Lemmas in need of Proofs here at youngersocrates.com, 2017


The primary intention of this website is to give fuller access to a good ms. of Plato’s writings.   This is the so-called Marciana, curated at the plaza San Marco national library in Venice.  As a second aim, it will draw some support from this evidence and from elsewhere to build a fuller picture of the somewhat puzzling linkages among  Plato, Aristotle and the disciple-teacher whose dates roughly coincide with those of Eudoxus.  This was Philip of Opus, who seems to have adopted one or two alternate nicknames during his career there.   Other colleagues, such as Menaechmus, Amphinomus, Calippus and Eudoxus can also be brought into clearer focus.   All four of these men (or all three, if “Amphinomus” and “Calippus” turn out to be the same author under two different names) 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 today drawing attention from number-theory experts, such as those of the very recent research efforts in  “Toward the Eudoxus Real Numbers” (R.D. Arthan, 2004).

This very high rating of Eudoxus can already be gathered from A. De Morgan’s magisterial analysis of Elements Book V in the late 19th century,and also from the final pages of A. Robinson’s ‘Non-Standard Analysis’ (1966)).  This website will also try to stimulate more detailed analysis of the ‘orphaned’ work, now preserved only in the Bologna ms. of Elements, an alternate version of Book XII.  This little work (book XIIA) consists of analog-Eudoxan “exhaustions”, of circles, cones and cylinders.   Heiberg has preserved it as an appendix in Vol IV of his critical text of 1888.   It is likely that we are seeing here in this orphaned text Philip’s editing of Eudoxus’s Book XII.  Part of the confirmation is to be found in Plato’s paraphrasing material in which both of the two near-Eudoxus versions overlap.  Plato’s paraphrase, which mirrors Book XII more exactly than XIIAlt, occurs at Soph 264e.

This paraphrase occurs at Sophist 264e, and is an almost exact replica of the ‘continued process’ step of the geometry of divisions.  On Plato’s side, the divisions are those of the so-called Later Dialectic, and the material under subdivision is philosophical conceptions.   We may suitably name this little orphan work ‘XIIA’ and the standard (Vatican Gr. 190) edition of Elements “XII”.  W. Knorr had a high opinion of XIIA, and of the Bologna ms. generally.

Let us carry out a thought experiment, as follows.  Suppose now that the chancy crosscurrents surrounding the ms. transmissions of Euclid’s works — especially the texts of of XII and XIIA — had caused us to lose all good copies of XII itself.   This orphan work would then be a good source from which to re-construct the ‘missing’ Book XII.    We would be given a major assist in our re-construction work by Plato’s paraphrasing its characteristic ‘Dichotomous Exhaustion’ step, at Sophist 264e.  A major asssist here would be the marginal comment relayed by Heiberg at his Vol V, p. 109.  Heiberg assigns this scholion the number 3.   It includes remarks on alternate ways of defining The Right Angle   This scholion brings in the specialist word ‘dichotomEma’ [ διχοτόμημα ], and what is being ‘dichotomised’ is a straight line.   LSJ does not find many examples of this specialist word.   Nor the philological experts of Genoa.

This same Scholion deserves detailed analysis.   It makes use of a key term which is also to turn up in Epicurus’s fragments.   Epicurus may  have borrowed from it from an earlier atomist, such as Eudoxus’s predecessor, often coupled with Eudoxus, namely Democritus:   ‘parenklisis’ [παρέγκλισις] an inclining line or trajectory ‘leaning toward’ its reference figure, from the inside .   It is uncertain what the various uses of this specialist term were at and after the late-4th century time of Epicurus and Euclid.   Epicurus was then writing atomistic physics, and was certainly in the tradition of Democritus and Leucippus.   He was also laying the groundwork for the famous ‘swerve’ or ‘clinamen’ of Lucretius.  This technical term in Lucretius’s atomistic physics has as its precise ancestor, surviving in Usener’s edition in the atomistic term   παρέγκλισις.   

The Harvard book of 2011, on Lucretius, Goldblatt’s book entitled “The Swerve” remains nearly silent on these earlier traces of Greek ancestor terms.   But such ancestor terms are seem to be there to be found, in Euclid’s margins.   In our text –likely coming down  from a source at Epicurus’ time or earlier, perhaps the time of Democritus or Leucippus, we find such terms — were perhaps inherited from work of Democritus.   Democritus is often cited alongside Eudoxus in pre-Euclid works, such as those of Aristotle. )   David Sedley might have arguments at the ready, either to help with the proof of this Lemma, or to discourage our looking back so far as Epicurus and his Greek atomistic predecessors, to cast a different light on it.   So might F. Ademollo, who will be well versed in the recent ( 1991 ) Italian research on a key middle person, ‘Polyaeno’, teacher of Epicurus.   Scholion 3 shows some signs of early authorship, perhaps going back to the time of the mathematician Polyaeno, whose fragments make provocative references to indivisibles, both of ‘platos’  (flat) and of ‘baros’ (in depth).   The recent Italian edition of these fragments  (1991) could be helpful in boosting our efforts to trace out the earlier history — in geometry and in physics and philosophy — of  this central concept of  παρέγκλισις.



The add-on book at the end of Plato’s LAWS is named from its position as an add-on, “Epinomis”.  In antiquity it was reported to have been written by Plato’s student, Philip of Opus.  It was the part of the platonic corpus on which B. Einarson was doing a commentary when he died in the late 1970s.   We can reasonably hope that one of his students and followers, — say Wm M. Calder III — might publish portions or all of Einarson’s non-completed work. If so, the very great powers of Einarson’s writing would likely result in more light than we today get from parallel writings, even those nearer completeness.  Here you will see an excerpt from its final chapter, from folio 299r of our best ms., the Paris A:

(bis5) semi-Aeolic AIEI in final chapt. of Epinomis, at 992c1 length=3.5, rev6



Lemma One here will be to show Philip’s original authorship of the orphaned version of Book XII — the pseudo-Eudoxan version, we may call it, following out the suggestions of a scholion on Euclid.   The orphaned edition has various revealing textual signals of its origins inside the Early Academy.  It is a near-repeat of the regular Eudoxus versions of the so-called exhaustion arguments admired by Archimedes — doing what today might be called “definite integral” forms of measuring circle, cone and sphere.   In the manner of an editorially modifying writer, working to cover up his way of removing Eudoxus’s locution ‘kai touto aiei poiountes’, he leaves just a single theorem of the total 5 ‘integrations’ positively including the offensive locution — relayed in exactly the Eudoxan wording !

