὶ γωνίας [‘p. gwnias’], in which infinite divisibility is a background issue. Also in the near background is the range of ‘aporiai’ linked to the then-famous Horn Angle, the mixed angle whose one side is the vertical tangent, other side the ‘bent’ circumference of the circle being touched by it.
Some of Polyaenus’s phrasings concerning the ‘touching’ of the circle inscribed in the regular pentagon (the rectilineal part of the argument being said to be extended — ‘ekteinein! — Plato warned against such ‘physical’ expressions) stretching past this point of tangency.
This may be an opportune moment to “listen” to a busy solid geometer, Theaetetus, his image being on Boston Common, industriously crafting a (physical!) polyhedron to be surrounded by a physical (finite) sphere:
Theaetetus’s argument (Eucl. XIII ad fin) depends for its setting the finite limit ‘5’ on Platonic Solids on the angle-sum about any point in the Euclidean plane being 4 right angles. But what if we were to drop the excluder phrase from the definition of Right Angle, thus admitting planes with either 4 right angles exactly or 4 right angles plus 4 weighted-infinitesimal ‘clinamen’ s ? Supposing a near-regular plane figure, a hexagon one of whose angles incorporates a ‘parenklisis’ — might this also complicate the truth or even spoil, the final argument of Theaetetus, his “five and only five”. Perhaps this would have a bearing on any strictly equivalent ‘reduction’, equivalent to that “5 only” theorem, sometimes now numbered 18a at the end of Euclid’s Elements. Might there be re-opened Amphinomus’s questioning? Can we be entirely sure about the ‘classic’ reduction of that potentially infinite spectrum of inscribable regular polyhedra by Plato’s colleague Theaetetus. Prof. Amie Wilkinson’s August publication speculated about that Amphinomus question, probably put forward within a decade or two of the death of young Theaetetus — by Plato’s other colleague Amphinomus. The recent pubication by Prof. Wilkinson is her piece in the NY Times, its section “Science Times” of 7 August 2017 polyhedra — were such an equivalence to come to the surface via Mirzakhani’s work in Rigidity Theory, it would add to both the historical and the a-historical items of interest here. The real-life Theaetetus (I am supposing there was such a man or boy) was a colleague of the young man who lived and wrote over a longer period, Younger Socrates as we know him now.
This was precisely the kind of construction to create the aporia-rich substance of an infinitesimal angle (of its two lines, 1 is a rectilineal, tangent to the circle, the other is the circle’s own curved boundary.) The circle, not incidentally, has a philological specialty about its standard names, there at the early Academy. Polyaenus, a late contemporary of Younger Socrates, refers to it neither in the standard Euclidean manner nor in that of Seventh Letter, thus: ‘περιφερεία‘. Perhaps such circles are thought of so as to obstruct or replace the idealising envisioned in Seventh Letter, The Circle Itself.
Aristotle sometimes named its center “K”, after “kentron”, as for example in his Meteorologica. (parts of which seem to have originated elsewhere than Aristotle’s own hand). The alternative, conceivably with some ‘atomistic’ theorising behind this, might be said to ‘gather in’, or to ‘surround’. Like the first letter of ‘Ouranos’ (and unlike the first letter of ‘Diaphora’), it may well include some ‘matter’ ? A scholion to Euclid I, our best ms. of it, takes the two letters ‘Omicron’ and ‘Delta’ as representing curved and rectilineal plane figures. This is a point on which I have consulted Prof. William Falcetano of Newark, to whom the ‘clinamen’ is a familiar concept. This is all the same as the atomists’s ‘paregklisis’.
In any case we may guide ourselves by some specialties of the text of LAWS XII,6 to try to get more definite about who these academic ‘outsiders’ were, and why an embassy to them might appeal to Plato. That is a chapter where proposals for academic ambassadors are asked to venture widely. The idea is to make the most serious possible intellectual exchanges with “outsiders” who may chance to know more than even the academy’s currently best minds (Aristotle, recall is still very young and no part of this Nocturnal Councillors’ Commission. This a slightly premature outcropping within LAWS (the full account will not surface for another 3 chapters, i.e. 3 chapters closer to Philip’s initial chapter of Epinomis).
Prof. England’s 1921 edition had an imaginative name for these plans by Plato: Plato’s ‘Foreign Office’. They were to be travelling academics engaged in service teaching and learning from ‘allotrioi’. Their travels perhaps guided by Apollo’s brother Hermes ? No fuller sketch of the character of Hermes exists in Plato, fuller than that of the early chapters of LAWS XII. On their return, these travellers must be careful to avoid the manner of the ‘sophist’ — so England also reminds us. Hermes and his somewhat untrustworthy truthfulness perhaps still guiding ?
All this ambassadorial work (Epistle XI suggests that a favorite ambassador may have the name — or nickname — “Socrates”) is pointed to the gathering of the very best current research and knowledge — to be then formally presented (perhaps in the form of ‘Socratic Synousiai’ ? likely so, given what XII,6 says of the Nocturnal Council.) [In particular the messages might connect to the paradoxical definition of the swerve-free standing of the Right Angles very rectitude.] The most relevant text of Plato will be brought in (somewhat boldly) from a passage only a few chapters short of the first pages of Younger Socrates’s Epinomis: Book XII, Chapt. 6. (952 bc). If Democritus and his interest in tangencies of circles wrote anything of παρέγκλισιν, we seem not to have any surviving traces of this. But any of this would be of interest to the methodical researcher Michael Frede, warmly remembered by many of us.
Of the possible interpretations of Venetus T’s marginalium to fol. 259r, on Tim. 42 b1, this might be one of the better ones. It will be recalled that someone somewhere ‘ornamented’ this leading Plato ms. with that Eubulus-like comic complaint or outburst. (‘Plato playing the Fool’, says the scholion, when he puts to shame [in the selfsame language, about mastery and being-mastered, followed by the suggestive phrasing ἄλλον ὑπ’ ἄλλου. The language points exactly the same place as it did in Ch xviii of Rep. , a kind of injustice or ill health in the soul, ‘akrasia’, and its all-too-human roots in our created Cosmos. Someone associated with the words or comically linked to a stage-name whose homeoteleuton points to a ‘- Krateia’. Euthydemus Chapt 22 had experimented with name-surgery, factoring in the the ‘-KlEs’ to either a HeraKlEs or an IphiKlEs or a PatroKlEs. Why not experiment with factoring in a ‘-KratES’ to form ‘HermoKratEs’ ? The ‘Hermes’ factor is prominent here, and the name ‘Hermocrates’ will certainly have recalled (to academicians of the day) both (1) Dionysius I’s father-in-law and (2) the speaker in Timaeus named Hermocrates. In addition, from here we may make still a further point although it must go via historically unattested persons, and even historically non-extant characters within Plato’s depiction of these — history as Plato distills it. It seems that the intended speaker for Plato’s projected dialogue The Philosopher was to be ‘Hermocrates’. Reinforcing these evidences of historical or literary personages near Plato, we have the report relayed by Plutarch. Dionysius II intended to pay honor to Plato, when he named his own son after him. This will have been the natural result of some name-factoring by Dionysius: by factoring out the ‘Hermo-‘ from his grandfather’s name and factoring in the ‘Apollo-‘ (taken from Plato’s legendary ancestry), one gets a fitting compounded name — ApolloKratEs’ . Let a brother stand in for a brother, Apollo the replacement for his brother Hermes.
This may be the place to review a rival view of Plato’s own intentions, his own literary and philosophical purposes in bringing the persona ‘Younger Socrates’ into the world. It is Holger Thesleff’s view that Plato intends us to find behind the mask ‘Younger Socrates’ — Plato Himself. This is a strikingly elegant and ingenious idea, and the careful analysis of Deborah Nails has led her to adopt it. In my own view, it is easily the strongest rival possibility to the one being presented here, so I would not stand behind my own rival view — but rather would be won over to the Thesleff view — if it were not for the testimony of Metaphys Z, 11 and the ‘blood and bone’ astronomer wanting to be Plato’s replacement at the Academy. Taking as provable the lemmation, ‘the actual writer of As Aristotle can be seen to gaze admiringly at the man — no mere ‘man capable of being the victor’, but rather ‘true and actual victor, thus the one to be crowned’ in this major contest. Were we not to have a good reconstruction of Philip of Opus, the Thesleff theory is easily the strongest, and best. The present website, however, has outlined an argument, based on (1) more detailed work on ‘dialectal’ touches in works such as Symposium, Euthydemus and Minos and (2) based more fully on interpreting the scholia on Euclid collected for Teubner by J.L. Heiberg (1888). This second array of evidences can help strengthen our portraits several personages in F. Lasserre’s catalogue of academic technical writers. Also portraits of Philolaus and Archytas. Amphinomus [alias Socrates Alternate] and Eudoxus can be made clearer also, two personages depicted in the Naples ‘Philosophenmosaik’.
One way of imaging the Thesleff view is to draw upon the Rafael-inspired picture of Plato, with a fullscale replica of the ‘Scuola d’Atene’. Here we may have it that the central Plato figure is a ‘seer’ contemplating the true Academy, along with the background it brings along, peopled with men such as Archytas, other contemporary pythagoreans, Friends of Forms, other rival thinkers with a bewildering variety of advances in the exact sciences and mathematics driving them to excel and outdo every known rival.
[Here, we must fill in further from the ‘Lemmas needing proofs’, and guide by the maxim of Eudemian Ethics about ‘not coronating merely could-be victors, but rather reserving our crowns for actual victors’]
The analysis will need to bring into focus the want-to-be ‘King Socrates’ as in the ‘Prognostica socratis basilei’, struggling for ascendancy (via the ‘exceptional’ science of Astronomy) [see H. Joachim’s notes to DeGenEtCorr on that one exceptional science… ] Thus a new status of ‘dialectician’ can emerge, crafting mathematical advances so to speak ‘in noetic matter’, or ‘in geometrical matter’; Thus the ‘intended heir apparent and Successor, to Plato’s teaching and entire legacy’. ‘Cratistus’ is no mere ‘potential victor’ but ‘a ‘actual and active victor’, of the contest, whom we coronate after it is over. [A curious anecdote has come down from the annals of wrestling contests in antiquity — where such a coronated victor came home from the contest dead. A choke-hold by his opponent near contest’ s end had led directly and suddenly to this actual victor’s dying, yet this did not deprive him, or his corpse, of the actual crown. Such is the dominance of the actual over the potential: in this case even death can not compromise the dominance.]
