At other times, the scribe may adjust the ‘kerning’ to form a kind of ligature, as here:
My marginal comments seem now more broadly based, in a pair of ‘libella’: Epinomis and De Mundo — with Phaedo’s insertions to Phaedo ch. 58 ad fin and 59 ad init.:
SLIDE1 Blass’s edn of ars astronomica, 1887, pp 5-6
We have two strong testimonies, from JBurnet and Ulrich von Wilamowitz-Moellendorf, pointing to the existence of a personal relation between the two leading intellects working alongide Plato at the Early Academy — Aristotle and Eudoxus of Cnidus. Here you will see the evidence, in Burnet’s 1900 edition of Nicomachean Ethics, at 1172b, its Book X:
Wilamowitz (cited in Burnet’s EN 10) on personal relations between Ar, Eud
Eudoxus’s work on the anaxagoras-style “homoiomereiai” expressly in Euclid 12,3
homoiomereiai slide of Euclid 12,3
homoiomereiai and ‘mixture’ theory, schol to Met. 1079b
SLIDE4 rep 5, ch 20, Shorey r4
9.viii.20
plz. see OED entry for ‘plumb bob’:
OED s v ‘plumb bob, with my notations
A dissertation of nearly a centenary ago now spotlighted a habit of High Attic prose style, at least in its most highflown: ‘Alliteration bei den Drei Tragikern’ the author called this. It will have required an effort for the researcher to try to find a better case than this following in Philip of Opus, a kind of “fourth tragedian”. Less flattering to Philip and likely more accurate given his grotesquely repetitive phrasing at Epinomis 973c8-d1 following close after another alliteration — also using the same consonant! — often Philip is flamboyant in his verbal wizardry. He indulges in a more extended assonance/alliteration in the work I judge to be also his: at De Mundo 399a14 . The rhyming words here are “akosmia/kosmos/akoloutheia/akolasia”. It is as if he were purposely sounding foolish, by gathering an overabundance of word-plays: Saturnian priests were apparently in these same habits, as a historical companion from Oxford Press explains — some generations after Philip and Aristotle. A fragment from Sophocles seems a caricature of comedians.
please look, especially if you think me to be exaggerating about the excesss of word-play:
akosmia calling the Pan by the name ‘Mundo’ i e Kosmos v.20 r5
yellow circle zenith, plumb bob, paired _sticks of Eudoxus_, enlarged
broader view of astronomy lab and its practitioners here:
yellow circle zenith, plumb bob, sticks of Eudoxus r2
yellow circle zenith, plumb bob, paired _sticks of Eudoxus_, enlarged
broader view of astronomy lab and its practitioners here:
yellow circle zenith, plumb bob, sticks of Eudoxus r2
10.vii.20
Use of a ‘chisel’ is connected, and rather directly — to Plato’s ‘gold example’. The man performing deceitfulness wants to take unfair advantage of gold’s foundational feature, its having no least part, but is so constituted as including a universal goldness in every ‘shaving’ or ‘comma’: their foundational feature is the precise etymological meaning ‘like every other shaving, and like the whole gold coin, it is all pure gold.’ I believe an Anaxagorean form of ‘abstraction’ to be under review here. Eudoxus wanting the least part, if any there be, of the Idea of Whiteness being fundamentally like all others, and like the Whole Idea, Whiteness Itself, mixed together with things such as are large enough to escape above the bar of the ‘unclear’ or the ‘unperceivably small’ or fully obscure-to-sense. Eudoxus’s theorems now in Euclid XII, 3 and 5 are explicitly ‘homoiomeric’ about solids, and their infinitely continued subdivisions. Shavings we may call the below-notice levels of this continued ‘salva qualitate’ level of smallness inside the mix.
homoiomereiai for JBarnes in the Anaxagorean infinity if bits & pieces
Plato refers at Timaeus 52b2 to a certain ‘logismos nothos’, combined with ‘anaesthesia’. Interpreters often think him referring to aesthesis rather than to an-aesthesis. But he may be pointing in the direction of Eudoxan ‘similar parts, resolved via triangle-based pyramids’ and to the Eudoxan theory of forms, alluded to in Parmenides. Again the evidences are written.
OED s v ‘chisel’, colloquial verb, relating to coins in Roman times, r2
8.vii.20
Here you can see a short ‘aside’ on the subject of ‘successors and pseudo-successors, ancient and modern. In Bk V of Rep. he is sharply critical of ‘technudria’ (little arts) and ‘philotheamone’ (spectacle seekers) — 475E.