Lemma Two will be to show that if we follow down the precise formulations of Plato’s dichotomous ‘divisions’ at Sophist 264e we can locate buildingblocks for a reconstruction of the lost ancestors  [Theaetetan] to Euclid X, 1-3 and also to the lost ancestors  [Eudoxan] to Euclid XII, 1-5.   The rebuilding is to be closely guided by Volume V of the Teubner Euclid — J.L. Heiberg’s magisterial collection of the work’s marginalia, which has now been entered into computer-searchable form as  ‘Scholia in Euclidem’, or TLG5022.  One piece of the history of these dichotomies (h.e. pre-Euclid Academic history) is the occurrence of two specialist terms going back to the time of Epicurus or earlier:  ‘dichotomisms’ and ‘swerving’.  Much is to be found in Aristotle’s texts about ‘dichotomy’ and the provocations from Zeno of Elea — but I think you will not find this “-ema” ending, nor the special way a ‘non-parenklitic’ dichotomEma has fastened itself into Euclid’s Elements at a foundational level.  We have Parenklisis-free serving to form the definitional level of analysis of Right Angle.   It is not remote from an idea of a practical craftsman who has just finished sectioning off a DichotomEma from a line he has taken pains to make entirely straight.  He need only be sure to explicitly rule out any ‘leaning’ or ‘alongside-leaning, and he has got to the elemental foundation of Rightness.   It is of foundational (definitional) importance that we to keep vigilant against any residual suggestion of mechanical efforts by the craftsman — a great harm if Plato’s warnings about excluding any suggestion of the mechanical or time-bound.   Precisely here we have the crux of the issue pressed hard by Philip, vigilant in preserving the ‘pure timeless, matter-free’ status of geometry as pure mathematics.   Philip’s warnings are echoed by Proclus , and in Epinomis Chapt1, where the shudder of alarm against ‘the very epithet produced‘ rings out.    This is the familiar alarm, here being echoed by Philip is echoing from Republic VII.   He may be the overzealous disciple, neglecting the qualifier Plato’s canonical passage included “unless necessary”.    Thus the alarm sounded on Plato’s behalf by his disciple Philip includes what a disciple’s second-hand relay of the teacher’s pure (even purist) doctrine seems to him to mandate.   We must double the cube, or lay our foundation for Rightness all the while rigorously abstaining from any ‘descent into gross matter’ or any ‘constructiveness’ in the otherwise entirely Platonic course of thought.

[ 26.iv.17, 09.x.18 — Excursus on the pair of specialist terms διχοτόμημα   (dichotomEma) and  παρέγκλισις   (swerve).  The latter term, due to be used repeatedly by Epicurus, as in his frags. 280, 281 (Usener), qualifies as a PAWAG [= acronym for PoorlyAttestedWordinAncientGreek, this designation due to lexicographers in northern Italy] in early Greek thought.   Its outcropping here might be a by-product of its having lain dormant within a ‘protected’ foundations_of_geometry environment, thus hidden from re-uses by the wider public of writers, in science and philosophy.   This would make it — like the also highly technical term ‘epakoumenou’ in a scholion to Euclid X, an ‘insider’ term.   Even a young Aristotle might be unaware of these terms from within some overeducated ‘sophoi’ or ‘sophistai’ working inside the ‘Garden’ (Epicurus) or the ‘Grove’ (Early Academy), or perhaps a school at Lampsacus (can there have been any contributions to this early technical work from a man said to have intersected with Epicurus — Aristotle of Stagira ?  A topic perhaps worth the kind of detailed research for which Ademollo’s colleage D. Sedley is well known.  Among the fragments from Epicurus’s colleague and friend Polyaenus, we find several references to his having written ‘commentary’, for example on the construction soon to be incorporated by Euclid in his Bk IV, prop 12.

More research needed to form more a more distinctly stated Lemma, strip it of unwanted side-issues, and to develop a proof, if possible.  One point to investigate:  whether the three Uncial letters “Delta”, “Omicron”, “Lambda” used by our anonymous scholiast, should be expanded to a foursome, allowing an easier form of ‘image-formation’ for the concept ‘paregklisis’:  the fourth letter would be the standard symbol, likely so at Plato’s and Epicurus’s time, for our numeral ’90’.   “Koppa”.   Its downward straight vertical stroke forms, with its circular top segment, a ‘keratoeidEs’ angle, mixed from straight and not-straight.   Again, Scholion #3 makes efforts to picture, or iconise, the straight, and the line which is not straight (Socrates’s nose a famous embodiment of either the convex or concave species of curves).    Inscriptions from before Plato’s time (ca. 600 BCE) let us see more clearly the looks of Delta, Lambda, Omicron and Koppa:


inscribed Greek letters, dating to 2 centuries before Plato

Following suggestions from Euclid III, 31 Schol. about (a) old-fashioned opposites of the Pythagorean inheritance, with notes on their limitations, and (b) the Early Academy’s more nuanced analysis of ‘one and the indefinite dyad of greater-less’, more about the topics we may picture as contained in Philip’s tract ‘Kukliaka’, or in discussions of ‘The Circle’.    We would speculate that at least some of these latter discussions (reflecting on Seventh Letter and some live-voice exchanges) would have satisfied Plato.  Thus would NOT be subject to his veiled criticism of writings ‘ouden … kata ton emon logon’.  Not so ?      -08.x.18]

Lemma Three, Part One to show that the little tract De Mundo was written by this same Philip.                 Part Two to show that Philip is a plausible candidate to be the initial author of the Timaeus Locrus , subtitled ‘p. physios’ [ περὶ φύσιος  ].   Our venetian ms. ‘T‘ includes a phrase of interest here, curiously particular to itself:  ‘Peri Sufios’  Philip is reliably said to be from Menda, near Rhegium, and his preferred dialect may have not been neither Attic nor Attic-Ionic, perhaps whence the Italian  or Sicilian sounding ‘fusios’ and ‘sophios’.

                             Part Three is to identify the original author of several lemma-form propositions now appearing in our main texts, as regular parts of our ‘Euclid’:   in Elements, Bk IV, most notably its sixteenth and final proposition, about the 15-sided polygon and the circle.  Plato’s disciple Philip seems to have been the original  ‘midwife’ assisting this proposition to see the light of  first day.

Lemma Four, Part One

The two men Amphinomus and Philip may match each other more closely still:  it may turn out that we can  show that these two men differ in name only.  Thus these two may be utterly undifferent in their blood-and-bone Early Academy reality.    This site aims to show Amphinomus and Philip are likely the same man.  David Wiggins’s nuanced concepts of sameness and substance apply here.  [Sameness and Substance, Renewed].