Thesleff’s is the most elegant and the best decoding for the name ‘Younger Socrates’, were we not to see a way to an individual of ‘blood and bone’ differing from Plato’s. Thesleff has ‘Younger Socrates’ a mask behind which we do best to see: Plato Himself. ecoding brings him, logically enough, to an explanatory equivalence ‘Younger Socrates’ = ‘Plato’. Deborah Nails’s careful work with the personages near Plato accepts this decoding. I hasten to concede that these quasi-logistic maneuvers, resting as they do on on an early Academy meaning of ‘symplokE’ [sc. the lexical art of unweaving and re-weaving these key names] does not point uniquely to the conclusion I am drawing. It points, rather, just as much toward Thesleff’s conclusion, equating ‘Younger Socrates’ and ‘Plato’. In any case, ‘symplectic’ patterns, decompoundings and recompoundings we may say, lightly generalising, would confer honor and authorship on the young tyrant’s mentor, — Plato himself. [More analysis and a wider collection of evidence is admittedly needed here…]
All of this cleverness in naming will have been of a piece with other strokes of academic wit. For comparison, consider F.M. Cornford’s humorous little tract Microcosmographia academica. This was intended to put on display the cantabrigian wit. So in the parallel ancient microcosm, that of Plato’s early Academy: names such as ‘Younger Socrates’ (another -KratEs derivative !), Amphinomus or Ctesippus may serve as the mask behind which we have reason to look for Philip. In the Cornford pamphlet’s dictionary, Younger Socrates will have played the part of ‘Young Man in a Hurry [to gain royal favor]’. Our astronomer depicted stage-right in the Napels ‘Philosophenmosaik’ stands unmasked, and stands proudly before the admiring (backstage) figure Plato. Do click on this photo from 1894 AD, from a second edition of Cornford’s modern academy. The modern case has the humorous suggestion in it: We of noble stature stand ready to sponsor the young and ambitious geometer here at our academy: May you hurry to find for yourself a ‘Royal Road’ to knowledge, of geometry, astronomy, or other mathemata:
Echoes of tracts authored by a certain (not easy to identify) author-pair, ‘Dionysius and Socrates’, come down from antiquity. The Socrates is not especially troublesome, and one scholar proposed to emend the name to ‘Xenocrates’, a colleague and successor of Plato’s at the early Academy. The name Dionysius troublesome too. Yet consider what we find if we proceed from inside the Early Academy. It may well be non-accidental that Plato inserts the name ‘Philip’ very early on in Symposium, referring to a man — or a figure of legend at least — who for scholars has remained largely an indecipherable name [careful students of Plato RG Bury and L. Robin are included here, who seemed to agree in the surmise that some historical figure was behind Plato’s name ‘Philip’]. Echoes of various other writings from Philip, among them the little tract, De Mundo [ περὶ κοσμοῦ ] — likely academic in origin and now attached to the corpus aristotelicum — treat of such ‘first and last things’. So also the intellectually ambitious piece, of which we have only its title: the one which (so reports SUDA) Philip entitled Peri Thewn [περὶ θεῶν] .
In the margins of our best mss. of Euclid, and in Proclus’s compendium expanding on them, one can find references to names such as ‘AristoclEs’, ‘Aristaeus’, ‘Cratistus’, ‘Carpus’, ‘Amphinomus’, ‘Athenaeus Cyzicenus’, ‘CratEs’ and ‘Cratistus’. More work is needed on this list of names. Possibly it includes aliases of the mysterious man Proclus names ‘our man Cratistus’ [to Euclid I,1, Friedlein 211,16]. This is the same proposition where Scholion #18 makes a forceful appeal against the ‘then-triangle’, i.e. the ‘pote trigwnon’, and indulges the neologistic word ‘epidEmiourgomenon’. This latter term is otherwise only found in a ps-Democritus letter. This would fit extremely well on the interpretation offered below, of Scholia 59-62 (to I. 15) of Euclid’s Book I. In point of mathematical content, there is a further linkage. I, 15 leads directly toward I, 32, where the ‘two-right angles’ property is fixed upon the triangle.
As Amphinomus would say — and perhaps a very young Aristotle might echo this [Proclus has someone named ‘Philip’ advocating this] — we want to be speaking and writing about Triangle Timelessly and according-to-Itself. The thought that some ‘extending’ activity carried out in a this-worldly fashion on a ‘then-triangle’ points to a real contamination of the argument, so say the Amphinomus people. At worst, this defect might seem to reduce that standard ‘eternal truth’, to something merely ‘proved by a sign’ — the example of our then-triangle. A then-triangle is like a diagram or herebelow triangle, thus not a thing elevated to the Epi-demiurgic level of realities. Amphinomus and Younger Socrates (if they were two separate individuals) hold out for Essences, or hyperrealities.
Can this be the same author who appeals for time-neutral phrasings in the geometry of Book I, where it speaks of ‘extending’ &c a triangle’s side and speaks as if, — after that ‘extension’ process or operation at least — the then-triangle actually has a newly installed ‘external angle’? This would be a shock. In any case our I,1 commentator stands very close to Plato’s nephew Speusippus in outlook — and to the man called “Amphonomus”. It is worth setting forth this following possibility, in our ‘Younger Socrates’ context of interpretation: there may well be a man behind Plato’s allusion at Polit 257a8, under the innocent sounding common noun ‘kratistos’, who fits in with the two young mathematicians ‘Socrates Alternate’ and ‘Theaetetus’. The common noun there is κρατιστὸς Polit. 257a8, and it seems to apply to the teacher Theodorus . A parallel to this word’s being used allusively and with deliberate ambiguity is the story of Alexander the Great’s way of identifying his successor. “Mr. κρατιστὸς“, was to be the great man’s successor. The pseudo-proper name: ‘Cratistus’ fits naturally on either successor — its common meaning is ‘he of the greatest strength’.
There may be a surviving fragment from the περὶ θεῶν included within the marginalia to Euclid collected by Heiberg from Euclid’s Elements. The scholion in any case is likely an inheritance from that same Academy. With a bit of luck this will turn out to have strong marks of pre-Platonic origins. These specific scholia are relayed in two of the best of Euclid’s mss., and attach to Book I’s Definition 15 “the Circle”. Either of Philip’s two reported tracts, ‘kukliaka‘ or ‘p. thewn‘, might fittingly be sources of these extant marginalia. A dominant metaphor in Schol. 61, to I, 15 speaks of the divine and ‘fertile’ power behind our world herebelow. The rhetorically high-flown remarks about our Heavens include phrasings about their circular motions and the ‘perpetual reincarnations’ τὴν ἀείδιον παλιγγενεσίαν . More pointedly, we have fragmentary material from Polyaenus himself indicating that he had published an attack on Euthyphro. Conceivably, if Polyaenus found Philip’s tract ‘p. Thewn’ too close to the Platonic line, his work πρὸς τὸν τοῦ Πλάτωνος Εὐθύφρονα, the ambassador from the Academy may have been confronted by a combined polemic, partly against Plato, partly against ‘Younger Socrates’ and the ‘academicised’ versions this teacher and his student Aristotle, a ‘Younger Euthyphro’. Certainly there is much within the Euthyphro, as we now have it, that seems to profit by work at the Academy, notably its precocious young logician, student of both Plato and Younger Socrates.
Embedded inside these scholia we find surviving traces of ‘dialectal’ form of language [traces of non-Attic dialect, but also touches of phrasing foreign to Euclid’s Alexandrian ‘koinE’]. Heiberg had two favorite descriptions of such anomalous wordings, which catch a philologist’s attention (1) sprachliche Anstoesse and (2) ‘a sermone Euclidis abhorret’. These come through to us via Heiberg’s edition of the Scholia (Vol v, p. 95, line 11 a noteworthy example). Happily, a set of good images of Heiberg’s Volume 5 is available to any ‘someone’ with good access to a computer and with reasonably good skills in ancient Greek. If such a τις chanced to reside in Greece, well, so much the more good fortune for our project here. Such a person might in any case to be equal in interpretive power to the son of Dionysius and Doris (= Dionysius II). If so, still the better turn of fortune’s wheel here at youngersocrates.com.
Are there better candidates than Philip, candidates familiar with Plato’s Seventh Letter and its detailed analysis of The Circle? If so these will be candidates to have been original author of this scholion to I, 15. Philip is at least one good example. This exact ‘pythagorist’ formulation, with its high-flown rhetoric, its special non-KoinE spelling of his modifier word, its unabashed reference to re-incarnation, they are all in good agreement with what we know of Philip. Perhaps from Philip’s tract ‘kukliaka’, or perhaps from his ‘p. thewn’ ? As the famous Eudemus catalogue of geometers reports Philip, he took pains to monitor mathematical writings, asking of them that they remain Plato-faithful, or anyhow faithful to Plato as Philip thought was the true Plato.
There may be a trace of ‘tampering’ with the text of Timaeus, in the form analysed in detail by Whittaker and Dillon, where a key term PoiEton is inserted displacing and contaminating away NoEton, in the final page of the dialogue. Archer-Hind had already come down forcefully and with a perhaps overly dogmatic set of convictions behind his words, defending Plato against his intrusive early editors. I would suggest that in Tim. Chapter 13 [41c5], the variant reading manifesting indicates an intrusion of the hand of a tamperer. This same sort of tampering, likely by the same hand, and with a ‘peri Thewn’ set of motivations driving it. Philip of Opus wrote into his ps-Platonic Epinomis some unorthodox theology, advocating worship of the sun. In any case, several mutually independent lines of evidence will have our author nicknamed Socrates Alternate writing contemporaneously with the later period of Plato’s chronology. Sometimes writing, it seems, contentiously and with self-will.
All four of the academicians, Eudoxus, Philip, Amphinomus and Calippus practiced theoretical sciences proficiently, and near enough to both Plato and Aristotle to influence both these men powerfully. In the case of Eudoxus’s pure mathematics, the theoretical depth of the thought has long been acknowledged by historians of science to be on a par with either Plato’s or Aristotle’s mature writing. It is still in the 21st century drawing attention from number-theory experts, such as those behind the recent research such as “toward the Eudoxus Real Numbers” (R.D. Arthan, 2004).
More on this subject will be discussed in a separate page forthcoming here. The sources will be scholia to Euclid’s Elements (alongside Proclus’s digest and modification of these). A key extra conception to be factored in there is to be from the area of hyperreal numbers, its concept of ‘weightings’ of infinitestimals. There will have been motivation to think of such things when puzzling over the ‘mixed angles’ or ‘horn angle’ so troubling to the mathematicians shortly before Eudemus’s tract ‘p. gwnias’, and perhaps near to the coining of the rare word ‘gwniaka’, parallel to Philip’s attested title ‘kukliaka’. Some of these things will have been hinted at inside the Academic quasi-mathematical tract De Lineis Insecabilibus. Especially suggestive are its Early Academic phrases (1) schedon apeiron [ σχέδον ἄπειρον] and (2) ek duoin onomatoin [ ἐκ δυοῖν ὀνομάτοιν ].
As to early calendar work, from Euctemon on, carried forward at the Academy, 4 Tropic Points are possible to recognise, within the solar year’s calendar. This point draws upon a medieval designation, which may well have ancient roots undernearth, by John of Syria, calendarist of the 6th century. John allows each of the two equinoxes to be counted as additional ‘turningpoints’ in the solar year, curiously). A quite formal point can be offered first, about how the symbol-pair Alpha and Omega often serve as mutual reciprocals, thus share the role of the two ‘extremes’ [akra], where the non-extremes [mesa] will be held in the intermediate place, by the two of them jointly. Zeus-Olympian was saluted as a symposiast’s libation, then as a reciprocating Third, Zeus-Savior. Much research has gone into the the range of symbolisms here. Summer and Winter Tropic extremes will serve as mutually reciprocal places on the continuous line of the ecliptic. The pair of points (Plato refers to them with the uncial Greek letter X) where the ecliptic and celestial equator circles doubly intersect are the pair of equaliser of ‘middler’ points between Summer and Winter.
One of the most curious points about the late ancient sciences and arts of parapegmata — calendaric tabulation — comes via John the Syrian (John Lydus, 6th century A.D.). The point is his calling all four of the marker-points in the solar year by the specialist term ‘tropic’, or ‘turningpoint’ . John counts into this foursome the two equinoctial points, an added two ‘turning points’. If he had chanced to come to the New World, he might have said “behold our Inca colleagues, who agree that Equatorial points let us mark out more precisely the ‘periodicities’ down here on Earth, the ones we commonly call seasons; and the middles of March and September, when the noon sun was directly overhead, were crucial points as well”.
The city of the upper Nile in Egypt named ‘SyEnE’ (can Plato or Eudoxus or both have traveled to it?) was later to be made prominent by Eratosthenes. Eudoxus’s work on the Zones (or periods) of Earth in any case reported measurements of maximum day-lengths in various known geographical locations. The “fourteen and a half hours” at Spina is of interest in falling not far northward of Dionysius I’s colony at Ancona. The mystery of the reference in Phaedrus to site of Plato’s “sweet elbow” or “sweet [safe harbor of] Ancona”, associated with sailors on the Nile may have its solution: this new colony in Italy, today known as “Ancona”. Yet another marker from southern Italy, ‘little-Scylla’, is not at all distant, geographically or culturally. It too is mentioned in a fragment of Eudoxus. This town is sited not far east and south of a town with which our Philip of Opus has strong associations, — Menda adjacent to Rhegium.