Proclus’s comm. on Euclid I, its palinggenesis
8.vi.20
Historians of mathematics whom I have consulted on the matter have been to a one convinced that Book III of the Elements is reliably traced back to writers very near Plato and the very young Aristotle — at the Early Academy near mid-4th century BC. There is some uncertainty and further discussion of this is ongoing still in 2020, about precisely where the work of Theaetetus belongs, within the litany of mathematicians set down originally by Aristotle’s student and colleague Eudemus of Rhodes. The date of Theaetetus’s death, early on in the scholarly discussion set to 369BC, remains a matter of lively presentday discussion amongst classical scholars. Strong arguments have been presented for pinpointing his death decades earlier. However this may be, this litany of early mathematicians is repeated and discussed in some detail by Proclus, his Commentary on Euclid Book I. This website will take it as one key point the dating of work within Books III , X and XIII of Euclid’s major work. This will require detailed attention to the Scholia to Euclid, and to his texts also. Here is a sample, from late in Book III, which will have relevance to both the logical and the sequences, both the sequence of history of mathematics, and that of the internal stemma of argument-structure. Here is a sample, which exhibits both:
Proclus, as officer within the succession of heads of the Academy (his standard descriptor is ‘ ‘, meaning just that: as Pope Pius XII was official successor Vatican, so Proclus in the Academy. One might expand the metaphor with help from both the ‘philosophenmosaik’ in Naples [a primary theme here at youngersocrates.com] and from Rafael’s famous mural. Men of the eminent stature of Michelangelo and Leonardo carry the special signifying weight on this side of depictions of Plato’s school. Here again we have standard descriptors in ‘divine’ Plato and ‘inspired’ Aristotle. It is a very Greek set of ideas, this of a Diadochos following on certain progenitors, higher up than mere Heroes or even Saints per se. A little etymological sidelight can help here, a comment on the name ‘Desdemona’ Her roots are a pair of Greek words, the first part being ‘fear of’. The second goes back to demonology, or above-mortal sources of inspiration.
Few would begrudge to him what E.R. Dodds claimed about his central ‘person’ (“Missing Persons” 1977, its final chapter) an indwelling ‘demon’, making use of Dodds’s name. Was he not patient and passive and experiencing some form of trance as he cried out words [in Greek, of course] — words from the chorus of Euripides Baccae ? He fairly exploded, and passively observed as there coursed out of his lips, there as he did a para-psychology exorcism. His report has him performing this exorcism, whereupon presto!, all the 4-footed earth-crawling vermin were tele-transported off the premisses. Clearly not Dodds’s own person at work; rather the indwelling demon of whom he writes, it was ‘using my name’. Odd, but likely true. Recall the desi-demonion that our colleague Socrates used, or that used Socrates. This Renaissance Man Dodds turned up historically somewhat too late to be a proper part of the Renaissance. But if we prescind from history, he stands as a spirit, capable of publishing an anti-Nazi screed warning in the London of war-torn 1939.
Europe has known wars aplenty. A certain jewish man in Amsterdam, when I spoke to him about ‘Armistice Day’, made a telling remark. This conversation took place place aboard his floating rental houseboat in a former jewish ghetto within Amsterdam. I had noted that in the US of A we commemorate Armistice Day, as near as possible to 11 AM local time. He posed a sharply worded question: ‘which war was that, settling of which is today commemorated on 11 November’? Probably 2010AD. Our family had invited a guest aboard, a man from Massachusetts and not so incidentally with a jewish ancestry. The landlord had named his houseboat ‘Te Koop’ which I later discovered means ‘For Rent’. In any case this houseboat owner was not entirely unlike Spinoza — about whom our landlord knew much more, as soon came out, than he did about the Versailles Treaty. The conversation stayed up at the trans-personal level, however, so it never came up that some of the inequities within The Versailles Treaty may have impacted a man his age (about 60). Spinoza and this man were rejected — by the ‘monde’ of the West of his day and by his own flock or school, or tribe. In those ways Spinoza and Dodds — and Oliver Sacks too, I may add, Sacks the grateful-for-life man — they all stand shoulder-to-shoulder ‘brother alongside fellow being’. They all went out, or were soon to go out, in a way our anglo-American mathematician Lord Bertrand Russell admired. Russell cordially disliked the hyper-Christian Leibniz, whilst he just as cordially revered Spinoza. I went ashore and fetched a photocopy of Russell’s popular book [from Free University’s copy] on Philosophy of the West. which my landlord read eagerly. Quasi Pythagorean, we may think these people, successors of Pythagoras. In Russell’s case, this traditional fealty was publicly avowed (preface to his Autobiography).