  [this point is to be argued independently of the hypothesis that Philip assumed the name “Socrates Junior” or “Younger Socrates” at the Early Academy;    Some of these identifications may be difficult to prove with sufficient conclusiveness.  If so, there may emerge some additional Lemmas helpful in giving them a boost, lemmas needing their own individual proofs at youngersocrates.com.
there are subtleties about how or when a ‘speaker’ might — just by what he says — count as a ‘silent man’.  It is possible that the handwritten message preserved from Samuel Clemens which begins “I am writing this from the grave…” qualifies as such a self-silencing speaker, its author a problem-substance.  In any case LSJ has preserved a specialist word from Plato’s LAWS, Bk XI, ‘eirwnikos’.   Sam Clemens once reportedly said of himself:  ‘I am not an American, I am THE American’.   Plato wants us to contemplate a person who is not ‘a Speaker’, but ‘THE Speaker’.   In Laws it is the “eidos” of the “eirwnikos”.
Suppose that, out of his unique and ideal mouth there should emerge things of a self-extinguishing type of speech, one that proves to be self-extinguishing.   Self-silencing is the way it goes in Euthydemus.   Prof. Calder has wondered why late Platonists debated about the Socrates who ‘was silent at his trial’.    Plato, Xenophon and others represented him as talkative, characteristically so.   Dionysiodorus and his brother are illustrative of self-silencing speakers, or even substantive self-nullifiers.    Can Maximus of Tyre’s legendary ‘silent Socrates’ have been just that, a mere legend ?  Or can he have been a self-silencing Speaker in the mode of Euthydemus ?
In any case, Wiggins and Barnes are equipped to explain who is being referred to by an untruthful ‘Post-Truth’ soul, when trying post-truthfully to refer to him- or herself.    I mean when saying ‘I’, as in “I am  not an ironist, but rather the ironist”   (εἰρωνικός  ) .   The very idea of Socrates, the quintessential Socrates(n).  What thing, if anything, is referred to when such a being utters “I” ?     Some things local to Euthydemus may possibly make all this less incoherent.   The analysis would go via the self-silencing of those, some of them Ionians, trying to reject non-contradiction, and via the history-of-logic antecedents of this in Euthydemus.  Maximus of Tyre used a vivid figure, writing of a Socrates who had had his tongue removed.
As a matter of history, imagine how much more difficult the above paradoxing will have been, before Aristotle really got started on his Organon.    What are we to make of the specialist term ‘potency’ used by Plato  at Euthydemus 296c6.   The exact phrase is  ‘ οὐδεμίαν ἔχει δύναμιν’ [= ‘it has no potency’].     This dialogue dates perhaps near Plato’s writing — with Philip’s help — The Laws.    But that early in the history of logic, logic itself as a science was pre-natal sort of being.   A logic in intention, one might say, rather than call it ‘ embryonic ‘. ]

                         Part Two proposes to itself to show that Younger Socrates is a stage-name or assumed name, likely of this same Amphinomus, birthname Philip of Opus.

A significant challenge to Aristotle (not a counter-challenge by Plato) came from the side of Amphinomus(=Philip).  This challenge amounted to his rejection of Aristotle’s doctrine that that geometers never seek out causes, since, as mathematicians their Ergon is not the same as the ergon of first philosophy.   They are bound by their essence (as mere mathematkoi).  Bound, that is, to remain within their art’s hypothetical framework.   They do not approach causes, or the very Essences behind their reasonings, except to the extent that such Beings can be inflected into the parlance of mathematics.   Amphinomus argued against Aristotle (Proclus on Eucl. I summarises this) by takikng his own personal case as counterexample.   His work as a mathematician led him to claim, and in effect also on behalf of his fellow mathematicians, this following:

” I am iconic of the man producing work as much mathematician-geometer as philosopher of Being (or Truth).   The example inquiry [and I emphasise that this has me investigating Causes] I put to my senior and junior colleagues here at The Academy, is the following.   We can prove mathematically that  a particular finite number, which sets the limit for types of those special regular polyhedra soon-to-be-famous ‘Platonic Solids’   My senior colleague here at Plato’s side in the Academy proved it mathematically — the finite limit is ‘5’.”  Why is it impossible for me, Amphinomus is summarised by Proclus as asking>, Why, if inside the circle we can inscribe an infinity of regular rectilineal figures, what would cause the similar thing for polyhedra inside the sphere — Why is this not true ?   Amphinomus pressed the anti-Aristotle position forcefully enough that outlines of his argument are echoed in Proclus’s treatise on Euclid Book I.    Worth noting here, in close proximity to the ancient academic scene:  this student of Amphinomus, echoing his own teacher’s doctrines, is now challenged by a man both fellow-pupil and fellow teacher.   Pupil of Plato, teacher of Aristotle.   And all of this likely before Aristotle’s writing of Posterior Analytics !   Perhaps a generation before Polyaenus, Epicurus and Euclid.
(Similarly, if a prize-winning post-Einsteinian mathematician and philosopher, R. Laughlin, speculating on the “Partial Hall Effect” may know that one of the partial values is 1/3.   As of A.D. 2017 he seems not to know the reason why just a finite number of values are permitted here.  What prevents him from investigating the cause of this — without forfeiting his status as a mathematician ?   The man both Plato and Philip might describe in Academic terms as “our junior colleague here, Aristotle of Stagira,” is not entitled to make this forfeiture automatic and apodeiktic, “even if he comes bearing text and doctrine from my Repub. VI-VII” with my mutterings about the over-mechanical language some ‘recentiori’ have indulged in?).
An entirely parallel point can be made about the first woman ever to win the ‘Nobel Prize of Mathematics’ as the Fields Medal is nicknamed.   Her name:  Maryann  Mirzakhani.   She reduced the seemingly ‘surd’ truth proved by Theaetetus to a mathematical issue, within mathematics:  Rigidity Theory.  And despite her premature death (this she also shared with Theaetetus).  She never forfeited her standing as mathematician, nor has Laughlin, may he live long and happily, despite pressing for deeper causes of the 1/3 Hall Effect.

At the risk of speaking presumptuously, let us continue this micro-epic episode, asking our Philip to add words to this effect:  “Perhaps the most curious of these is the Dodecahedron, notable because of its being the Exception to Plato’s rule, One solid, One Element, (a rule I modify substantively in my little tract nicknamed ‘LAWS, Book XIII’)”.   We might paraphrase him further this way:

“There are further reasons for the Dodecahedron to stand out, reasons of interest to critical readers of our best mss. of Euclid-to-be.   I mean the various lexical singularities in both (1) the distal end of The Bridge of Theaetetus, i.e. XIII, 11, and  (2) in the Attic spellings that copyists will continue copying, despite their dialectal irregularity, in all of Book III and in a critical passage within the final Chapter of Book XIII, ( some ancient sources so denominate Epinomis.)”

No ancient source is here being claimed for these above two paraphrases.  But something like the result of the paraphrase can be shown to be traceable to Amphinomus at the early Academy.   Also, it is pretty clear from Epinomis that its author, like Aristotle, believed in Aether.   That was a major reason many scholars advanced for disbelieving this dialogue’s author to be someone other than Plato, a Four Elements man.

All of this comes up over our horizon as we look at the Leonardo Taran evidence and manuscript attestation (1976). A.E. Taylor had vigorously defended the minority view (mainly his own) that the work was direct from the hand of an elderly and somewhat enfeebled writer, the aged Plato Himself.   Some recent German scholarship has worked to de-attribute the ps.-Aristotle work De Mundo from other and later authors, and (surprisingly) attribute it to Aristotle Himself.   This may well seem deeply implausible to one very special man, Oxford’s distinguished successor to W.D. Ross, — Jonathan Barnes.   (This is the same Jonathan whose farming and gardening in central France has recently been described — in an affecting and affectionate tone — by his younger brother Julian, “Nothing to be Frightened Of”.)