Again, the politics of Plato and the dynasty of the Dionysius dynasty are intimately connected. And the Locrian peninsula is the very neighborhood whose name Plato uses in Timaeus: ‘the city Locrus in Italy’ [ πόλεως τῆς ἐν Ἴταλιᾳ Λοκρίδος : Tim. 20 a2). If Epistle II was written by Plato (or equally so if it comes from a different nearby hand), its phrase ὦ παῖ Διονυσίου καὶ Δωρίδος [‘O child of Dionysius and Doris’] is a striking vocative aimed quite personally at Dionysius II. Boeckh and others have given reasons for linking the composing of “Minos” and early books of The Laws, — all of this writing activity — to Dionysius II’s activities in Epizephyrian Locrus a little later than the reliably dated Epistle II.
It can hardly be an innocuous coincidence, innocent of any underlying intentions on Plato’s part, that the man at whom Socrates Elder addresses these words — that this man’s name is Hermocrates . We have the further co-inciding of this name with that of a leading statesman of the era, Locrian Doris’s father Hermocrates. Doris’s Her native dialect, the one she will have taught her son one way or another, will have been some variant of that very Locrian. There will be reason to return to some of these names, as well as to the further name used by Dionysius II to make of his son something like an honorary ‘nephew’ of Plato himself.
We may venture to extend this work with names a little further. Hermocrates grandfather to Dionysius II was great-grandfather to the baby named Apollocrates. It seems young Dionysius named his infant son after Apollo, in honor of Plato. Can we defend against an objection, “over-refinement of name-surgery is hazardous” ?Please consider this reply: the pair of names ‘IphiklEs’/’HraklEs’ are aligned in the text of Euthydemus and brought under what was clearly a rule of the art of name-surgery, this art as practiced then and there: παραπλήσιον μὲν τοὖνομα Ἰφικλῆς, ὁ Ἡρακέους ἀδελφός [‘Iphi-kles is a parallel and neighbor, in name, of the brother Hera-cles’: 297 e3]. The name ‘Patro-kles’ is only a few lines above, which it is better not to lose from our text. It had been present in Ephraim [as you can easily confirm at his folium of the ‘Euthydemus‘ ]. But it was secluded by Heindorf, then bracketed by Burnet in his 1903 OCT. This present argument, if it can bear the weight, goes in favor of the new OCT’s citing Venetus T and Ephraim’s sources, and keeping Patro-kles in place.
You may want to click on this link, about Euthydemus and Younger Socrates.
If there should prove to be a distinctive outcropping of ‘locrianisms’ such as the ‘Iota-added’ feature in certain key words (leading example αἰεὶ ), we may rightly hunt for an underlying cause of this. And if Philip from that same Locrian sub-peninsula had some editorial powers over Plato’s texts, at least for a period of time, this perhaps intermittent cause will be found to be temporarily at work, through the hand of Philip (or Socrates Alternate).
We ought to beware of erring on the side of overcautiousness here. Consider the implied advice of Plato’s brother Adeimantus, delivered with some irony to Elder Socrates at R. VI, 3 (end) this way : Σὺ δέ γε, οἶμαι οὐκ εἴωθας δι’ εἰκόνων λέγειν (487e4) “And you, of course, aren’t used to speaking in similes [di’ eikonwn]!” Here is a black-figure eikOn of young Phaethon:
please click on this red-lettered link, to see finer detail of this ‘Phaethon’ image:
Plato’s colleague Eudoxus reportedly said of Phaethon (pictured here under poor control of his celestial chariot): “My desire to know of our father, The Sun (a) his shape (b) his size (c) his itinerary ( σχῆμα =schEma) is all-consuming“. Our report has him speak as if in the manner of the striking Ionian scientist: “if The Sun would reveal these three things to me, I would willingly suffer the fate of the Phaethon of legend (immolation in the sun)“. Eudoxus the Ionian astronomer was in a personal and historical position to say such things in the hearing of Plato, a Calippus of Cyzicus and a young Aristotle. In one British edition of Aristotle’s Nicomachean Ethics we have Aristotle and Eudoxus bound together by close bonds of teacher and student, and personal affection.
About these latter two ‘astronomers’, the Lambda, 8 story comes very close to the famous ‘amicus Plato, sed…‘ formula. The story there in Lambda, 8 runs φιλεῖν μὲν ἀμφοτέρους, πείθεσθαι δὲ τοῖς ἀκριβέστεροις [1073 b16] — “both of them [Eudoxus and Calippus] are my Friends, but I am won over by the fuller Accuracy” Will there not have been some rivalries there and then, inside the Academy ? Imagine if the phrase of Plato’s “Ho to onti astronomos” appearing in Book 7 of Plato’s Republic, as clearly it did appear. Not much distant from the Book 10 formula where Plato declares his own friendship to Homer, strictly undercut, however, by his greater friendship to Truth Herself. In such a context we can easily picture this formula’s doing what is now called ‘morphing’, and re-forming under the ‘Socrates et X amici sunt, sed…’.
Subtle scholarly work has been done on the variant versions of this saying, by Leonardo Taran. He may go to an oversubtle extreme, however, when he asks us to dismiss the instance that substitutes [some variant form of] ‘Socrates(n)’ for the ‘Socrates’ this formula. Taran himself dismisses the possibility of Aristotle’s having any teacher named ‘Socrates’. Here the counter-proposal is to be maintained: we should substitute Socrates(Alternate), or Socrates(Reborn) or Socrates(The Younger) or Socrates(Junior) in Aristotle’s use of the formula, whereupon it becomes factually informative and true .
Under one or several of these aliases, we have a historical man, blood-and-bone present alongside the young Aristotle at the Early Academy and writing tracts such as Epinomis or De Mundo, De Medietatis, De Deis, or Kukliaka. Will he have been called ‘Socrates’ under that very name (eo nomine so to speak)? We have not reason to say No to this, and some positive reasons for saying Yes, the text of the Venetus T’s Politicus, and Vienna’s W also giving us good authority. Some of the agreeing consequences to be spelled out here will reinforce this.
In these high ranges of cosmology and theology not many of Plato’s contemporaries found it easy to avoid excesses of what we may call “epipnoia”, or high-breating zeal. (We also have a passage in Timaeus about the physiology of ‘enthousiasmos’. Zeal is found to corresponds (at the nanocosmic level) to a type of uncleanliness we sometimes experience as ‘bitterness’, inside the physical organism of a person. There is a kinship between Timaeus and Symposium their tendencies to remain open to the enthusiasms or ‘deeper mysteries’ of arcane sciences, and the enthusiasms that susceptible temperaments amongst us experience when studying these. Zealous states of mind or soul, we may rightly call them.
Now it is plain that Plato had a guarded or skeptical attitude toward various of the ‘mystery doctrines’ preached in his day, or preached in the earlier days of Pythagoras, Theano, Ocellus or Philolaus. He seems to have associated them with those mathematically trained [or naturally gifted] geniuses, whose sciences he at once admired and had critical attitudes towards. Useful parallels can be drawn to the work last century on Symposium and Timaeus by continental scholars like Oskar Becker or B.L. van der Waerden or Simone Weil on researches into specialist mathematics at and before Plato’s time. Historically, that was the pythagorean side of Plato, not always fully understood by, or not found empathetic material, by Aristotle.
On the English-speaking side, J. Adam deployed his own skills and some of his Cantabridgean contemporaries contributed their efforts in this direction, before World War I. Adam wrote careful words in his App. IV to Rep. IX, but left a number of riddles unresolved there, about those he called ‘pythagorean preachers’ or ‘wise men’. Plato’s difficult allusions to ‘third libations’ or ‘Zeus Savior’ or the variegated quasi-theological allusions , some under the mysterious umbrella word ‘Olympia-wise’ [ Ὀλυμπικῶς ] give hints about where solutions may one day be found.
Chapter X of Republic Bk 7 begins with a striking phrase, the interrogative [ Τί δαὶ: 527 d1 ], an echo of that same overcolloquial phrase two chapters earlier, at 526 b4, where Stallbaum had written a polemical defense of it, against a powerful philologue, Schneider. Other German scholars of high rank in the peak pre-Wilamowitz period of the 19th century had written on this colloquialism, in prose writers and in the poets, and rendered their considered judgments on whether or no Plato’s prose might be willing to welcome it. The Oxonian consensus, meantime, strenuously excludes it, except for a few rare reports of it (not either of these two in Rep. VII, and none of the half-dozen in earlier books of Republic, oddly.
In any case, even if the topic of Chapter 10 were not the exalted one of Science of Astronomy, and even if this teutonic controversy had not erupted over its opening phrase, and even if a striking image of ‘ten thousand eyes’ were not present in its first few lines — all the same there would have been enhanced scholarly attention to this portion of this major book of Plato’s Magnum Opus. The facts aree as follows: 12 lines into this chapter there jumps up a compounded play on words, a variation on the major factor within the name Eu-Doxos. Factoring out the Ksun- and eliding the Eu-, we have a two-layered word-play. Just 13 lines into the chapter, we find this: ταῦτα ξυνδοκεῖ ἀμηχάνως ὡς εὖ δόξεις λέγειν [527 e3]
[In a private communication, Holger Thesleff has reported to me about some further efforts in Paris, still going forward in the 2d decade of the XXI. century in Paris — detecting more evidence of the ‘true’ pythagoreans behind the abundance of pseudepigraphica which we have extant [he was responding to a letter in which I had asked him about the Timaeus Locrus, his views about the true identity of its author. Our Venetus T codex makes TL the very first item of content].
Mark Twain, in his “Roughing It” and also in a handwritten note, both concealed and revealed. Kindly inspect — after taking a deep breath — the following copy of this self-validating piece of handwriting:
Coming back to formulas such as the ‘third libation’, to Zeus. They likely have reference to what will have had been, even then, somewhat veiled meanings, perhaps with implied number-play contained. One divine Third term represents being a kind of reciprocal-return to first, heroes held in the middle position. J. Adam cross-refers to Republic Book V, where similarly puzzling ‘sophoi’ are present, although only in a veiled way. If Dodds was right in placing Gorgias near to Seventh Letter, at least when Plato was moved to modify or extend its text, this would put it nearby adjacent to Socrates Alternate’s writing about the calendar, or about writing his ‘p. Thewn’ or ‘p. HedonE’.
Here is a glimpse of what we see in Venetus T, shortly before a striking scholion, harshly criticising ‘the most wise Plato’ [few other than Thrasymachus, Diotima, Pindar, Solon are directly addressed with this of this adjective, perhaps undercut by irony here and there]. “Right here,” says our scholiast pointedly, “you play the eminently wise Fool, O Plato”. This from the margins of fol. 259r, its Timaeus, Chapt. 14.
This is the chapter following immediately after the one (Chap 13) linked closely by the theme of ‘seeding’ the cosmos with an ‘isarithmic’ number souls. It is likely to be an innocent variety of co-incidence that we have a count of 11 there in the Sistine Chapel. That is the count of secondary ‘celestial spirits’ which Michelangelo has caused to foregather by the feet of the Creator, iln his ‘sparking of Adam’ image. Wilamowitz puzzled over the number 11 in this connection. But Wilamowitz declined to make any connection to the point Plato makes in LAWS about Eleven: it being one of the few small prime submultiples of our number 5038, this last being an ‘additive factor’ of 5040, the ‘factor (additive)’ being a ‘minus two’). Plato’s allusion is veiled and mysterious, but possibly fascinating to pythagorising companions there amongst his ‘pyrhagorean preacher’ friends, including Socrates(Alternate).