Some would certainly think it presumptuous to construct parallels between ecclesiastical and secular this way. and of the divine to the merely super-heroic amongst or mortals, stand-out from the flock or herd though they surely are. The Renaissance Human was more-than=human, even where of impiety in the very in his official successor. No unclarityissues concerning quadratic and cubic irrationality, to include specifically what Plato has his young Theaetetus point to in the classical locus of ‘dunamis’ theory in the form we now have elegantly preserved by recent editors Heiberg [late 19th cent.] and Stamatis [late 20th]
5.vi.20
Can Hesiod have charted, prophetically, this theogonic procession of generations? Can his prophecy have foretold an early Academician’s fondness for alliteration (just like the fondness of Die Drei Tragikern up through Euripides)? If so he will have made an impact on this prodicus-like wordplay which makes Saturn the son of Time. Producing such progeny, can Time have had a parellel life, otherwise paralleled by his Timaeus ‘ active diagramming Eternity,’ or being Eternity’s moving image ? To the side, there is this further item to report. Walter Leszl and I, then both junior fellows at Center for Hellenic Studies, made ourselves ambassadors to Harold Cherniss, in his Princeton Institute office. It was in April of 1970. We two ambassadors pressed him some (I recall myself pushing back rather hard after his first reactions had been defensive and seemingly a bit irritable. Leszl’s specialty was Aristotle, Plato and the Early Academy mine. Cherniss gestured toward the massive personal library which he had located so as to be what physically surrounded him, saying (I paraphrase) “Here you can look directly at my intended Volume II of “Aristotle’s Criticism of Plato and the Academy“, still in process of being produced”. The two of us later agreed in thinking this a somewhat evasive way of speaking; why not publish Volume II after all these intervening postWar decades?
I then posed to Cherniss this question: Can the Timaeus serve the modern reader as a specimen of what in the Sophist Plato seems to be somewhat tolerant towards, namely a non-idol branch of his divisions where one might locate myth-making and Iconic diagrams ? Plato seems quasi-empathetic with what might be poetry rationally defended. His phrasing, which I quoted to the entire office from memory was the not-sophist’s kind of defensible ‘mythmaking’ or ‘mimesis’ ? ἱστορική τις μιμήσις is the Sophist’s phrasing for this idolatry-free mimesis.
The conversation then trailed off into a Departure Scene and sociable banter. So much for Volume II. Now, some 50 years later, and the internet’s ways of doing the alternate-Princeton work of Hungary-based Prof. Harnad, we can do ambassadorial work of the very type we first heard about from him at Princeton: SCHOLARLY SKYWRITING.
All 3 ambassadors, if you add the virtual presence of Prof. Harnad, seem to remain alive today, though the farewell piece by Taran, also then of Princeton, “Plato amicus, sed…” , — with its various autobiographical suggestions –had yet to be published. Cherniss’s name of course lives on, but chiefly in memory or in the quasi-memorial form of Jacob Fink’s 2012 volume from Saxo Institute, on Plato, Aristotle and dialectic. And neither Cherniss’s Volume II nor Einarson’s study of EPINOMIS has yet done what Younger Socrates called Ἀναφαίνεται , a specialist word amongst astronomers for what happens to us all daily — the stars of the night heaven are occulted by sunrise, and then re-encrypt themselves again the dawn following. Eudoxus had a title of his book ‘concerning the de-occultings’. Einarson’s hidden work may yet de-occult, with much effort by humans and with some encouragement from classicists.
Plato is likely aware of the god served especially by Saturnian Priests ? These were writers who out-Prodicus’d Prodicus in their obsfondness for Alliteration. Do however credit Plato with the crowning achievement in the line of alliteration’s cousin, Assonance. Can any tragedian compete for an over-clever Assonance with Plato’s REP., Bk6: “E)PI\ TA\S TW=N PLOUSI/WN QU/RAS I)E/NAI, A)LL’ O( TOU=TO KOMYEUSA/MENOS E)YEU/SATO . . .” [489b 7-8] ἐπὶ τὰς τῶν πλουσίων θύρας ἰέναι, ἀλλ’ ὁ τοῦτο κομψευσάμενος ἐψεύσατο… (sic) here you will see the Kronos/Chronos wordplay, by Philip or Amphinomus:
(bis9) DeMundo 7 and its rarities ‘philios’ ‘sOtEr’, all neologisms
3.vi..20
Causing a string of letters to come apart, but only at that word’s joints may be just one thing. But it is quite another to ignore internal articulations, as Julian Barnes wrote recently in his book “Nothing[ness] to be Frightened of”. It is a book about various ways of coming to terms with one’s own dying. He has a dramatic flair, Julian does, and has an author busily doing his writing activity when, — FLASH — he dies at once. In mid-word even: it gets logged on his typescript at the word-torso ‘wor’ The END, finis, that’s all he wrote, and was. Prodicus the seductive would be proud of such a wordsmith, or (pardon the expression) a wordsm .