These words claiming to trace an ancestry to Plato’s friend and disciple (Philip, a.k.a. Younger Socrates) are as of course not traceable to him by customary pathways.   Perhaps not traceable even under any nondisreputable way of doing this kind of detective work.  We have precious few intermediary texts to put under and underpin this paraphrasing of Amphinomus.   Also we have little or nothing in modern languages, such as doxographies of the type traced by L. Taran, writing in Renaissance Spanish (to underpin his work on ‘amicus Plato, sed…‘)    Few if any such underpinnings from Brasil or from Italy or modernday Greece.  All the same we may find further data to give guidance and to support reconstructions.  Here we have S. Slings to hold open one or two doors, per his statement at the end of his commentary on Clitophon.  He there warned against an overconfidently sceptical position, holding that nothing advanced by modernday scholars can both be new to the scholarly public but yet go back to a good ancient source.  If work on Euclid X, Euclid XIII and their scholia are to be advanced as helpful ‘middles’ here, and even if such doorways are not meantime closed, much sober reconstruction work remains to be done.

In our Timaeus world, five and only five regular polyhedra are possible, Philip and Theaetetus argued.  But Amphinomus (a.k.a. Philip) insisted on getting a sufficient explanation.   What caused  this limitation, there being no comparable limit of regular polygons inscribed in the circle ?   Yes, Amphinomus apparently argued, my view runs counter to that of our  student Aristotle, which he holds to whilst he dutifully draws a line — a famously platonic line — dividing brightly between Dianoia and NoEsis, and thus dividing also between mathematician and dialectician.  Thus Amphinomus is disagreeing with both his own teacher Plato, this being the same man as Aristotle’s grand-teacher.   when he denies that the ‘what causes this?’ question is properly posed by a mere dianoetics person, a mere mathematician.

Proclus preserves a running sequence of remarks outlining related issues.   Proclus’s summaries run from his Friedlein p. 201 through p. 207 (On Euclid I).  He takes pains to preserve the ‘saltiness’ of the exchanges Philip-Aristotle by holding onto a sequence of γε μὴν lexical touches which we may reasonably trace back to the Early Academy itself.   [Constantin Ritter tabulated the intensity of this phrase — within Plato’s texts — in works near LAWS, and the absence of it in the early dialogues.  It is well worth noticing that, in the Friedlein edition of Proclus on Euclid One, there are a record high concentration of γε μὴν’s (sc. 4 of them compressed into 7 Friedlein pages, easily 5-fold above Proclus’s average)]

Taking Plato’s corpus as a reference, we may usefully refer to Constantin Ritter’s painstaking work “Platon”.    Ritter documented the frequent use of this phrase γε μὴν in and near to LAWS (more than 5 times as frequent now than when Plato was writing his early and middle dialogues).    The formidable students of Attic style and mannerisms, Denniston and Dover,  of just a generation or two now, did the further linking of this vogue to the prose of Xenophon.   Denniston counted over 20 in just one minor work of Xenophon, the p. HippikEs.

Another point of lexicon invites close attention:  twice in this Amphinomus-vs.-Aristotle summary, which runs for 7 Friedlein pages, we come upon an idiosyncratic spelling of the phrase  δίχα τεμεῖν .   Philoponus spells it in this peculiar way, commenting on Aristotle’s remarks about the very same proposition, due to appear at I,9 when Euclid has finished his edition, but our best texts of Euclid have the standard spelling, whilst Aristotle, this portion of Proclus, Philponus all have the variant, apparently from the Academy just before Euclid.   Do we have an author well-read in Zeno of Elea, but too early to have read Euclid?



The add-on book at the end of Plato’s LAWS is named from its position as an add-on, “Epinomis”.  In antiquity it was reported to have been written by Plato’s student, Philip of Opus.  It was the part of the platonic corpus on which B. Einarson was doing a commentary when he died in the late 1970s.   We can reasonably hope that one of his students and followers, — say Wm M. Calder III — might publish portions or all of Einarson’s non-completed work. If so, the very great powers of Einarson’s writing would likely result in more light than we today get from parallel writings, even those nearer completeness.  Here you will see an excerpt from its final chapter, from folio 299r of our best ms., the Paris A:

(bis5) semi-Aeolic AIEI in final chapt. of Epinomis, at 992c1 length=3.5, rev6


Something closely parallel turns up in Scholion #3 to the JL Heiberg edition (1888) of Euclid:  ‘dichotomism’, or ‘dichotomeme’   .  Our best text of Euclid makes this the main word in its definiens of Right Angle.    It occurs so rarely in ancient Greek, among primary authors of commentators, as to remain unlisted in LSJ:   διχοτόμημα.  Conceivably it found its way from Polyaenus or earlier mathematicians (no adequate edition of Polyaenus had appeared until 1991) — found its way down to ourselves via a scholion in the margins of Euclid, unnoticed by lexicographers.

A point of some refinement logically, which may possibly be at home in this pre-Euclidean “Eleatic logic” environment.  Zeno’s “dichotomy” perplexities naturally did not require a young Aristotle (or his Physics) to come onto the early Greek scene and force something like ‘actual infinites are an impossibility, even if infinities in potency’ may exist.   Already in Parmenides, Socrates had put the leftward dichotomEmata of his own personal body apart in one logical place, the rightward ones kept logically distinct, there is a felt threat of what Aristotle repeatedly and tirelessly condemn as an impossibility: an “infinite regess”.

We might put it thus, in the light of this ‘newly discovered’ term dichtomEma: the full dichotomia will  force us to recognise an uncompletable set of ‘halved’ dichotomEmata.    Paradoxically enough, however, all of the body of Socrates, including his initial ‘first half’ and onward, — all of these seem intact and in place.   Not so much as a single ‘dichotomEma’ missing — on pain of our admitting that we lose our entire Socrates ! Nevertheless our physical Socrates here must be held to encompass not just an ‘. . .and then further’ subset of them ALL, hypothetically complet-able, but never (except ‘for the sake of argument’) actually complete-d.    Do we have other examples, also traceable to pre-Euclidean times?   Whoever authored the little tract “P. Kosmou” — Philip of Opus, on my theory he can have conversed with the young man soon to write the ‘De Caelo’ or ‘On the Heavens’ will have had easily available texts  of Timaeus.   In fact several of the hypotheses advanced here agree well with the idea that the p. Kosmou is alluded to by title at Tim. 28b,.   This is the little anacoluthon which AE Taylor translates “as to the whole heaven or order of the universe — for whatsoever name might be [optativus urbanitatis!] most acceptable to it, be it so named by us…[Archer-Hind, lightly edited]”   Plato comes very close to alluding to both non-Timaeus treatises, the De Caelo  and the Peri Kosmou in the same clause.  Late in the p. Kosmou, in any case, the author asserts with a certain doctrinaire confidence “the infinite is not possible in this world”.

Conceivably if we had more Polyaenus or Neocles (Epicurus’ father) we would detect a nuance of ‘physical’ meaning.   A periphery has to surround something (perhaps a gathering of atoms), a circle [still less The Circle] may pay no heed to what stuff, if any, it holds within itself.   Polyaenus and Epicurus might say a ‘periphereia’ and a ‘kuklos’ are not quite the same thing.