One further sidelight here comes from the anciently acknowledged metrical form the ‘hendekasyllabic’. This has some linkages to the Venetus T . John the Syrian’s non-standard numeral word ‘dekakaimia’ is a stimulus to further research in this direction, as is the strikingly no-standard numeral form ‘AI’ obliquely finding its way into fol. 4v and elsewhere in the leaves of Venetus T. Other reversals of numeral names turn up in a cluster of words relaying numeral-names of an unorthodox type. Forms such as the ‘(theta)(Iota)’ meant to express our numeral ’19’. But there is perhaps overmuch depth in this direction to be dealt with here.
The ‘foolishness’ by the ’eminently wise Plato’ at 42b is being attacked by the anonymous critic, who is clearly offended by the Timaeus doctrine about the ‘cosmic footing’ of human ‘akrasia’. This scholiast has not yet had his attack published in the critical edition of Plato’s Scholia (by Domenico Cufalo of Pisa). But this is lack of publication is sheer accident of history: Cufalo is soon to be publishing it, when his Volume II appears, and includes Tetralogy VIII of Plato’s works. Our scholiast appears to have taken Plato’s points about ‘akrasia’ (‘weakness of will’, or ‘character weakness’) personally. The scholion is in any case attached to the very same same column of this same leaf of our Venetus T ms. — leaf 259r:
click on this red-lettered link to see details of Venetus T’s f. 259r, Col A, line 1:
Burnet’s OCT does not give this variant reading any notice in its apparatus, unhappily. Scholars might make use of it to add some clarity to cosmological speculation in the Early Academy. This will have been at or before the time of Aristotle’s writing his De Anima, with its dismissive reference in I,3 to some anonymous ‘someone’ (Bekker and Bonitz give him the name ‘Philip’, but with only scanty textual authority behind them). The man under Aristotle’s reference seems to be a veiled Democritus-like expert, writing things about the Daedalus ‘pseudo-live’ statues — ideas about how a physical body might be thought to be moved by its soul. E.R. Dodds once warned (himself) against “the booby-trapped byways of psychical research” including tele-kinesis. He congratulated himself for staying away from these. He only succeeded in resisting the allure of such topics after being warned — by his “demon” (“Missing Persons”, 1977, p. 194).
A number of writers — Eudoxus, Menaechmus, Dicaearchus, Helicon of Cyzicus, Amphinomus, Callipus and Philip of Opus to name 7 of them — were at the Old Academy and writing. Not many of their works have come down to us, at least not in their original form. Often we must resign ourselves to reading what we can extract responsibly from later writings or doxographies. In a few cases, such as the pseudo-Platonic Epinomis or the pseudo-Aristotelian On the Cosmos, we have material plausibly attributable to one or more of the early scientists and mathematicians near Plato himself. Euclid, about whose life we know little, came along some seventy five years later. He was one major collector, though he was in some part an original writer too.
Euclid drew upon — one may almost say he anthologised from — Plato’s leading mathematical colleagues. But in Euclid’s particular case this anthologising effort, and especially for the little ‘orphaned’ work inside one manuscript of Elements XII, not much detailed reconstructive work has so far been done by historians of mathematics. This is the good early manuscript now residing in Bologna. It is a work within stereometrics. It makes special use of the so-called “method of exhaustion”, much admired but somewhat diffidently deployed by Archimedes.
A variant of Book XII on exhaustions is traceable to Eudoxus, but this particular reduced and orphaned edition (Heiberg includes it in Appendix ii to his Vol. IV) is of especial interest as background for modern mathematics, the part now called “integral calculus”. It is also of interest to modern researchers into number theory and set theory. This and other materials from before Euclid’s time contains challenging mathematics, about which 21st century mathematicians have recently been publishing new results.
Gradually scholars have been getting better access to our primary and early witnesses to Plato and his Early Academy, including now the Venetus T text of Plato’s own writing. This is a fine witness. It is my hope that it will one day earn a place very near the top of all our witnesses to Plato’s writing.
The Venice ms. of Plato has certain peculiarities about its style and format which especially invite closer attention. Some of these have been examined already, especially since the monograph by M. Schanz in 1877. It may be preserving, both inside its texts and in its abundant marginalia, some pointers helpful to those of us doing this reconstruction work. This is true both of pointers to the Early Academy itself, and also pointers which we must move outside of Athens, to the Alexandria of Euclid’s time, to see in their historical context.
Euclid’s writing — which is in a number of places derivative from the work of men near Plato — can be shown to include material from his own pre-Euclid Academy — and alluded to by Plato himself. In some particular passages the allusions are pointed. Other than the famous “Plato was sick that day” reference in Apology, it is fair to put on display the example from Rep IX, 6. It is alluding to some individual man (whom the author praises, as “best”), by the phrase Son of Ariston “ho tou Aristwnos uios”. This can have been close to Plato ; it can have meant to point to the man in that same sentence ‘being King over himself ‘.
Philip and Aristotle are diplomatically referred to in Timaeus 28b; again, Theaetetus and Eudoxus are admiringly referred to in Plato’s paraphrase in Soph 264de; further there is the still warmer pointer to the man Eudoxus at the Slings Rep, 527 e4. If some or all of my personal claims to have found ‘references’ were to fall victim to scholarly dismissal, I have in reserve several more to bring forward. Some of this is a tad taxing for the historical imagination, — but some may prove plain convincing. Rep. VI, Chapt 4 is a source for some of this, though the late chapters of Book IV, especially its Chapters 18 and 19, are likely to be a better source.
It may be helpful to call attention to material that comes down to us via the margins of Euclid’s Elements. A series of Scholia to Euclid I, 15 (esp. Scholl. ##59-62) have much to contribute. We are taking the path pioneered by JL Heiberg in the late 19th Century. Heiberg’s Teubner edition collected and published (1888), the scholia to all of Euclid’s Elements. The Scholion of great interest in our present context is the one leading toward an opinion of Philip’s (Proclus decisively connects this to Philip by name, at I, 32). It is the same opinion expressed in Epinomis, and further in Euclid’s margins, where Heiberg numbers it Schol. #18. It expresses strong skepticism towards ‘poiEsis’ language, on the grounds of its controversial concessiveness to ‘time-dependence’ inside mathematics. We should be wary of a so-called ‘construction’ (poiEsis) if it causes us to think the mathematics of I,1 is really about a ‘tote pragma’, a ‘then-outcome’ or ‘then-thing’, rather than something more elevated, and worthy to be called ‘epidEmiourgic’. This is a quite special word, prefixing its ‘epi-‘ to cause the equilateral triangle before us so to speak to ‘jump up’ into our (platonistic?) notice. Additionally, Schol. 18 includes the distinctive verb ‘diamphisbEtein’, rare in classical Greek, but also written by Aristotle in his sections ‘On Friendship’.
We may pause to add some remarks on one or two subtle lexical habits inside the Academy in Plato’s late years. The scholia to I,15 (leading up to the famous ‘2 right angles’ theorem much discussed by Aristotle in his early tracts, Analytics) has much material which will later find its way into EN, at Bk IX, 2 1155 a 32ff. Lewis Campbell, analysing the diction of the late Plato, had called attention to the relative novelty of the specialist term διαμφισβήτειν , novel inside the Early Academy. Yet it stands in Schol 30 to Euclid V, Def. 9.
There is nothing specialistic about the unprefixed form ἀμφισβήτειν — really a quite common term. But Plato in his later years was fond of prefixing δια- to otherwise common verbs, fond of forming distinctive variants. A quite special illustration can be drawn from the margins of Euclid: the extremely rare word, inside or outside the Academy, διακαταχρήστικον . LSJ does not recognise it. A sophisticate like Cicero might conceivably have known that word (in his work Orator he uses only the rather common variant, and translates it “abusio”. In English we have “catachresis”.). Not even the refined Cicero ventures the ‘perabusio’ variant, so latin dictionaries do not include this word. More needs to be said about sophistic extremes in perverse experiments with overturning non-contradiction. In particular, the point needs developing about the legendary Maximus of Tyre legend of the ‘Socrates remaining silent at his trial’ The trial needs to be removed from Elder Socrates and transposed to Younger Socrates, its date moved from -399 to nearer -362. The forensic clues for detecting this newer defendant and this newer trial are many and various. But some of them are rooted in habits of language nearer to Doris of Locris and remote from those at the Academy in Athens. The forensic clues will sometimes center on linguistic peculiarities like the “added Iota” in Symp., Phdr. and Euthyd., but as to date we need to be nearer to the time of the De Soph. Elen. , to which Euthydemus is a main provocation. It is not some “outside force” that causes the silencing of Young Socrates, but rather the logical force at work under non-contradiction, made dramatic and vivid at the time of the aging Plato and the embryonic Aristotle. Stones and iron and inanimate beings can ‘give voice’ even when the master of ‘giving voice’ is rendered mute, internal logical contradictions reducing him to silence. More on this topic is developed at the page on Euthydemus.
In Aristotle himself, however, διαμφισβήτειν occurs several times, and also makes an appearance (singularly !) in the interesting suspect book of the Metaphysics Book Kappa. This is the book that repeats earlier material from the same treatise, and further draws scholarly attention to itself in suffering from a rash of the DeMundo phrase ge mh\n ( γε μὴν ). As C. Ritter had shown, this was a distinctive mannerism in the late Plato, especially in his Laws . Metaphysics Book Kappa has an oversupply of unAristotelian lexical features, to the point where scholars beginning with W. Christ and continuing past W.D. Ross advocated for its deletion from Aristotle’s work entirely. Herbert Granger has recently shown a disinclination to comply with this scholarly consensus, but in the main these two eminent Aristotle scholars have carried the day. All six of Book Kappa’s γε μὴν ‘s [Aristotle’s entire corpus elsewhere has only 9 cases] and all of its other irregularities have been removed (alongside the removal of the tract also rich in γε μὴν ‘s , the De Mundo.]
please note the dialogue-specific jump re LAWS of roughly ten-fold for this ‘marker’ particle
Much more needs to be said about the authorship of the De Mundo, a work of much-disputed authorship, but sometimes attributed to Aristotle himself. It is a tract of astronomical, theological and meteorological scope, but has side excursions into unAristotelian issues such as Zeus’s wide variety of names (and their variegated etymologies, some forced). It could easily have been written at or near the time of Plato’s writing Timaeus.
A mysterious presence on this same astronomo-theologico-Platonic scene was a figure whose name comes down to us as ‘Amphinomus’. Another is the man who worked alongside Eudoxus and Plato, the man known in antiquity as a kind of successor to Plato, Philip of Opus. Olympiodorus, one of the good early commentators on Plato, in fact uses the very word “diadochos” (our word is “successor”), but is careful about qualifying this term. Not Plato’s successor in the unqualified way of inheriting the Academy’s leadership — that role fell to Speusippus, not to Philip.
[Some work is needed parsing the trio of names ‘Speusippus/Philippus/CtEsippus’. It is likely to be revealing if we use the ‘orthographical paraplEsion‘ technique of name-parsing — so-called in Euthydemus, Chapt. 22. This amounts to a kind of word-based factoring out the ‘-klEs’ factor, from ‘Patro-klEs’, Hera-klEs’ and ‘Iphi-klEs. In our present case it is the ‘-ippos’ suffixes that set up the homeoteleuton, or same-ending feature. This in turn make the ‘weaving together’ more plausible, the very weaving together which will soon enable the young Aristotle to weave the conclusion ‘Socrates-Mortal-(because)Human. Such a ‘symplokE twn eidwn’ is a logician’s derivative of the already established ‘figure’ of ‘symploce’. It surprised Gilbert Ryle in 1967 when I called his attention, live voice, to the OED’s having an entry ‘symploce’, seemingly derived from Ars Rhetorica handbooks already in circulation at the time of Euthydemus. It seemed that, as of that date, neither he nor Ackrill of Oxford were aware of this Oxford reference. To resume our ‘factoring out’ story now, which is a sort of regression, or pro-syllogistic movement. The figure from Homer’s list of Odyssey suitors, the one named ‘Ktes-ippus’ is a man who (1) belongs as a matter of ‘parabolE’ and ‘factoring out’ with ‘Phil-ippus’, but as a matter of epic background story, (2) belongs with his fellow suitor named Amphinomus, the named colleague of Speusippus who had defended hyperplatonism aganst the mathematician Menaechmus. Menaechmus, it will be recalled, is a man whose logician and mathematician standing was much admired by three prominent British scholars of last century, Alfred North Whitehead, Sir Thomas L. Heath and Sir Jonathan Barnes. ]
Here is the Matthew of Paris set of figures, focussing in on the alarmed Plato and ‘Socrates’ the writer (Epistle II has its riddling ‘Socrates’ managing to ‘write’ the entire corpus of Plato, Plato himself writing none of it (!)