So would Philip of Opus, who wants to recite names, in his p. Kosmou , and to create clever variants on public or intra-academy schemes of naming, often drawn from the hypercleverness of Cratylus — which manages to decompose ‘swphrosyne’ into a pair, SWTERIA+PHRONESIS. Or, equally overclever, decompose ‘noEsis’ into ‘tou neou+Hesis’ Amongst the various meanings of this last phrase is this rather naughty one: OF THE YOUNG MAN, A CRAVING (!).
Plato seems to have had a personal craving for a young man Aster, whom he nicknames as Iros in ILIAD is nicknamed too, after his expertise, in our case Astronomy. So it is written in Epigram1 attributed to Plato by John Cooper (Hackett 1997) Can Aster have been a disciple very near Plato personally, like the certified astronomer Philip ? In any case it is Philip who calls himself in the final chapter, one filled with astronomy, the final chapter of EPINOMIS, by phrasing we could render: the ’eminently wise, sophwtatos truly astronomer man‘ [=Ὁ σοφώτατος ἀληθῶς ἀστρονομος ]
In Philip’s account in p. Kosmou, some individual gods experience decay of consonants within their names, ‘Kronos’ decaying into ‘Chronos.’ One prominent individual is the chief sufferer under his own ‘polyonymy’ [this is a rare word in classical Greek], Zeus SWTHR or Zeus HETAIRIOS/PHILIOS (Bekker 401).
Do please consider the ms. evidence of some super-refined, we may even call it Rococo in its Prodican mannerism, of lengthening a word by inserting an Iota above the line in the middle of a 3-letter long word. Maybe its phoneme is nearly a hiccup or gastric belch ? Our best ms. of Philip’s work, the one some have facetiously nicknamed ‘the thirteenth book of Plato’s 12-book work NOMOI’ That is, Philip’s Epinomis. It is a central point at this present website, the equating of Philip, Amphinomus and Younger Socrates. Speusippus must have known all 3 men well, and known also if more than a single name was taken on by one or another, or still another.
There may be in addition a sly allusion to a man sometimes called ‘the Aster who can attract all eyes, including those 10,000 eyes of the star-struck man Plato. This allusion seems to come near the surface in a stretch of the Astronomy chapter (i.e. Chapt 10) of Republic VII a man whose name-fragments trace to the word-pair SWZEIN+KRATHS, at Steph 527e2, just 2 lines above the manifest allusion to the man there called the ‘true astronomer’, namely EU+DOKEIN: Philip=(SocratesAlternate). Part of the proof is this flock of supra lineam Iota marks, a mere quarter of the 4-letter word AIEI:
(bis5) semi-Aeolic AIEI in final chapt. of Epinomis, at 992c1 length=3.5, rev6
Consider further this evidence, based on a persistent unorthodoxy of Attic spellings:
(bis9) Plato’s AIEI citation from Hesiod at Symp. 178b6, with note to Euthyd 296ab
(bis5) semi-Aeolic AIEI in final chapt. of Epinomis, at 992c1 length=3.5, rev6
1.vi.20
The material about religious belief from Tetralogy Nine rivals that from Tetralogy Eight. Drawing on a favorite specialist term ‘episkepsis’, which comes to dominate the infinite-process steps in all-but-one proposition of Euclid on Cones and Cylinder one is enabled to put it ‘nearly a Whole Heaven remote’ from Euthyphro.
I call special attention refer to Books 12 and 12a of the Heiberg edition(s) of this work. Much more work is now needed, possibly by T. Echterling and ‘those around him’. Some of these latter overlap with the ‘flock’ or ‘cohort’ in Paris and Helsinki. As I now judge this to be, Heriberg gets full answer to his implied question: what is going on here in 12a ? He wrote that its purpose is near unintelligible: its Zweck seemed kaum erkennbar. This little appendicated piece to Euclid12 may be by Philip of Opus.
Likely Copenhagen/Saxo alongside Paris and Helsinki can be co-hortative, conceivably some near Cambridge USA in shifting the ‘home’ position ahead. What Nancy Demand calls metoikesis. As I diagram this, the needed move is leftward. From the North ‘when one looks downward from above, this is rightward. New Socrates, the one emerging now, is at the ready. My hunch is that 12a has like the same relation to 12 which the present editions of Epinomis have to present editions of LAWS
27.v.20
If (as I believe true) this below quip about ‘akosmia’ was written by Plato’s student Philip during the lifetime of Plato, and if (as I also believe true) my friend and colleague from the Massif Centrale Jonathan Barnes has the right range of dates for ps.-Aristotle’s Peri Kosmou, namely -350 through -200, many of us, myself included, will want to locate its date at the very earliest point, the mid-4th century BC, Plato still alive.
akosmia not so when I call the sum-Pan by the name ‘Mundo’ i e Kosmos v.20
This little pseudepigraphic tract on the World (or Cosmos or on “Heaven Entire”) has its author achieving his wordplay and his witty multi-level jokes, but only after paying a high price. I mean a price in the matter of an anomaly or inconcinnity inside logic theory: He commits a serious confusion, confounding his mentions with his uses. He mentions “akosmia” (indispositioned) and “akolasia” (indisciplined), and yet deliberately omits any markers showing that it is the signs, not the things-signified, which are at issue. The first item, he says, ‘follows’ from or after the second, the indispositioned from the indisciplined — alphabetically this is true, in Greek or in various other languages.