What good reason, Amphinomus seems to have asked, — good reason find for prohibiting him, as a mathematician, from raising the “why” question ?   Naturally it would not suffice merely to cite young Aristotle’s opinion, later to become rather standard.  I have Philip rebelliously refusing to comply with such a prohibition, and putting it to his fellow academicians, why shouldn’t any of us here be licensed to ask a “why” question of no matter what subject-matter ?

It is a curious and related point that whereas “noetic matter” is explicitly written about by Aristotle, “geometric matter” seems also to have been a reputable Academic concept also.  It seems only to have come down to us but only relayed to us via commentators on Euclid, or on the mathematicians Plato and Euclid shared.    There are some evidences pointing to a disposition of self_will (authadEs in the language of Letter #8, later echoed by Theophrastus) amongst members of Plato’s group of colleagues, and not all of it local to his promising young pupil Aristotle.

Philip can have cited a famous line from Republic VI in support of his schismatic opinion.   This is the passage Stephanus will later give the number  511 d2,  where there is created a distinctive blurring of the division between mathematics and pure noEsis.   Not only is the bright line insisted upon by Plato between Dianoia and NoEsis taken away.   The division between the two is made positively blurry.   Philip will have wanted a similar blurring of the boundary between authors of a ‘peri ouranou’ and a ‘peri kosmou’, precisely the blurring supplied in Timaeus at 28b, Plato telling the reader that ‘heaven’ and ‘kosmos’ are the same, except only nominally.   As to their quintessence, this pair amounts to the very same thing.   The tract includes AITHER among its 5 elements.

This present website will want to stir hypotheses about various sides of the controversies over dialectic, mathematics, cosmology  (even theology, which is understandably in the near neighborhood of all these higher end topics at the Academy).   Do some of our texts, notably those forwarded to us via Ephraim and his Venetus T, support a theory that Amhinomus was an important agent, even perhaps in some actual insertions into Plato’s works,.   Such insertions as Slings removed  recently from R 511d2,.

The marginal expansion on Timaeus 42b2, if it traces all the way back to the Early Academy — whose anger was it ?    Philip may have had special motives for wanting the boundary between mathematics and dialectic to be made blurry.   G.Ryle speculated a generattion ago about why ‘dialectic at the academy’ needs so much explaining and reconstructive work.   Can it have been made obscure in part by ambitious young men (some building careers, said Ryle) ?   In any case we can usefully look for more clarity about why Plato needed to plead for civility and rationality in his contemporaries’s and colleagues’s quarreling, one against the other, intramurally.   The Academy seems to have invented a new word with a ‘dia-‘ prefix:  diamfisbEtein [ διαμφισβήτειν  ].   It is infrequent before the late Plato, but becomes more frequent in Aristotle, witness Bonitz’s Index.   Like Cicero’s word ‘perabsurdum’, meaning a bit more absurd than just standard absurdity.  Perdisputing and perdisputatiousness of behavior, we might call it.

There are many signs that Amphinomus was a man of no small ambition.  A treatise by Plato on “Nature” (Timaeus) and a treatise by Aristotle “on the Heavens” looked to him on a par with the not-yet-prominent Academic work “De Mundo” [ περὶ κοσμοῦ ].     We may borrow the term from Plato’s intense quotation from Diotima at 206d6 — a likely polemical  passage of Symposium —  ksunspeiretai, ‘co-disseminated’.   This has strong textual authority (though not based on Venetus T).

For sheer earliness, the Clarke ms. at the Bodleian Library outdoes every other — c. 895 A.D.  From the Oxyrhyncus Papryus we find an earlier witness, but scholars have reasons often to prefer the Bodleian ms.  Here is fol. 215v of that special Clarke handworking of that crucial word — with its exotic ‘ns-‘ pair of consonants holding onto a real phonological curiosity:



These polemics may have been aimed by Plato at targets hypothesised by Bury and Robin.   This is the dialogue whose date of composition will have been near to the ‘Theban Hegemony’.     Several special features of the Venice ms. may point to this historical context.

If some of the dialectal information concentrated in Venetus T turns out to be a convincing guide to further study here, the DeMundo may be indicated to be a work originally authored by Amphinomus, or Philip of Opus.    On the pure mathematics side of things, it is plausible that Amphinomus took  the doctrine of “Platonic” regular solid figures, and also took the closely related subject of the “procreation” of irrationals such as medials as iconic subjects.  We must guide here on scholia to Euclid X, Chapt 4, as collected by Heiberg).

Scholia to Euclid which are likely traceable to the mathematicians at the Early Academy point to “mother propositions” or “ancestral propositions” from which certain progeny or later propositions issue forth.   These seem likely to have been the discovery of Plato’s academic colleague, young Theaetetus.  It is Plato himself who puts it into the mouth of Elder Socrates (at 151), that both Socrates and Theaetetus are alike adept at the art of “midwifery”.   Philip of Opus is credited with a work whose title also embodies the same imagery:  “On Fertile Numbers” (unemended SUDA, — pace von Fritz).    Some of Theaetetus’s work resulted in propositions that were “progonoi”, say these scholia.   Ancestors to other parts, — and both parts in turn will be made applicable (via XIII,11) to the final chapter of Euclid’s entire work, Elements.    This is the entire work’s final chapter, rightly given the title “the Five and only Five Regular Solids [of Plato]”.    Some early academician, before Euclid but after Theaetetus, seems to have taken both these subject areas and put them together.   It may seem a distant analogy, but there is in truth some similarity to the issues involved.

This thought experiment may help clarify the point.   A mathematician today may presume to ask (at an informal gathering in Cambridge Mass. a mathematician was in fact observed to be asking this, in early January 2017) :  “why do the descriptions of areas and volumes differ, as these are conceived in Quantum Gravity theory ?”   Only a narrow dogmatism would reprimand him for raising such a question, or would accuse him of abandoning his status as mathematician.    Amphinomus seems to have been counter-challenging Aristotle on a parallel point.    So Proclus on Euclid Book I.

Philip (so says SUDA) did a little tract he called “fertile numbers” (arithmoi polugonoi).   The same dictionary has him entitling a treatise “kukliaka”.    All these were matters into which Philip can have claimed to enjoy an especially personal insight.  In the case of the 5 Platonic solids, Amphinomus or Philip wants to ask “What causes the number of such figures to be 5 — and only 5 ?”    And he will defend himself against any complaint from Aristotle to the effect:  “You are not entitled to raise that question, O mathematician, as Plato has reserved the deeper “why” questions for pure dialecticians.”     Aristotle can have pinned down his platonic message with uncommonly precise pointedness if he referred to the text of Rep. 511d2   This is the precise location (reviewed above) where the issue of introducing a blurring of Plato’s sharp division DianoEsis/NoEsis occurs.

Slings took pains to explain why he was excising it from the Oxford text of Book VI.   Already it had been a crux of interpretation.   Adam had found Plato “contradicting himself” in mid-sentence, if we take the received text as correct.   [This precise text, beginning from its odd-sounding    καίτοι νοητῶν  … (incidentally these words as they appear on folio 235r, col A  of our Venetus T ms. commit a tell-tale error, perhaps pointing somewhat independently towards the spuriousness of the pre-Slings editions, Oxford 2003).