Olympiodorus’s more qualified phrasing has it ‘the teaching of Plato’ [ ἡ τοῦ Πλάτωνος διδασκαλία ]. Rather than see Olympiodorus as putting Philip (wrongly) into the position we know to have been that of Speusippus, the present argument will both be more generous to Olympiodorus and likely not unkind to the truth, as follows.
We may have Philip in exactly the relation to Plato that Eudemus of Rhodes was soon to be in relation to Aristotle — a combination of follower, expounder, excerptor, paraphraser or interpreter of The Master. Still further varieties are possible, one of which has great plausibility, under which Olympiodorus’s qualified formula for Philip is likely to be not the least misleading — but rather simply true: Philip may have written or sketched dialogues –such as we now have in the form of Epinomis and Minos, — carrying forward the “teachings” past where Plato left off (either at the end of his Laws or in his supplementary thinking to Gorgias, or to a kind of ‘mikro-Laws’ comprising just its first 3 books). Much needs to be added here, building on the powerful work of the “early Boeckh” edition of 1806, and his exemplary labors of love. Love, clearly, of Plato and even of the almost-Plato which survives in “Minos”. This is a durable love, as witness its vigorous survival here in Massachusetts, now more than two centuries later. Boeckh’s painstaking and precise work is incidentally all the more admirable for its humility of expression. Another ‘page’ here at this website will follow down some of Boeckh’s insights into Plato, and into Philip, especially on the side explored by Boeckh, the astronomy and astronomers of Plato’s day at the Early Academy.
Philip (or Amphinomus) may have served the Academy as a kind of ‘publicist’ to the extramural world. How ? Doing the analogue to what Adam urged us to put under the then-current term of art ‘epaggelomai’, or ‘I make an announcement’. What we might call a poster of notices, of upcoming events, perhaps challenging for the outsider. These would be something resembling symposia clearly were. A publicist will have been needed to do what people helpful to Gorgias or Hippias will have done. Displaying some ‘teacherly’ guides or notices of foregatherings aimed at getting Academic insights out to the public in a digestible form. ‘Sunousiai’, they are called in Philebus. The results should be as accessible as a play of Euripides, or a recitation of some sort of a dialogue, even by a Plato or (not much later) a Dicaearchus or an Eratosthenes.
As with Eudemus, the ‘didaskalos’ might be adept at what Plutarch is to call ‘sumposiaka’, meaning making arrangements, extending invitations, giving digests and explanations of what the public may anticipate hearing. Our expression ‘for the non-specialist’ carries the idea for symposia held today at places of advanced or very-advanced learning. [Here is an example, from November 2016 a billboard in front of Harvard’s Science Center building announcing a series of talks, with question periods following, ‘for the non-specialist’. This announcement, about quantum gravity:
Traditional applications of gauge/gravity duality: We can gain new insight into strongly coupled gauge theories, e.g., [quantum?] geometric picture of confinement For the non-specialist.
An addendum, this 2016 billboard continued, by way of clarifying:
The gauge theory has enough microstates to reproduce the entropy of black holes.
and adds further:
It does not lose information. Unfortunately, this does (yet) not [= not (yet) ??] tell us how the information comes out. Still very mysterious.
Some of the intricacies of homonymy theory, or the Cratylus theory about natural names, including notably the name ‘Dionysios’, or puzzles about infinity in Parmenides, would have needed an interpreter ‘for the acousmatics, or non-technical people’. For these arcane messages to come through to the wider public, they would require work by a ‘didaskalos‘ to announce them. Extramural learners would be helped by a summary or extract, what was commonly called a ‘didaskalia‘. Quite commonly a staged play, say by Aristophanes or Euripides, sponsored by an athenian ‘choregus’ — say a member of Plato’s family — would require publicizing work. The didaskalia was what first made the whole thing public, in advance of the actual staged event. Sometimes (as Prof. J. Henderson of Boston University has clarified, especially for Aristophanes) a theater in a large city in fact had capacity for audiences of literally thousands.
Naturally, foregatherings centered about a Hippias or Protagoras or Plato will have been miniatures. Scaled down to a cast of speakers such as we encounter in Symposium, for example. It is appropriate to think of a kind of middle to interpose between a Hippias, proudly self-announcing a foregathering of learners and a rhodian Eudemus sending out extracts or summaries, to help us imagine an intra-Academy event such as a Symposium or Sunousia or lecture (as with Plato the speaker, The Good his topic). The middle person would be close to a Philip-didaskalos, at a time near the end of the Theban Hegemony. This puts him where he naturally belongs, within an Olympiad of Seventh Letter, one or two Olympiads distant from the Battle of Mantinea. His ‘ergon’ or ‘function’ will be the announcing, via semi-technical exhibits of some kind, learning leading to ‘teachings’ by The Master, Plato Himself. It is a main claim here at youngersocrates.com that we are in a position to take further steps toward de-enigmatising the Early Academy. We can consult evidences of a ‘Socrates Alter’ or ‘Amphinomus’ or ‘Philippus’ interregnum, much short of the time when Aristotle (or perhaps Aristotle and Alexander).
Scholars of some century ago now, such as RG Bury and Robin discussed Symposium especially, and made efforts to unriddle a man named ‘Philip’, referred to in its opening pages. Major efforts have gone into decoding the polemics involving the independent spirit of the young Aristotle, the awakening giant. With some patient work directed to unriddling out character ‘Younger Socrates’ and his contemporary ‘Amphinomus’, we may have come upon a man with varying nicknames and varying functions over the years there. But our Philip can point the way to some Aristotle-independent unriddlling work. Not entirely independent, of course, but partly so at least. It was Aristotle who called him ‘Socrates the Younger’ (or ‘Socrates Junior’ or — following a hint from Plato — ‘Socrates Alternate’).
One late platonist, Maximus of Tyre, relays the story that “Socrates remained silent” in response to his accusers in Athens. He even draws on a term of art from Rep IV to help him round out his picture of the silent Socrates, and replies on behalf of Socrates, that his silence was quite deliberate. Maximus has his Socrates-figure recoiling from what he calls the anger and jealousies of his ‘Epanastatic‘ contemporaries. It is quite likely that Maximus is drawing on material he knows (now largely lost, but not completely so), about a man nicknamed ‘younger Socrates’. Aristotle refers to someone by that name, in Metaphysics Zeta, and several scholars have found indicators that such a man was present at the Early Academy. Two of our best Plato mss. (T and W) give Plato’s dialogue character the variant name ‘Socrates Allos’ or ‘Socrates Alter’.
Much of this about the ‘uprising’ or ‘palace revolution’ can be connected in a text-anchored way to the term-of-art written once — and only once — by Plato: “allotriopragmosunE” [ ἀλλοτριοπραγμοσύνη Rep. 444b2 ]. This extremely rare word co-occurs in Republic in close co-ordination with the language of ‘uprising’. Disturbance and ‘straying’ are also key ideas here, again surfacing in our text of Republic. It counts as a non-innocent co-incidence that ‘uprising’ language occurs where Aristotle’s biography points. This is the so-called Vita Marciana, which speaks of ‘epanastantes‘. On this present theory these will be all be somewhat veiled references to dissidents within the Academy, living and writing nearby when Plato was very much still alive. Painfully so, in all likelihood, for Plato himself, when he was in direct contact with them. A comment on Plato’s Timaeus, preserved only in Plato’s Venice ms., may trace to the little circle of them, even to its central figure, this very Socrates. As with many academic environments, there will have been considerable differences of view. Some of these are likely to have predated Aristotle’s dissident views. Younger Socrates will not have been under any requirement that he always agree with Plato, or with Aristotle. He will not have been different from ‘Amphinomus’, or perhaps ‘KtEsippus’, in this. These two are named suitors, of the ‘Penelope and her estate’ legacy; in a metaphorical way these will be equivalent to suitors, seeking to inherit’Plato’s legacy, suing to be successors and inheritors of his writings and teachings.
One possible retrospect to the turmoil of that time near the Battle of Mantinea is the one taken in a NY Times effort to look back 150 days from early in 2017, going back just to the sudden and surprising change of regime late the previous year. Fierce factional quarrels within this political factions and in-house quarreling came forward, and one regular columnist re-invented the French notion of a ‘commune insurrectionelle‘, from the middle of the French Revolution. 2017):
“given the fears that the recent American election stoked,. . . it was possible to imagine something. . . insurrectionary …”
The Vita Marciana, reviewing the troubled times within the Academy of Aristotle’s extreme youth, wants us to be able to parse its specialist word “epanastantes” with reasonably good historical data to rely upon. Alas far more must be left to deduction and inference, if we must go back to data from near the termination of the ‘Theban Hegemony’, than just the quarter-millenium back to the commune insurrectionelle. One thing surely in common, however, was turmoil and chaos, and there were signs of various factions’s promoting rather temporary stop-gap new constitutions. Plato is soon to make up a Greek word, ‘stasiwteia’, or ‘distitution’, by way of mocking such poor ways of legitimising the dominant faction of today or yesterday. Overall, however, an insurrectioniste must be like the reciprocal of a reactioniste. In any case, we do better to guide by language and thinking from a Thucydides or a Plato, writers near the time and place of the ‘epanastasis’ itself. Thus ‘tarachE kai planE’ , ‘disturbance and unguided wandering’. In such times we are almost certain to locate one or several figures like Philip of Opus, more than a little inclined to the ‘authadEs’ extreme of conduct, and motivated at least in some part by low ambition. Better to have our ‘leader’ and ‘celebrity’ not maked under the loosely fitting mask ‘Socrates Allos’ or ‘Sokrates Alternate’, or under the still looser names borrowed from Homer’s ‘suitors’, Amphinomus or KtEsippus. Helpful if we can guide upon the name likely invented by his most able student, Aristotle. That makes him ‘SokratEs ho newteros’, or ‘Younger Socrates’. Wandering from the true course and ‘figure’ [ σχῆμα ] of Plato’s own mind. The reactionary proceeding may have been in reaction to an insurrectionary proceeding, by an author claiming to know to mount lawsuits.