Here is an analogy, our joke that goes : “sure I’ll help find the sympathy you’re seeking — You’ll find it very near the end of the ‘S’ section of our dictionary here’ [pointing to Timaeus-the-Sophist’s dictionary, or the SUDA. By this we mean its physical letter ‘Sigma’ right down here]” A more compounded example can capture more of Pseudepigraphus’s witticism, trying to capture some of the meanings. “you can see that disunity follows dissipation as we may say without any disrespect using such names” .
Douglas Hofstadter exercised his own mathematician’s ingenuity in forming a word for looking into theoretical causes. He called sequences of this kind “Seek-Whence’s.” Our present historical seek-whence points back to Philip of Opus, who is lightly veiled behind the anonymity of our author. I will advance several reasons for this in due course. Meantime these following summary points may suffice.
(1) The time of composition will have been before Aristotle’s Posterior Analytics, to which the Eudemus report refers explicitly [Friedlein 384,7-8] Scholars recently have often renewed these references to Eudemus and his recent pythagorean colleagues, several including Aristotle with close acquaintance with pythagoreans and their manners, including in matters of mathematical terminology.
(2) When Eudemus echoes material from his own 4th Century milieu about the famous theorem, that the interior angle sum of the triangle, it will repay the effort to reconstruct some or all of the 16 specimens of his dual forms [Friedlein 379,1 – 384,21] Proclus relays reporting from Eudemus of Rhodes to the effect that Philip had made various comments to Euclid I,32, a version of this proposition.
(3) Yes Euclid’s version differs very slightly in language and formulation. Oddly enough our later authors Proclus and Euclid, from whom we might expect a plainer dialect, indulges in an elaborated series of dual forms, echoed via our monastic ms. from Eudemus and from Aristotle, whose wanted the dative plural of our word for ‘two’ to match older pythagorean manner of phrasing, thus his ‘[δυαῖν] ὀρθαῖν’ Friedlein 384,12 — cf. 299,9 for the ‘δυαῖν’] later and Alexandrinian language before he had written this little 7-chapter tract that Timaeus, would know as “our alphabet”.
(4) elsewhere in his Commentary [Friedlein p. 52] Proclus reviews arguments for avoiding the “pathemata” and too much attention to the “organa” by which we, as mathematicians or astronomers receive our data.
A little harmless aside here, parallel to the main task: Jonathan Barnes is as hellenic in his lexical interests as is his twin-in-lexicography Julian Barnes. Witness the famous never-ending “END” to Julian’s recent (yet ongoing) book on a subject we may call Barnesian end-of-life questions. There is a causal sequence which takes the listener or reader back to Odysseus and the second of two logician-jokes he plays on the one-eyed or no-eyed giant POLYPHEMUS.
Recall the first paradox from Odysseus : it was perhaps prefiguring DeMorgan’s naming the editor for that singular edition of Thales. It got prominence much earlier than the epic about the hunt for Thales (Itinerario de trenes, 2002) — ‘2 volumes, Folio’ — of Thales’s quasi-complete works. DeMorgan called him Prof. Niemand ( = call me ‘Nobody’). Where was the location of the actual publication ( = call it ‘Nowhere’). It is a set of expressions that do not truly refer, not at all. But what about the #2 point, applicable after Polyphemus has had the poignant first encounter inside Homer’s cave: I am deliberately making you, O Nobody, my final meal, final for this little flood or flock of quasi-sheep, — comedians such as Mark Maron have since A.D. 2005 called us ‘sheeple’ — all of whom I intend, O Nobody, to devour !
I do not hold that the ‘incertus Auctor’ of the π. κοσμοῦ is to some low level of confidence Plato’s amanuensis Philip of Opus. After all many another tract fits comfortably under SUDA’s final phrase ‘…and many others [sc. works]’. I hold, rather, this to be true, but at a reasonably high level of confidence.