No  comparable finite limitations on the number of regular figures occur in  the 2-dimensional case.  That is, polygons  inscribed in the circle.   We don’t have strong indications about the contents of Philip’s tract “kukliaka” , but it may have situated it in the near vicinity of Plato’s example of “The Circle Itself” in Seventh Letter.    Let us try to spell out some further particulars here.   Philip’s tract will have provided a nearby home for such questions, and perhaps for his own tendentious answers to them.  Tendentiously pointed against either a Timaeus-author or a DeCaelo-author.   And who is young Aristotle to legislate against Philip’s being at once a mathematician, a cosmologist and a student of Being Qua Being  ?    Yes, I am suggesting is that there is some deliberate and even contrived blurriness here.  The blurring in the passage at Rep. 511d will have been designedly unclear:  designed, namely,  to blur the distinction which blocks Philip the mathematician, and his upward-glancing ambition.  Thus is enabled the Philip-triumphant, we may even say self-designated ‘king Socrates’, the imagined downward-glancing Platonist dialectician.   A prognosticator into the bargain, fit to author the Prognostica Socratis basilei.

This may be explained further, using language of early Greek astronomy, the language of Eudoxus language specifically.   This website intends to cause a certain set of ‘de-occultations’ to take from the title of a work by Eudoxus.  In its meaning in this title, this was a kind of doubly negative concept: a de-disappearing, i.e.  a cancelling of a given star’s regular occultation.   Each one, even the moon, is regularly occulted by background sunlight.   This is the same thing as that star’s “appearing” in the sky, some hour later than sundown. The star will have been occulted all day — so to say automatically — simply being outshone by background sunlight.  In the familiar way and at the appointed moment the star will appear, or “come out”, as we sometimes say.   These are the exact words used by Curtis A. Wilson

This series of de-occultations is not particularly deep or mysterious, as it repeats itself before the public eye with nearly every body in the heavens, repeats both the being-occulted and the being-de-occulted, or appearing — once daily in a cloudless sky.   A striking example: unless cloudcover made this difficult, citizens in Athens on 21 June -353 will have seen Alpha Ophiouchus culminating at roughly 8:35 PM local time that day.   Reliable calculations confirm this.

If you were to doubt the reliability of these calculations, you should feel free to express these doubts either publically elsewhere, or here at youngersocrates.com.   Do please, O Doubter, have a close look at these following two indicators, that they are indeed reliable:


This above pair of references gives a direct look at the detailed work of Curtis A. Wilson.NY State’s Congressman Christopher Gibson (now of Williams College) was fond of calling work like that of Wilson “virtuous”, drawing upon striking usage — similar archaisms to his usage, startling from a sitting Congressman — of Plato and Aristotle.  Pope Francis used similarly startling and old-fashioned language in 2016 when retorting to then-Presidential-candidate D.J. Trump.  Trump had used invective, calling The Pope “a politician”.  The Pope retorted by inviting Trump to consult a known writer, on the concept “political animal.”   He actually believed Trump had heard of Aristotle.    Be that as it may, these above calculations of sun and stars were carried out by Curtis Wilson, and later confirmed by an expert at the US Naval Observatory.  This same expert, an admirer of Wilson’s, made a pointed reference to this very calculation of Wilson’s in the obituary note he wrote for him.   He thus has something like the relationship to Wilson that Augustus DeMorgan had to his departed friend, famous mathematician George Boole, on whom DeMorgan wrote a touching mini-obituary.  [see DeMorgan’s Budget of Paradoxes 298,ff].

Plato was the main cause of these occultings of his nearby colleagues, the chief and memorable exception being Aristotle, who is often seen shining even in broad daylight. Unlike the others’s, Aristotle’s occultations, being sparse, need few cancellings.

Ingmar Duering did considerable work many decades ago now, clarifying the obscure biography of this Socrates near Plato and Aristotle at the early Academy.  Gilbert Ryle outlined the issue about what became of Dialectic at this same time in the Academy.  Barnes and Brunschvig have since developed this.

Aristotle in his writing kept within matter-of-fact boundaries. He was not of Plato’s temperament and turn of mind, thus not much given to creating colleagues of “out of whole cloth”. Now he matter of factly describes this man whom he calls “Socrates the Younger” Σώκρατης ὁ νεώτερος (SwkratES ho neOteros) in Metaphysics Z,11. There are other mentions of this same Socrates nearby. Scholars tend to agree that the ‘Socrates’ mentioned in Plato’s Eleventh Letter is this same ‘blood and bone’ human, to borrow-back a phrase which Aristotle had borrowed from Plato (in his Symposium). In both of these literary points of reference, we find both activities and thoughts attributed to this man they call ‘Socrates’, a man clearly different from Elder Socrates.    Our younger Socrates, Philip, was likely younger than Plato, and perhaps not a decade or so older than Aristotle.

It is my opinion that we can do better than to rest content, as some scholars do, in the belief that there was no such man “Socrates, teacher of Aristotle”.   They commonly rationalise the fact of reports by supposing an erroneous or artificial multiplication of persons, or perhaps simple confusion in the stream of reporting (a common enough phenomenon).   I will be suggesting that we attribute to Philip several substantial writings, and that we also attribute to him initiatives and polemical activities perhaps tied to these writings.  Some of those activities at the Early Academy will have earned him disapproving words and antagonistic attitudes from time to time in each of Aristotle and Plato.

We may well be seeing one  example of this in, Aristotle’s disapproving words in De Anima I,3.  They are directed toward of an anonymous ‘comedo-didaskalos’ [in many texts he is given the name ‘Philip’, strangely enough, though not by Averroes].    The man disparaged there as having opinions like those of Democritus, or perhaps ‘Daedalus’, is writing about the soul’s motions.  It is not likely to be a friendly comparison Aristotle is making, saying of him that he writes in the vein of of the Academy-foreign thinker, Democritus.   All of this may have counted as ‘Epanastasis’ and ‘allotriopragmosunE’ in Plato’s judgment.   Some passages in the middle books of Republic strongly suggest that this is so.

[1.v.17]  It may be worthwhile to insert an excursus here, based upon a series of Scholia to Euclid I, 15 (esp. Scholl. ##59-62).   This will take us down a path JL Heiberg laid down.   He collected and published with Teubner in 1888, the scholia to all of Euclid’s Elements.      The Scholion of greatest interest here is the one leading toward the Philip-like sentiment also expressed in Schol. #18 (skeptical towards ‘poiEsis’, on the grounds of its debatable concessiveness to ‘time-dependence’ inside mathematics).   We might take steps to follow the distinctive verb ‘diamphisbEtein’ written by Aristotle in his piece ‘On Friendship’, — on some good accounts of Aristotle’s early writing this will have found its way into EN, at Bk IX, 2 1155 a 32ff.   Campbell had called attention to the relative novelty of this term of art as of Plato’s time.    In Aristotle himself, however, it occurs several times, once in the suspect book of the Metaphysics, namely  Kappa.     This is the book that repeats much earlier material from the same treatise, and that is further peculiar in suffering from a rash of DeMundo-style phrasings   ge mh\n  (‘ge mEn’).     Various of these peculiarities were too much for Aristotle scholars beginning with W. Christ and continuing past W.D. Ross.   They agreed that Book Kappa should be deleted in its entirety.    Herbert Granger has recently shown a disinclination to comply  with this scholarly consensus.