On one meaning of its title there may have been extant Philip’s tract ‘On [bringing] Lawsuits’, [ περὶ γραφεῖν ]. On this hypothesis, even the turmoil itself will be in part traceable to the very same man. We have seen that the ‘silent Socrates’ — as legend has it, remaining silent at his own trial — can be unriddled with help from Symposium and its reference to a kind of courtroom litigation. To be sure, that argument called for a ‘perjudicial’ format, rather than a standard Athenian ‘judicial’ one. All the same, a man who is credited with a ‘p. graphein’ (be he Philip, or be he Younger Socrates) can have been writing about that business associated with the ‘Axwnea’ town, the town of litigants. It is not far from Athens and is mentioned in both Laches and Lysis. These are two dialogues where some of Plato’s biography (in a veiled form, of course) may be found. Unveiling some of this will make part of the unriddlings here at youngersocrates.com. The man his mother in Opus called ‘Philip’. It would be one of the deeper ironies if the ‘trial’ of Younger Socrates were from a reactioniste badly injured when Athens put his teacher to death, the plaintiff being Plato himself, the defendant being the earlier man in the formula ‘let Athens not sin twice against The Perfect Philosopher’. [the phrase ‘Perfect Philosopher’ is available from a source that has considerable material from Amphinomus and from Philip: Heiberg’s edition of Scholia in Euclidem, TLG 5022]
I will want to be investigating the concepts, Epanastasis and AllotriopragmosunE as applied in a particular way to the Early Academy. The analysis should fit with what we know of early astronomy, early geometry, early logistics and early ‘spherics’. Even early ‘logic’, if resonances of the Organon are already present inside Plato’s Euthydemus. There should be room for some ‘rebellious’ thinkers, willing to follow some of the lines of Ionian physicists like Democritus — or with others of ‘the wise’ at Plato’s time. These extramural points of view will include those about whom Plato had serious doubts, men of a rhetorical or poetical sort, or of an ‘eristic’ temperament. Also the extramural sources of Pythagorean thinking. It may be that controversies proliferated, with ‘traditionalists’ facing off against ‘modernisers’ of various sorts. These will be advancing variations on the ‘(elder) Giants battling the (newer) Gods’, the Telemachus’s countering the Suitors trying to ‘insult their way’ (philo-neikia a key conception here), insult their way to putting on the mantle of Platonism. To become Plato’s Platonist as Plato was the Elder Socrates’s Socratic.
Particularly within the ms. in Venice there seem to be traces of manners of thought (even touches of dialect) echoing non-Attic habits of speech. Such habits might incline toward dialects often grouped under the ‘Aiolic’. Some lemmas are needed, bridging gaps in the present state of the argument. Over time, some of these can be set out here at youngersocrates.com and also argued. Here is a specimen from the Clarke B ms., to document the idiosyncratic spelling (paralleled in an early Menander ms., where the ‘sunst-‘ prefix combination also manifests and Sandbach keeps it; and also paralleled in a fine ms. of Euclid housed at the Medici Library in Florence, and Heiberg keeps it. All these cases have the phonetically ‘difficilior’ reading ‘sunst-‘, very similar to the Symp. 206d ‘sunsp-‘
The ancient elementarians clearly availed themselves of this lemma-form manner of proof. In the later books of Euclid’s Elements there is an abundance of lemmas, as a matter of fact. We can document some self-consciousness about this very thing from a good ms. of Euclid’s Elements, its Scholion #21 in the Heiberg edition. That scholion includes a definition of the lemma in general. In a nearby comment to the same foundational item (i.e. Postulate 5), we find a pointer to ‘Aristocles [this is the spelling of the name reported by Heiberg, net of his emendation].
First principles and other preliminaries were argued about by ‘AristoclEs and the geometers’. We may prefer not to follow Heiberg in his emending the scholiast’s ‘AristoclEs’ to ‘AristotelEs’, — but rather venture to see in it either a politely veiled reference to Plato, or a more general pointer to ‘X and the geometers’, where the X will have included astronomers, number theorists, calendarists, mineral scientists — exact scientists of the sort we know to have been there. All writing somewhat earlier than Aristotle, reflecting on their work in his magisterial analyses in Posterior Analytics. As to date, we need only go back as far as one or two Olympiads earlier than the Battle of Mantinea. Pamela Huby dated Aristotle’s Topics plausibly, around the end of the Theban Hegemony time (Olymp. 102). Some of the proposals here are outlined in :
More work is clearly needed. We can build upon the more historically responsible components of writings by platonists of late antiquity. These will date back to the time of Libanius and earlier. Academicians of those later epochs all looked back on Plato’s own texts from a vantage point considerably advantaged over our own. Still later, there will be insightful academic work about abstract mathematics, especially axiomatics and Continuity. This has a surprisingly direct bearing on Plato’s pythagoreanising cosmology, with its specialist term ἰσαριθμός a crucial manifest at Tim. 41 d8. Wilamowitz’s comment in 1920 that wants this to be ‘zahllose’ is misleading in a major way. The work of his countryman Georg Cantor — at the end of the preceding century — can guide us forward, with help from R. Rucker, towards the final sections of Abraham Robinson’s seminal treatise “Non-Standard Analysis”, published in 1966. And the line continues, from reals to hyperreals. We might call this last the early XXI. century work on so-called “Eudoxus Reals” [their designated name in Notre Dame Jrnl of Symbolic Logic].
This is all entirely different from what A.E. Taylor a century ago wanted us to think of, Taylor seeming to base this on generically German insights. These hypotheses of Taylor’s turned out to be idiosyncratic ideas, a variety of short-lived ghosts summoned from times before the Elder Socrates. Taylor was somehow led, along with Burnet, towards ‘irrational numbers’ of his own devising, which he was over-ingenious in retrojecting back before Elder Socrates, to early Pythagoreans, forebears of Plato. Far better to look to what was, at the time of the Theban Hegemony, the near future, and to begin from the vantage point of Plato’s companion Eudoxus of Cnidus. Chapters 2-3 of Timaeus are of great help here. Further work on these two chapters can provide firmer textual basis from the time of the late Plato. Powerful recent foundations theory has been appearing in Notre Dame Journal for Symbolic Logic, Arthan et al. 2004-. More on this in a different place. If our efforts here in NorthAmerica were to be supplemented by other efforts (say from Brazil, or from Greece), we might aspire to unriddle several of these riddles. Including, incidentally, the major riddle of the “Socrates who remained silent at his trial”. Does some Oracle speak to us, — down here in Greece and the USA, — so as to cause Maximus of Tyre’s “Socrates” to come out from behind his veil ?
The gist of the proposals here is as follows. Under a name which the medieval encyclopedia SUDA converted either to ‘Philosophos’ or (confusedly) converted it to ‘Philip’, it proceeds to outline the life and works we know to be those of Philip of Opus, known to us independently to have been an astronomer at the Early Academy. A significant sampling of his writings on astronomy and calendars is extant. Material from the late calendarist John the Syrian (‘Lydus’) helps with the decipherment here.
Late ancient writers variously report that Philip composed the ‘Platonic’ work Epinomis. A.E. Taylor, in the first half of the Twentieth Century, vigorously argued that this little appendix to Plato’s LAWS was in fact written by Plato. An aging and debilitated Plato, he conceded, and one who appears to have made a few major modifications in the Plato we have in the remainder of Plato’s regular body of writings. L. Taran, by contrast, found Philip in some guise there even on the title page of Epinomis, and published his evidence (Columbia 1976).
Taran’s work has been key in turning the scholarly consensus back to essential agreement with that pre-Renaisance consensus. Philip seems (again) to be credited with having authored this little work. You will be able to confirm it with any manuscript expert that a datum from a work’s title page is always worthy of his or her close attention. In our present case, Taran’s ms. of Epinomis has a name as close to ‘Philip’ , h.e. ‘philosophos’ as to be interchanged in SUDA with the name his mother gave him directly — on its title page. The importance of this stands independently of your choice of ms. expert whom you choose to consult, whether from Athens, Amsterdam, Venice, Milan, Florence or Genoa (were he still alive, this list would include Einarson’s Chicago, with Einarson’s unhappily unpublished commentary on Epinomis.)
Philip seems to have been ambitious enough to claim for his little piece the status of an almost-Plato template for the famous Nocturnal Council at the end of LAWS. Or he may have been ambitious enough to write a disguised model of an almost-Plato edition of the work left in promise form only by Plato, the missing dialogue “The Philosopher”.
We may be able to identify two seemingly distinct individuals (1) Younger Socrates and (2) Philip of Opus. Evening and Morning Stars, given distinct names, were known to Philip to be just the one body in the heavens, the one we customarily call Venus. Both Socrates and Philip were very close to Plato. If the Academy included a newer Socrates, the likeliest hypothesis is that Philip and this newer Socrates are one and the same blood-and-bone man.
Investigating this set of philosophers and scientists will ideally improve our understanding another associate at that time and place, Dicaearchus. The link would be via then-current work in the mathematics of ‘doubling the cube’. This problem, with its special pointers to the Hellespont, will be of some help in demystifying some of the ancient reporting.
Leonard Brandwood, in his 1975 work “Word Index to Plato” sorted out some of the special lexical features which are observable notably within Venetus T. Key cases may rightly be described as lexical variants of an ‘Iota-added’ form. These are prominent especially in dialogues in Plato’s late-middle period, though Brandwood’s compilations of them remain incomplete. This late-middle period is the time of his writing Parmenides, Symposium, Phaedrus, Euthydemus, Sophist and Politicus.
Leon Robin did detailed textual work on some parts of this matter, especially in Symposium and Phaedrus, but the more recent Bude editors have eliminated Robin’s results from their apparatus, unhappily. This forces us back to as direct inspection of the Venetus ms. as is permitted by its curators in Venice. With the images now available here, — their Stephanus pagination markers inserted — a close reader or editor can confirm the readings Brandwood asked to be confirmed (his Word Index to Plato, 1975), less travel and fewer hurdles for him or her to surmount.
Here is a specimen from Venetus T to illustrate the way Robin’s work and Brandwood’s supplements to it might be extended. Consider the Robin non-Attic 4-letter spelling of αἰεὶ. Robin reported literally scores of them in the texts of Symp and Phdr. Try clicking on this active link, to get a direct look at a 4-letter variant spelling (4 of the total 4 ‘openings’ in Alcibiades are filled with this ‘Robin’ non-OCT form, as are 30 of the 30 openings in Symp). This glimpse gives you a direct look at nr. 34 of the continuous series, starting from beginning of Symp and running to end of Alcibiades I. To put the matter somewhat rhetorically, let us ask ourselves this: “Can this high-quality ms. by a 10th century scribe have committed a series of 34 consecutive “misspellings” of one of Plato’s favorite words, not once getting it ‘right’ according to the OCT orthodoxy in this pair of dialogues ?” We might set up a crude analogue: Think of a series of 34 tosses of a coin, with ‘Iota Added’ on one side of the coin, ‘Iota Missing’ on the obverse. How likely would it be that (without some special underlying cause being at work) that ALL THIRTH-FOUR would come up “Iota Added” ?
If we deploy an admittedly simplified statistical measure, using 2^34 as our formula, we would get odds against this, over a billion to one. Then what can be the missing causal explanation ? Dialectal preference ? Old Attic ? Aiolic ? Theban ? Heraclean ? In any case, worth investigating. And if Euthydemus is either everywhere, — or even locally — in line with this, can there be a common force at work, causing this ? I believe there was a cause, connected to Epizephyrian Locrus. Can new things turn up about Plato’s chronology as a result ? I think so, especially if this evidence is added to that from Euthydemus, and the pointers there to the “dialectic”. It was a major puzzle to Ryle, for example, who found it barely comprehensible that something so central to Plato as Dialectic, would somehow recede into an occult former-presence at the Early Academy. This puzzle provoked Ryle to publish detailed research and intricately developed articles a generation ago now. All of this requires considerable extra work, much of it centered on Socrates Alternate, or Younger Socrates. The present website, intending to center on Younger Socrates, will start out from the jump-up phenomenon within Plato’s own orthography, the sudden strong profusion of the 4-letter variant AIEI conveyed largely via Venetus T. Here is a specimen:
Here is a specimen from the hand of Ephraim, his text of Euthydemus, where the a priori probability of innocent randomness is likely to be less than 1%, on a priori grounds — each occurrence assumed to be 50% likely, between the Iota-added and the one other choice. (This takes Chapt 22 as a unit, running as it does 294B – 296D):
please click on this red-lettered link to have a close look at Euthydemus, Ephraim’s handwritten text, with highlights on the AIEI variants there:
It may prove right to include Timaeus in this same time period, though not without an accompanying argument. According to E.R. Dodds, Plato will also have been doing revisions to his Gorgias. In any case Plato was likely doing fresh editing for select books of Republic, especially its middle books IV-VII, most especially the final chapters of Book IV. Even while Venetus T gives no direct ms. evidence here, its guidance within Tetralogy VIII is of great value for various reasons. One quite singular reason has to do with its text of Timaeus, where a striking reading turns up at 53 b7, and also a scholion likely to stem from the Academy when Plato was still alive, — at 42b2.