Two main thoughts promote my own confidence here: (1) The little and syntactically bumpy anacoluthion Plato added to his Timaeus 28 b2-4 near writing Letters #7, #8 is aimed polemically against Philip and (2) the multi-faceted joke about ‘akosmia’ and ‘akolasia’ and the alphabet is a snappy retort to the effect ‘I know how to entitle my DeMundo, thank you Dear Prominence here in our flock of academicians, and it’s a far better than the unCosmic name than your piece entitled ‘Timaeus’ !
Date of composition of π. κοσμοῦ same Olympiad as the Year -349
akosmia not so when I call the sum-Pan by the name ‘Mundo’ i e Kosmos v.20
[anacoluthon aimed at my friend Julian: have you recently met any ps.-Ar. “de-occultations” try Bonitz s.v. ‘anaphainesthai’]
Please give it the necessary close look, a look at this snapshot of the TLG text of Euthydemus. In particular please look closely at that dialogue’s cluster, or flock or herd of the specialist term aei/aiei,
AIEI, clustering in Ch 22 of Euthyd
23.v.20
If (as I believe true) this below quip about ‘akosmia’ was written by Plato’s student Philip during the lifetime of Plato, and if (as I also believe true) my friend and colleague from the Massif Centrale Jonathan Barnes has the right range of dates for ps.-Aristotle’s Peri Kosmou, namely -350 through -200, many of us, myself included, will want to locate its date near the very earliest, the mid-4th century BC.
This little pseudepigraphic tract on the World or Cosmos has its author achieving his wordplay and his witty joke, but only after paying a high price. I mean a price in the matter of logic theory: He contrives a serious confusion of his mentions with his uses ! He mentions “akosmia” (ill-arranged) and “akolasia” (ill-disciplined), and yet deliberately omits any markers or hints that it is the signs, not the things-signified at issue.
There is an analogy to our little joke : “sure I’ll help find the sympathy you’re seeking — You’ll find it very near the end of the ‘S’ section of our dictionary here’ [pointing to Timaeus-the-Sophist’s dictionary, or the SUDA, the letter ‘Sigma’ down here]”. The seek-whence points back to what Philip of Opus, before that Timaeus, would know as “our alphabet”. This of course puts the answer into an inconsistency or inconcinnity with anything so to speak ‘here’, like you or me or our lower world of winds and disturbances like those caused. In other words we must return to the sub-lunar world that includes personal emotions, such as fellow-feeling, the sympathy which was the true quaesitum.
See if you can work through this following on “follow” and “furrow”, a little witticism more narrowly limited to the English language: my theories have it written by Philip of Opus, in his tract π. κοσμοῦ , very near the date 5 years after Seventh Letter. My date puts its writing while Plato is still alive, still adding some harmlessly distractive anacoluthia to his Timaeus [please see webpage of Timaeus ]
A little harmless aside here, parallel to the main task: Jonathan Barnes is as hellenic in his lexical interests as is his twin-in-lexicography Julian Barnes. Witness the famous never-ending END to Julian’s recent (yet ongoing) book on a subject we may call Barnesian slow-motion dying. There is a causal sequence which takes the listener or reader back to Odysseus and the second of two logician-jokes he plays on one-eyed or no-eyed giant POLYPHEMUS.
Recall the first paradox from Odysseus : it was perhaps prefiguring DeMorgan’s naming the editor for that singular edition of Thales. It got prominence much earlier than the epic about the hunt for Thales (Itinerario de trenes, 2002) — ‘2 volumes, Folio’ — of Thales’s quasi-complete works. DeMorgan called him Prof. Niemand ( = call me ‘Nobody’). Where was the location of the actual publication ( = call it ‘Nowhere’). It is a set of expressions that do not truly refer, not at all. But what about the #2 point, applicable after Polyphemus has had the poignant first encounter inside Homer’s cave: I am deliberately making you, O Nobody, my final meal, final for this little flood or flock of quasi-sheep, — comedians such as Mark Maron have since A.D. 2005 called us ‘sheeple’ — all of whom I intend, O Nobody, to devour !
I do not hold that the ‘incertus Auctor’ of the π. κοσμοῦ is to some low level of confidence Plato’s amanuensis Philip of Opus. After all many another tract fits comfortably under SUDA’s final phrase ‘…and many others [sc. works]’. I hold, rather, this to be true, but at a reasonably high level of confidence.
Two main thoughts (1) The little and syntactically bumpy anacoluthion Plato added to his Timaeus 28 b2-4 near writing Letters #7, #8 is aimed polemically against Philip and (2) the multi-faceted joke about ‘akosmia’ and ‘akolasia’ and the alphabet is a snappy retort to the effect ‘I know how to entitle my DeMundo, thank you Dear Prominence here in our flock of academicians, and it’s a far better than the unCosmic name than your piece entitled ‘Timaeus’ !