There is a good sense of ‘halfway’ which permits us to say that “Halfway back to Plato, — if we began from Aristotle, — we have our filo-qeamw=n(“ PhilotheamOn”) adjacent to Aristotle’s chancing upon the etymology   fil[o]-ippoj  “Phil-ippos” of Plato’s student, Philip of Opus, Aristotle’s teacher in turn [see 1099 a 10 in the ‘E’ MS, commended by myself in a letter to J. Barnes, mine of early Feb 2010].

There is already some allusiveness in Aristotle’s alluding to the name of the man between himself and Plato, Philip of Opus.   But we can find much more in the vicinity of this allusion if we include the point that the word   filoqeamw=n [‘philotheamOn’] is more likely what Aristotle wrote at 1099 a 10.    We need not follow I. Bywater, who not only does not read this word, but also declines to mention its having some ms. authority,  even in his apparatus criticus.    Certainly H.H. Joachim’s high admiration for Bywater and his other early ‘Aristotelian Society’ scholars was well founded [his preface to the 1922 edition of De Gen. et Corr.].    All the same we ought to follow the example of Slings (his Clitophon, p. 342,f) in keeping the door open to there being some ‘ancient tradition’ behind any of various manuscript peculiarities which have survived these dozens of centuries in the textual traditions of Plato and of Aristotle.  In any case the present Oxford edition has the [considerably less plausible] reading filo-qeorw=n  (‘philo-theorwn’).    And, alas, Bywater did not preserve the Bekker note listing the “philo-theamwn” varia lectio.    This imports a quite different meaning, a difference of substance.   It is as if we let a ‘theoretician’ be put in for a theater-goer.      A lover-of-abstract-knowledge  (qeorhmata)  for a lover-of-spectacles qea/mata  (‘theamata’).      ‘Theama’ is in fact the root word meant to be echoed at  Bekker  1099 a10.     So  qeamw=n  has commensurate authority at   a10.

Roughly that same time (say early Olymp. 106, when Philebus  is being composed, and Plato in his very advanced years – those poignantly called ‘our sunset years’ in Laws VI, xiv  — see Slings on Plato’s using the first-personal plural form, in Clitophon for example, to indicate ‘myself’ at 406 a10.    Around this date we have Phil. 44B, referring to ‘some wise someone’ who is further described as  ‘deinos peri physin’.    John Adam made penetrating suggestions on the type of man here alluded to by Plato.   ‘Pythagorean preachers’, says Adam (app. x to Rep. Bk IX.   This would put our author at the Academy and make him not unlike the Empedocles referred to by Aristotle here in EN IX,2.     A threesome of men is put together in Problems 6, 30.    They have attributed to them a shared temperament or ‘personalilty-type’.     Something about their black bile.   This list has oddities of various sorts.  But one striking point is its listing Socrates after Plato:     Empedocles, Plato and Socrates.     The Elder Socrates kept his bile pretty well controlled, we might think:  “Go ahead and condemn me to death, O Athens !    As far as I know this may be a not so severe penalty, especially for a peaceable man, a reflective and perhaps even phlegmatic old man, now aged seventy”.

Can Younger Socrates, or Socrates Alternate have had something more bilious, even choleric, about him ?    He would have to have had considerable personal energy and a willingness to thrust himself forward there at the Academy, claiming  a position in that succession of eminent men beginning back at or before the time of his namesake (Socrates Simpliciter), and pointing ahead to such prominent men at the time shared by the late Plato.   Perhaps an arrogant claim, if it were to include such rivals as Eudoxus, Aristotle and Theophrastus.    Again, as we have reliable evidence to inform us, Philip put himself forward as having opinions worth publishing on topics under vigorous debate, such as pleasure, the passion of anger, and On Writing (p. graphein).

We must be methodical and sequential about the various possible meanings of ‘graphein’ in Philip’s title.  Several of the standard meanings of ‘graphein’ can be simultaneously at play, naturally, as is often true in Plato (Slings’s Clitophon displays a much-layered Socrates, in that little piece which is perhaps as authentically Plato as Epistle II is authentically his).  Here in Philip’s title.  Any of them make Philip a bold man:  (1) “On proving [as in geometry]” (2) On Writing [a major topic in Plato’s Phaedrus] or (3) a quite specialized meaning “On bringing a Lawsuit” [as in taking Socrates(n) to trial, and perhaps causing Athens to Sin Twice Against Philosophy] .    Meaning (3) is admittedly conjectural.  Yet it will be found to have a basis in Euthydemus, especially the in the part near the end, where some ‘panurgic’ misbehavior is on exhibit.  Much remains to be researched and developed here, conceivably in the manner of a ‘midrash’.   Thus spoke the caracters and caricatures of Homer’s stories, the ones Shorey’s translation has Plato say are ‘wooing’ him and his legacy [Republic V]. – and  where Penelope and Amphinomus and KtEsippus and young academicians slightly were doing ‘logically insurrectionary’ work before the De Sophisticis Elenchis



Let us make use of more of this (liberally provided) e-space to develop this theory further.   In today’s roomier surroundings, we need not fret over the cramped space Ephraim the Monk and his limited parchments, [in the XXIst century there will be no such calamity as befell L. Campbell at the beginning of the XXst — his Plato Lexicon being cut from 900 to 600 pages, fretful editors at Clarendon too illiberal with their printed printed pages].        Back in the fretful Ephraim’s time — a few years away from 954 AD — Ephraim was abbreviating his Plato and his Aristotle, squeezing in an odd example or two of the “half-H” character such as with his word “hidion”, all in order to save space.     Ephraim also crafted ligatures to keep within his space limits.    He was the dutiful copyist of the now proud primary witness to Plato, Venetus  T, and also the space-conscious mansusript called Marcianus 201, Aristotle’s Organon.   Two treasures kept in safety and cloistered solitude there by Piazza San Marco.  This present theory wants to sketch the third Academician near Plato near in time to Olympiad 106,  (Plato+Aristotle+X).     The formula  is designed to leave room for an Old Academy man capable of wearing  several epithets simultaneously, even wear them proudly and almost regally.     The author naturally wants to emulate his immortal counterpart, even in his deliberately assumed polyonymity.   The figure of  Zeus as  described devotedly by the author of the DeMundo Chapt. 7.      That is where Zeus gets praised as ‘polyonymous’ .    