[An analogy of a geographical type might call this a ‘tropical zone’ within Timaeus, centered on an Equator and guided by that famous Platonic “Χ ” at 36 b8. On the geography side we might almost say Brasil. When men like Eudoxus and Calippus and Philip wanted to anticipate the more precise astronomy research by Hipparchus and Eratosthenes — they struggled with such questions as “we propose to ourselves to show the inscribing of the 15-sided regular polygon into a circle”. In Euclid’s book of lemmas, namely Book IV of the Elements we now see a kind of outlier proposition, a kind of appendix. It is IV, 16, constructing the regular 15-sided polygon. It is never applied by Euclid. But this does not prevent us from seeing it prefigured in geometrical constructions first created at the Early Academy very near Plato. Likely by his colleague and amanuensis, the astronomer Philip.
There will turn out to be valuable extra indicators, some internal to Venetus T, of new information about various ‘awakening sciences’. Sleeping giants, one might call them after factoring in the sublime contributions soon to come up over the horizon in Aristotle’s time, the writings of Apollonius of Perga, Euclid of Alexandria and Archimedes of Syracuse. Such giants will have been awakened, aroused by Plato only slightly before Aristotle came of age. Some of these indicators point to early efforts in mineral science.
Within the proto-sciences such as those later to mature in Theophrastus’s “On Stones”. Plato may be condescendingly referring to such with his coinage ‘technudria’ [τεχνύδρια , Rep. 475e]. One provocative list of early authors (either early, we must concede, or possibly early) includes the pair of names ‘Dionysius and Socrates’.
If the ‘Socrates’ author there matches either the ‘Socrates basileus’ of our medieval tract ‘Prognostica’, or the author of Epinomis, he may have advocated religious beliefs and even practices, often linked to gem-cutting and to theurgy in antiquity. Sun-worship is clearly advocated, seemingly by Plato himself, there in Epinomis, but more surely in some of these early alchemy texts. Here are some scholarly pointers to further evidence about early mineral science and the Academy:
A man contemporary with the late Plato gave one of his treatises the enigmatic title ‘kukliaka’. Scholars have had difficulty finding parallels for it, at least in scientific contexts. The man was Philip of Opus, and he probably coined his specialist term somewhere near Olympiad 104, and at the Academy. It named his treatise (‘on matters relating to The Circle’). As a close student and follower of Plato’s, we may be finding him “publishing” this work near in time to Plato’s Seventh Letter, either provoking some of Plato’s reflections there, or being provoked by Plato.
Quite as likely, Plato’s reflections on the topic of circles, whether before or after Philip’s, will have had their scientific impact at the time. Eudoxus wrote on them also, in the early sections of our present Book 13 of The Elements. And Books 3, 4 and 13 of what now appear in Euclid’s Elements are likely to have been topics of serious work there and then. Aristotle will have been rather young at the time, but old enough to be writing Topics and Posterior Analytics, and to be working out many of his thoughts on Pleasure, on Anger, on Friendship, on Rhetoric and on Proving.
Many other titles of interest on SUDA’s list seem to be at home at the Academy of Plato’s later years. Three of these are “On Anger” , “On Pleasure” and “On Writing, or Proving”, (or, as will get further analysis here, its meaning can as well be “On Bringing a Lawsuit” :(‘graphein’ was a classic case in Attic prose of the Academic topic of homonymy or paronymy). As to its adjectival ending, Philip’s word is not far from ‘lithiaka’, an attested variant of the more common word whose second syllable is monophthontal: ‘lithika’. There are several pointers to material underpinning this analysis of ‘graphein’ as ‘formulating a lawsuit’. One goes via the text’s specialist reference to the ‘true muse’ at 548b.
You may want to click on some further thoughts, offered here: Lemmas in need of Proofs here at youngersocrates.com, 2017
Good scholars have made the claim that, Yes, there truly are ‘Book’ divisions traceable to antiquity — perhaps even good ‘Chapter’ divisions — for that major work. Keeping them in view will sometimes help make clearer the lexical comparisons, comparisons called for across works. Such demarcations also help with analysis of a given work of Plato’s. Still more they are helpful in close analyses of Plato’s own lexicon, comparing this to the writing of his close companions. Three specific examples: Republic I, Chapt 7 (with Adam’s analysis), Gorgias Chapt 5 (with Dodds’s analysis), Symp. Chapt. 19 (with Dover’s analysis), Rep. IV, Chapt. 18 and Phdr. Chapt. 64.
Can some of the so-called ‘Chapters’ within Plato’s works actually trace back to Plato’s own authorial intention ? I answer, Yes.
It will be fitting to pause here to deal with the delicate subject of “chapter divisions” and the scholarly uneasiness about these and other divisions within our texts. The recently published (2013) non-Shorey edition of the Loeb Republic lands in an extreme (and in my judgment untenable) view of such matters. It is illustrative of the extreme of over-caution and routine skepticism against which W. Burkert warned his fellow philologists. Here is their routinised hyperskeptical statement . You be the judge:
“The division of Republic into ‘books’ was almost certainly [italics mine] not made by Plato himself, but at some later date in the history of transmission.” [vol. I, p. ix, fn. 5].
It ought not be left as mere dogmatic assertion on my part to issue (as I do) my wholehearted rejection of this statement by the neo-Loeb editors. Rather, consider this argument:
- some evidence taken directly from our Venetus T, its fol. 235r :
FINAL 10 LINES OF REP. BK VI (VENETUS T)
please click on this link:
This segments off the final lines of the Book, indicating some form of very early emendation — at least consistent with the project of causing chapter articulations. Articulations, that is, by Plato or by some mathematician (Amphinomus?) or by both. Perhaps the two of them were co-seeding the text, to borrow from the technical term in Symp. 206d [ συ[ν]σπειρεται , as it reads in a combination of the Clarke ms. and the Oxy. papyrus ]. An image of the Clarke ms. of 206d is accessible in the link above, for you to look at directly. It is has the disadvantage of being an editorial crux. Or perhaps, as with the Slings emendation of Rep 511d, the textual variety is more of an advantage than a disadvantage. JL Heiberg used to write from a fascination (his own) of the ‘viel sprachliche Anstoesse’ within his text of Euclid — some of which provoked him to emend, to the advantage of Plato’s mathematical friend young Theaetetus in the case of Book X of Euclid, especially its Chapter 4. Yes, Euclid X has chapter divisions. The scholiasts to Euclid tell us so, — and Heiberg, praises be, held onto them for Teubner, and respected their opinion.
2. A reinforcing argument can be drawn from the series of “entitling” markers placed before each of the three final chapters in Republic Book IV. It is no harm to the text’s word ‘teleutaion’ [ τελευταῖον] at Rep IV’s 443 b7 that it has textual variants; on the contrary, this special marker-word [variant ‘teleon’ τέλεον] amounts to a ‘rule-probing exception’. For Book IV’s Chapters xviii and xix have definite markers also [recognized in all 3 of the agreeing editorial work of the Dies-Paris, the Adam-Cambridge, and Shorey-Harvard editions]: the distinctive sequence of three markers set off (a) prope-prope-final (b) prope-final segments, and then segment off (c) the left-over topic of injustice, treated off-handedly, as a brief afterthought.
Each of these last-named units of Plato’s prose has a strong textual marker pointing to an authorial intent to mark off a chapter unit. Chapter 17 had begun with the word ‘teleutaion’ [ τελευταῖον ] at 443 b7. Chapter 18 begins with the emphatic transition phrase ‘estw dE’, ‘further let there be…’ [ Ἔστω δή ] of 444 a10. We might, however, think of this objection: why in a 19 chapter book are there phrases pointing to ‘final’ or ‘ultimate’ segments ?’ Why do such phrases occur before the thought sequence has in fact come to finality ? This would suggest an ongoing set of revisions, or stages of Plato’s writing. But there is a good answer to these objections. Diogenes of Halicarnassus relays the report that, as the end of his writing career ended, he was found continually ‘combing and curling’ drafts of his works, down to minute changes such as ‘yesterday I went down/I went down yesterday). This means that a ‘postscript’ (Ch. 18) is not forbidden to have in its turn a post-postscript (Ch 19, postscripted to the already postscripted Ch 18). At 444 e6 Ch 19 begins with “to dE loipon” ‘on the other hand what is (still) left over’ [ τὸ δὴ λοίπον ] . This comes directly after Ch. 18, the one set off clearly by the ‘further let there be…’ phrasing. A rhetorical question to be posed now: Which of us has left our previously written prose entirely unaltered, entirely free from ‘combing and curling’ ?
(Schneider’s edition does not use any variant of our word ‘book’, but rather entitles each of the work’s major divisions as a “Logos”. Authorial divisions stand behind much of the textual work of our powerful continental editors of the past two centuries and more. Stallbaum’s note fairly rings out, at his 1859 text of Republic, its Book VII, the opening two words of its Ch. 10: “statim post Τί δαί … “. He was refusing to remove from his text a special dialectal utterance by Socrates, which led up to the significant words … τρίτον θῶμεν ἀστρονομίαν . This refusal in the face of the deeply authoritative Schneider. All of this special emphasis tends to go lost if one puts overmuch trust in the Oxonian viewpoint — so at least say I. [Similar critical words were written, but with much more fiery rhetoric, both by Slings in his 1998 review for Mnemosyne and by ER Dodds in the introductory materials to his 1959 edition of Gorgias, in relation to the OCT mode of editing Plato. ]
If I have decoded rightly Gaiser’s ‘Philosophenmosaik bei Neapel’, there will be no anomaly in thinking of both Plato and Aristotle as direct witnesses to some of Philip’s presumption and presumptuous writing. Even his offering to tamper with Plato’s text of 511d2 and to leave small markers of Locrian style such as Τί δαί or Τί δαί δὴ either here at VII,10 or in each of 3 chapters in a close sequence (all relayed by Ephraim in his early books of Republic, its II, 19, II, 21 and III, 1. More on this other set of markers — also seeming to indicate dialectical variants, in this case of the Dorian-Locrian variety). Much more needs to be explored here, some with help from some anticipated work in collaboration with the Perseus Digital Humanities and the Open Philology project at Tufts (and at Leipzig, spring of 2016).
Yes, some of these Continental ways of editing, now and then found to resonate within souls from Ireland such as Dodds and MacKenna — and even Derry Man R.G. Bury — may find some new ‘Entwicklung’ here in the Somerville-Cambridge region of Eastern Massachusetts. But perhaps only ‘Socrates basileus_prognosticus’ who had True Opinions about the Gods and a neo_Euthyphronian aspect to his Theology and Dialectic (both Bury brothers seem to have been protestant Irishmen ? Did R.G.’s brother know a good bit about the philological side of Xenophon or Thucydides ? If so, he will have known, even prior to the newer electronic searching results revealing the AIEI prevalances within Euthydemus and Symposium, (the first having only some 28 Steph page-references, whilst the second has over 51) This would be especially striking if Plato were in the presence of the astronomer, Philip perhaps with a draft of either his Epinomis, his P. Thewn or his “Little Timaeus, the Locrian version“. Stallbaum’s work, putting special stress on the initial words of Ch. 10 to Bk VII (h.e. 527 d1) — this work was well worth close attention when he did the work (in the 19th century). It was worth all the notice it got in the 20th also. And even if it were to get more fully noticed in the 21st, this would not over-do its importance. Had Schleiermacher in the 18th Cent. been led onto Stallbaum’s work of the 1850s, he too would have lent his authority to Stallbaum’s claims. So I judge it, here at youngersocrates.com, before the end of the first quarter of Century 21.