Date of composition of π. κοσμοῦ same Olympiad as the Year -349
akosmia not so when I call the sum-Pan by the name ‘Mundo’ i e Kosmos v.20
[anacoluthon aimed at my friend Julian: have you recently met any ps.-Ar. “de-occultations” try Bonitz s.v. ‘anaphainesthai’]
Please give it the necessary close look, a look at this snapshot of the TLG text of Euthydemus. In particular please look closely at that dialogue’s cluster, or flock or herd of the specialist term aei/aiei,
Now in Chapt. 22 of Euthydemus, which runs to only 32 lines, it is given a striking emphasis by being put inside quotation marks by the always-careful Oxford editor John Burnet.
Such ‘encrustation’ is of course open to a reasonable reader’s scepticism. John Cooper inaugurated this point of criticism in his Complete Plato, (Hackett, Indianapolis 1997). On the other hand this is Plato’s way of writing our ‘eternal’ or ‘always’.
This is clearly a term Plato puts much emphasis on. Further, it is a concept close to the heart of Amphinomus, who is well known to Proclus and other commentators on Euclid. It is likely he to whom we owe Scholion #18 to Euclid I, which complains about the opening proposition. What complaint, exactly ? Well it is not a Theorem proper, but rather a construction. Thus its product appears to be one of those hitherto-non-existent items, just ‘at this moment’ built by our geometer. He is scornful toward the ‘tote=trigwnon’, i.e. the ‘then-triangle’. It is as if Triangle weren’t an eternal object !
Plato had used the term in many of the centrally platonic contexts — well over 700 specimens of this occur corpus-wide — either in its 3-letter or its 4-letter variant.
This seemingly small variation of spelling has a very direct bearing on the report in Dionysius of Halicarnassus — the remark that Plato was fond of and preferential towards a diphthongal pair of letters, ahead of using the simpler monophongal variant. This latter variant, == which I have echoed here just a dozen or so lines below this — harks back to an earlier, Pre-Plato Attic.
Quite possibly young Theaetetus grew up writing this older style of Attic in Sunium, as witness the 70% preference shown at the beginning of Euclid X, where it very likely to be his authorship. This is exactly where potentially infinite ongoing processes come over the mathematical horizon in early Greek mathematics. the Theaetetus
On the literary side a chief model of that centenary-earlier writing is Thucydides, who favors it by a 128:0 ratio over the simpler form ἀεὶ .
Here is the snapshot of our ‘flock’ of αἰεὶ
AIEI, clustering in Ch 22 of Euthyd
Some Prefatory notes
We may here venture to draw from a later source, — from late-ancient times of The Church Fathers, also a later stage of the Greek language’s development — still and yet this following snapshot from the Patristic Lexicon is of great interest. John Adam’s remark to Republic’s Book 7 is of great general interest. It was about Plato’s wisdom, its sometimes saying of the ‘Savior’ aspect of our Socrates. Adam writes that it was of ‘prophetical import’;we make this clearer from a standard glossing of the word προφήτης [‘prophEtEs’] . We seem to shift perspective, to a standpoint at least as close to our day as The Church Fathers.
prophet defined as ( pan-)sophwtatos, by Clement
Now this Socratic era is regularly referred to as ”fifth Century”. Socrates death sentence at 399 BC could not be much later, without so to speak slipping into the fourth, which was the century of (most of) Plato’s life. Thus he was still writing at a furious pace in the “mid-fourth”, and we may have the ‘fifth century’ finishing itself in final form right at elder Socrates’s trial and death. However, that era stands distant from our present time by fewer than 18 of the units which DeMorgan helpfully gives to 100 year sub-intervals of prior time periods. DeMorgan defines his ‘centenary’ as a count of 100 years. Flavius Clemens, or Clement of Alexandria, thus writes at a time fewer than 18 centenaries now. It DeMorgan’s centenary units insulate themselves from our customary division B.C. from A.D.
We may usefully compare time-reference schemes, via Plato’s time of writing, in or near 354 ‘BC’), writing his Seventh Letter. We are as historians are in duty bound to re-paganise his personal calendar, thus make it recognizeable more clearly to himself — and also three other published quasi-theologians Empedocles, Plato Philip of Opus and Aristotle. To reach what ER Dodds called the “later years of the fifth century” (his Gorgias edition, p. 14). To be sure, Dodds was’ fully aware of the oddity of his own phrasings, such as the phrase ‘the early eighties’, a phrase he uses in a footnote. He takes care to make it clear for us, in his note 1 to p. 34 . Plato’s contemporaries cannot have had ‘conscious transition’ between 5th and 4th centuries BC.