There are several further signs of the Old Academy’s habit of playing on names.  Simplicius echoes elaborate plays on the name “Eudoxus”.    “Theophrastus” was a nickname, not his birthname.  No shame therefore if our DeMundo Academician with an epi-anthropic scope of vision [do you have an opinion on who originally wrote the Scholion numbered 18 in JL Heiberg’s edition, to Euclid I, 1 ?    His attitudes have a deeply reactionary Platonism about them, like those of Amphinomus.  He is a reactionary devotee, writing prose that is “more Platonistic than Plato”, and alive during the final years of Plato’s own life.   This was when Aristotle was reaching maturity, but perhaps had not finished working on his  Analytics, or Topics.    Pamela Huby demonstrated that the latter work dates to near the year 360 [Olympiad 106].    [there will some day soon be more on this subject in “Lemma 1 on Philip of Opus and the angle-sum within the Triangle”.    The date of this coinage seems likely to be close to Huby’s date forTopics.     In any case this scholiast creates the startling coinage “epi-dhmiourgesthai” in Schol # 18.   He appears also to indulge in word-plays on  “epi” in other passages now following their paradromic-course in our best mss. of Euclid.     Some kernels of gold (as Heiberg put it) in these marginalia.   This scholiast is leading up to his famous remarks on the #1 illustrative “Academic” illustration of geometry’, the famous “internal angle sum of the triangle,  I, 32.   An immediate pupil of Plato’s and immediate teacher of Aristotle’s.   Who better to claim the nickname “Socrates Junior” than a teacher at the Old Academy well versed in geometry and astronomy ?     This might well be Amphinomus, or Aristotle’s teacher “Socrates Allos”.


My lightly speculative Early Academy narrative has him naming himself “Amphinomus” as pretender to succeed Odysseus.    “Neocles” or “Neos SokratEs” [ Socrates-the-Younger] will be other suitable nicknames for this polyonymous man.   Call him a hero, a daemon, a demi-god.    After all Amphinomus and his doublet LeiodEs were heroes [B.  Fenik, “Studies in the Odyssey”, 1974, proves these two figures in Homer’s epic mutually dual].     Plato was soon to be called ‘divine’, Aristotle ‘daemonic’,  Theophrastus ‘divine in his phrasings’  [B. Einarson, in his Loeb edition of the De causis plantarum proves that the divinity of his prose style is only a notch below that of the divine Plato.  Einarson’s magisterial work deserves more attention.   He is on a par with Denniston,  Slings and Dover ].       We may speculate a bit further  towards Old Academy nicknames like Hermogenes [Philip was a devoted follower of Hermes] or Kal-Ippos (a fellow astronomer,  familiar to young Aristotle, obliquely complimented in Metaphys. Lambda 8 ( 1073b) ?   “Amicus Calippus, sed…”    I once tried to interest Jonathan Barnes in this ‘Amicus Kalippus, sed…’ formula, but not to any effect.    Perhaps he thinks this topic treated to a finality by L. Taran.   At least so I surmise).    If Plato did in truth compose a draft for his announced dialogue The Philosopher, this would have been near Olympiad 106 when all three men, — he, Younger Socrates” (if any),  Philip and the young Aristotle were hard at work.   If Plato were so inclined, he could weave material from it into Republic V, that draft might have been much the way Republic-scholar Campbell once imagined this.    [Campbell was crafting a speculative note to his edition of “Politicus” 257]       I would diverge from Campbell’s suggestion– that Plato has as his central speaker  a repeat character :  young Theaetetus again.    We might do better to imagine a repeat of our astronomical expert, Younger Socrates himself.    It will only be a fuller credit to his play-on-the-word-epi if this same blood and bone man also wrote the (now-lost) pair of dialogues, entitled “epi DialektikEs” [ἐπὶ Διαλεκτικῆς ]  and “epi Tyrannou”, deploying his genitives startlingly.   [see below, Lemma 2, “Philip’s bold and repeated uses of the prefix “epi-“, getting bolder on a pace with the devolving of Hellenic prose.   Heading downward, into mere Hellenisticising prose”].  

Scope of this website.

The main purpose here will be to furnish Plato scholars and students fuller access to the lead manuscript of the Family II ms., which resides in the San Marco Library in Venice. This is the lead member of one of the three ‘primary’ witnesses to what Plato actually wrote, and at this time there is some urgency about making access to it easier and more direct. Very good mss. are already online both in Paris and Florence, and others may soon follow. But as yet the one presented here is not very directly accessible. It is usually called “Venetus T”.

This website will supply both an index to the all dialogues to be found in Venetus T, and good images of a select set of these same works of Plato. The site will also provide some room for posting interpretative writing about Plato. Both your interpretations and mine. The images of the texts themselves will not be modifiable.   But few restrictions will be placed on the range of our exegeses, beyond those of WordPress.

A further purpose is to give an assist to the Oxford editors now working to complete their 21st century OCT edition.  The idea is to give both a wider and a more direct access to them and to other scholars, access to high quality images of this lead member of Family II.   This extra access will compound in a natural way if others take an interest.

If this proves helpful to the OCT editors, a further purpose will be to supplement the base of scholarly information on such lexical peculiarities as are associated with this Family II of mss.   I refer especially to special variants patiently collected and published now some 40 years ago by Leonard Brandwood in his Word Index to Plato.   Quite specially this website will assist in enlarging the list Brandwood presents on pp. xxvii,f, of        αἰεὶ   ,    δαὶ     and   δαὶ  δὴ  .     Other lexical variants such as those listed by Koniaris in his edition of Maximus of Tyre —    ἐς and εἰς  in addition to   ὕος  and  ὕιος .   All of these markers can be grouped under the description “Iota-added lexical variants”.   Some are not truly at home in Attic, or anyhow not at home near the end of the so-called Theban Hegemony.   So they may serve as discriminators of dialectal differences, or discriminators using known shifts of a diachronic type within a given dialect.

Another purpose of the present website is to underpin a more detailed study of various textual matters local to Sophist, its chapters 37 and 49 notably.  I will not hesitate to use Stallbaum’s traditional chapter articulations in describing these texts.  Chapter 37 is the one which includes the rhetorically provocative reference to Eurycles of Aristophanes’s Wasps.   Often verse writers for the various theatrical stages were sources for Plato’s allusive prose.   Chapter 49 includes a tellingly placed   γε μὴν, a phrase which Denniston proves was a predominantly Xenophontic mannerism, — and other pointed indicators.

Although the new edition of the OCT Plato has already printed its Vol I (1995), including Sophist, Vol. II and its successors have yet to appear (Republic excepted).  Thus Vol II with its expected texts of Parmenides, Symposium and others is still on the waiting list.   Scholars have frequently expressed reservations about aspects of the old Burnet edition.   Textual issues, some new since 1995, can be better resolved, if a larger public is given better access to Venetus T.

Of these, some key items fall within the texts of Sophist, Symposium and Euthydemus.  This last is a dialogue likely helpful in resolving issues about Plato’s chronology, especially during his ‘Early Academy’ period, prior to Politicus, Philebus and Laws.  Some of the needed extra work will best be done following the lead of Duering on the side of biography and history, and following the lead of Ryle, Huby, Barnes , Brunschvig and various recent authors on number theory and the continuum, on the side of Dialectic and ‘exact sciences’.

Malcolm Brown   09 May 2019