To resume. Such arrogant behavior would have amounted to something like a “slave-revolt”, or an irritating or satirisable insurrection, its leader being rightly named — a stasiarch (leader of insurgents). This disorderly interlude at the Early Academy after the third Sicilian travels of Plato can rightly also be named by Plato’s specially coined and ironically witty word ‘StasiOteia‘ [= Στασιωτεία ]. He coined it in his LAWS, a work thought to be co-written by Philip of Opus. A.E. Taylor interprets this word with his own fabrication “no-constitution”, an apt interpretation. Top people who head up factions in epoch’s of intense civil unrest are winners in the Race to the Bottom, Leaders and Followers suffering this form of ‘perturbation’. This will mean that this temporarily-coronated King (cartoon image supplied below) risks a satirico-comical treatment. F.M. Cornford’s ‘Microcosmographica Academica’ had its 17th century prototype behind it. This present picture suggests it may also have faintly forewarning indicators in antiquity. The scene will have been set approximately in the 104th Olympiad when Aristotle had yet to produce any of his major work, but was present and active, active and writing. Some of the enigmatic features of that Early Academy may find partial unriddling here.
Our Venice ms. T includes strong signals about this ‘Battle of Mantinea’ period of Plato’s writing. This point has already come forward, from evidence echoed here. A cluster of further examples is embedded in the Venetus T text of Euthydemus. This material has not yet been subjected to detailed analysis.
A fuller apparatus incorporating electronic enhancements might come about, thus making it unnecessary for a modification of a Perseus-Annenberg electronic text of Bury’s 1909-Symposium to be put up onto the Internet. Given such ideal conditions, such an enhanced-Bury might not have great value. But better preservation of Robin’s careful work is a reasonable plan. Scholars in various parts of the world may be stimulated to do further work. Some readers from Italy, Greece, Canada and the USA have shown interest in the early months of 2017, by paying visits to the site.
The needed ‘Middles’ for this reconstructive work are many. But they are not so many as to discourage further patient steps forward.
1 June 2017, rewriting of the ‘Hermo-‘ ‘Apollo-‘ kratEs point, with its connection to the Venetus T ms., its angry scholion at folium 259r —
This name ‘Hermocrates’ is mis-echoed, in the Oxford Press edition of Campbell’s Republic, Vol II, its ‘Excursus’ on the style of the late dialogues, [ his Rep. Vol II, p. 59 ]. Campbell’s Oxford volume of 1894 manifests ‘Herm-ogenes’, and the various reprintings of t his book since then have left this erroneous name (paradoxically enough ) precisely place, misprinted. [Co-incidentally enough, we can find a sort of parallel error in a Teubner Verlag printing of Xenophon’s Memorabilia I, 2, 48. Please note it carefully, that Teubner in 1886 , as if to interchange a disciple of the Socrates1 for a disciple of Socrates2, makes the exact same mis-substitution: it puts in the -ogenes man a disciple of Socrates1 ( Thebes) for the -ocrates man, associate of Socrates2 (the King, Socrates-Alternate as he is variously known within Ephraim’s text)].
In the 15th century ms. after which this site intends to produce a manual reproduction (or copy) , Diogenes sits in his tub poring over a book seeming to contain standard cynic’s fare. This would include comic plays, letters, satires and diatribes. Specimens of such writings survive from antiquity. All of this could furnish material suitable to be copied into the margins of (say) a IV cent. B.C. ms. behind Venetus T. Or copied directly into the margins of a mathematics text, such as we now have extant in Euclid. If so, we would have a plausible channel of transmission for the marginalium on folium 259r of Venetus T, with its stinging satire on Plato’s word-play with the root word “KRATHS/KRATEIN”. Such word-plays do in fact occur, at Tim. 42 b1. ‘Such-and-such -o-crates’ or ‘crates-a-so-and-so’ we might encode this line in Timaeus.
We may allow ourselves to borrow from Aristotle’s etymological dissecting of the proper and common names ‘Phil-ippos’ and ‘philo-theamwn’ at EN 1099. We will thus be choosing to bypass the detailed name-dissections in Chapt 22 of Euthydemus . In the Aristotle word-surgery of exactly this pattern occurs, and affects the whole word’s suffix, sometimes affecting proper names. Philo-toiouto or ”fondness-for-X’. Aristotle allows the instance of the proper name ‘Philippos’, or horse-fondness. In our Timaeus example we must vary the prefix. ‘toiouto-Krates’. Bywater’s Oxford text unhappily omits part of this word-play in Aristotle, blocking the reader from seeing the good ms. variant ‘philo-theamwn’ [ φιλο-θεαμῶν ], a word of great interest to the philologically-minded critic of Republic V.
Of all the efforts here to follow this path of ‘name dissection’ that which stitches together the ‘Poly-‘ and the ‘-ainein’ is the remotest from what the sober W. Burkert called (with faint praise) philological ‘Vorsicht’. No one is likely to doubt that some close reading of Rep. 389e has been carried out before the opinion was reached (as here) that S. Slings erred in ommitting any note on the Schneider-form ‘ti dai’ at e12, where it will have made a significant difference to the 1850s Stallbaum-Schneider philological polemic over ‘dai’ in Repubic. Family II’s mss. appear to go in the Schneider direction (and both Burnet and Slings print this), but Paris A is a remarkably heavy authority, often allowed to outweigh the others, going favourably to Stallbaum’s position. All the same, and given that it is closely guided by authentic text in LAWS XII, it is not uncarefully un-cautious to re-assemble the name Poly-aenus. And quite likely it has the greatest reward ( ‘kerdos’ or ‘profit’) resulting, if right. It re-opens a door on a very early Epicurean mathematician and physicist — which is a door to to a pre-euclidean writer on ‘aporiai’ and ‘horoi’ and possibly ‘paregklisis‘ .
It points to yet another doorway: between able mathematicians NOT in the direct line of work culminating in the “Five Regular Solids, but by non-Academy writers, parallel to Philip, who had publishable opinions on science, geometry, knowledge and that special knowledge-blockage which is the Aporia. We have seen that Proclus’s early sources, explicitly including Philip [however he may have been known — Amphinomus, perhaps, Socrates perhaps, Polyaenus’s recoiling from geometry altogether (as “false”) is just an extreme reaction to perceived controversial matters, such as keeping ‘theorems’ separate from ‘problems’ — and (compromising now) providing room between these two for ‘porisms’. It is no mere accident of language which gives room for a ‘porismatising’ activity standing between ‘proving a theorem’ and ‘falling into Aporia’. The Horn-angle paradoxes in the extreme cases are here shown compatible with either of two extreme reactions:
(a) Theaetetus’s writing of Books X and XIII, especially its ‘bridge proposition’ XIII, 11, — or the
(b) sheer abandonment of geometry (as hopelessly entangled in paradoxes and aporiai): this has a place in Polyaenus’s aporiai and (sometimes enigmatic) definitions.
Plato’s immediate successors will sometmes bring on his disapproval — witness the disapproval targeted on Helicon of Cyzicus for ‘injuring the essence of mathematics’ by reference to movements and human actions. Or Plato can in some manner ‘immortalise’ a fellow academician such as Menaechmus or Eudoxus or Theaetetus, who developed mathematical content of worldhistoric significance [DeMorgan, A. Robinson and A.N. Whitehead — three modern immortals — have in different ways borne witness to this ‘earned’ immortality amongst Plato and his colleagues at the Early Academy.
It is open to us to supply a clarifying hypothesis about Theaetetus’s comprehending Five (and only Five — as he proves, this the finite limit in the familiar space of Plato’s Timaeus.) Plato at 55A is discussing the ‘obtuseness’ of his series of Five, and clearly anticipating a maximum, namely 4 right angles, which fix the ultimate limit — no solid angle is permitted to equal this obtuseness, that of the plane itself. Our text (55A1) speaks of the “next” in order of obtuseness. But this may involve a continuity-hypothesis incoherence. Was this not precisely the incoherence which left A.E. Taylor in an unresolved perplexity ? The language of the text has a continuity paradox built into iteslf. Consider its wording with this hypothesis in mind: τρίγωνα δὲ ἰσοπλευρα συνιστάμενα, … τῆς ἀμβλυτότης τῶν ἐπιπέδων γωνιῶν… [γωνία] τῆς ἀμβλυτότης τῶν ἐπιπέδων γωνιῶν ἐφεξῆς .
When these words write of Plato’s set of regular ideal triangles, squares or pentagons (3 or 4 or 5 of these, as the case may be), he affects to believe there is a “next” in obtuseness, short of 4 Right Angles. Truth to tell, it might require a super-geometer to resolve this paradox. Nothing has this ideal completeness “next” to itself, unless we could paradoxically conceive of an “infinitesimally less obtuse” solid angle the ideal plane’s completeness of 4 right angles. Can there have been any such paradoxical ‘next lower’ (in obtuseness) than the ideal of 4 right angles — at the Academy.
Yes there can have been, and a question posed by Amphinomus in exactly this context leads us to associate with an immediate colleague of Plato’s. Amphinomus challenged Aristotle’s strict classifications of ‘mathematician’ and ‘dialectician’, where only the latter “ASKS AND SEEKS TO ANSWER THE QUESTION WHY?” Amphinomus is reported by Proclus to have exhibited (ekthetically, we might put it) an example “Why?” question — “Why internal to the circumference can I as geometer inscribe infinitely many entirely ‘regular polygon’ figures — but I am prohibited from inscribing infinitely many solid figures internal to the circumference of the sphere?” It seems that Amphinomus, colleague of Speusippus, put this challenge to their contemporary Aristotle: ‘ You have no good reason to tell me that I, who do in fact seek an answer to this question — am thereby forfeiting my status as “geometer” and arrogating to myself your title “dialectician” ! This from a man personally ambitious to qualify himself as the very highest of intellects (higher, perhaps, even than the author of DeCaelo, this in completition with DeMundo). If a 4-right angle plane is the ultimate in planar ideality, then the form whose stereometric form fell only infinitesimally short would leave no room for a rival nearer the Ideal than himself — but all the while claiming to put his penetrating question “as a geometer”, or “as a mathematician”. Sufficient in his ideality without having to submit to Aristotle’s uncompelling distinction between mathematician and the “next” or “efexEs”. This picture of Amphinomus debating a young Aristotle has a plausibility a human sort.
We may hypothesise a definite meaning behind Plato’s puzzling word “ephexEs” at 50e3. We may borrow a specialist term not remote from Plato’s word ‘parenphainon’ [50e3-4] and call their conceivings of ‘infinitesimals’ as somehow ‘weighted’ — thus the ‘next’ after the most oblique solid-angle being — not the 4-rt-angle plane Herself. Rather that plane after a deduction, sc. after taking away a set of 4 infinitesimal ‘paregkliseis‘ ! I ask it of the ghost of A. Robinson that he put a tentative seal of approval on these pseudo-Polyaenus ‘logically lessened’ right angles, constituting the ‘inappreciably less than right’ angles limiting the obtusest of solid angles. More work is surely needed here, to include an effort to connect to the mathematics of ‘rigidity’, with its allowance for infinitesimality. Also ARobinson or RGoldblatt (Hyperreal Numbers, hyperreal ‘topology’).
In the final book of LAWS, with either an elderly Plato or Philip of Opus executing the forced word-play, Philip’s Epinomis is to begin just a few chapters later in this same composition. There, in XII,6 we have multiple pointers to figurativeness of language and interest in the etymology of the name or epithet ‘Poly-ainos’, as above analysed.
M. Brown, 24 Feb 2018: ‘foreign emissaries’ as in LAWS XII,6 have been newly commissioned, to report back to the Nocturnal Council — some of their Overseas Missions may be imagined by those familiar with technical writing and controversies commonly found amongst those writing contemporaneously and freely.