Now drawing on DeMorgan’s term ‘centenary’ we can appropriately phrase this same point: we now experience a total backward interval larger than smaller than 23 Centenaries bit smaller than 24 Centenaries. Sub-intervals might best be reckoned down to one or several Olympiad units. These will not be a-miai units. Non-unitarian units to take a piece of ‘onomasia’ from Athenaeus VII, in a fragment he attributed to ‘Aristotle’ So when pinpointing the date of Plato’s writing Seventh Letter (354 BC) we may say ‘at most an Olympiad away from 23.5 Centenaries ago now.
That the time when there were foregatherings — i.e. flockings of a sort — of (1) a very young Aristotle, (2) a somewhat young teacher of Aristotle’s, Philip of Opus, and (3) an aged Plato then ‘in the sunset years of life’ as he puts it in LAWS. The earliest information from that Early Academy was likely not more than a few Olympiads earlier, h.e. 23.6 Centenaries ago. A little over a centenary back now, commonly known as 1893, Benjamin Jowett wrote a letter. He was proposing the idea to Lewis Campbell, a close colleague, a comprensive LEXICON to Plato, perhaps to run some 900 pages, to come out via Clarendon Press Oxford. His argument included the point that the “final ten years of a scholar’s life” might be well spent that way. By 1903 the proposal was in trouble — we may facetiously call it ‘early in the next century’.
The Campbell Lexicon has not yet seen the light of day. Two world wars did some damage there also. But still in all there has been less than a centenary back from the early efforts at world-dissemination of computer-assisted literary scholarship. A not often cited such early effort came from Prof. Harnad and his Princetonian concept of “scholarly skywriting” of the 1980s. Thus there remains hope for a renewed quasi-Campbell effort. University of Glasgow, where interest has been expressed on the Web, is one place this new Plato lexical research may yet surface. Gilbert Ryle, who once defended his research against the accusation “just lexicography” would follow this were one or several of our joint research flock to succeed.
A little PS may be in order here Curtis Wilson’s US Naval Observatory clock permits him to reckon out a star’s culmination on 20 June 353 BC, down to the hundred-thousandth part of a Centenary, an unit less than one afternoon or evening. Please give some study to this specimen of careful calculation, based upon Wilson’s near-Annapolis MasterClock, and locating the First Magnitude star in Serpent-Bearer’s head, when darkness was just arriving — in a part of Athens near Plato’s academy, as this is now agreed it was located:
calculation for June 20, -353 culmination of Alpha Ophiouchos-3
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Aristotle on an ETERNAL SOCRATES,&c, Met M5 1079b
unnamed’ persons over-eager ears and quasi-arts, e.g. writing comedotragic Didaskaliai (2)
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Aristotle and-or Philip doing Bonitz-collected etymologies 10-v-20
Aristotle, etymologies amphi- swzi- epi-
theaetetus, working at the dodecahedron, jpeg
philosophenmosaik, Archytoides added 8.V.20 r2
Why are these following two points documentably true ?
(1) in the dialogue Euthydemus comprising less than 10% of the total bulk of Plato’s corpus, do 50+ percent of his uses (or mentions) of “aei/aiei” occur, a whole mini-flock of them in one chapter (h.e. Chapt 22) ?
(2) why does our Ephraim opt for the Leon Robin preferred spelling in all but all of this flock ? Here you can sort over (=episkopein) some of the evidence, from the output of a computer search of this website’s ‘low-cost TLG’ file I have named, deliberately, TLG0059:
flocking unit, a flock of AIEI in Venice’s ms., Euthydemus, Chapt 22 296a r2
Plato’s favorite issue in solid geometry, DOUBLING THE CUBE — also at Polit. 266:
Hardy’s cube root 4, pure mathematics p 34 r3.pdf
Introducing quadrivium lover Archtytoides:
philosophenmosaik, Archytoides added 8.V.20 r2
We might imagine an EarlyAcademy scene in 1922 AD at the time when Ramanujan was still young and when he used variety of ‘factoring’ — a passingly odd variety. He subtracted 1000 from the ‘1729’ that had chanced to be the number atop his taxicab. He thus got the pair of ‘least factors’ (additive !) of that particular taxicab. Hardy was by that brave young man’s deathbed there at that very hospital.
Ramanujan remarked about his mathematical calculation that he had found the “least pair of additive factors, both perfect cubes” to be put together for that cab’s number. He was then, now nearly a Centenray ago [deMorgan gave reasons for preferring to write ‘Centenary’ rather than ‘Century’; think what that terminological improvement would do for E.R. Dodds’s saying what Plato was doing ‘in the early eighties’, or Thessleff’s think of the middle of that same unfounded decade? ]within days of his death then. Hardy was near his final bedside, and later wrote Ramanujan’s remark about the number of the taxicab deathbed all at the same time
Ramanujan’s death came when he was 32 ! Likely to be younger than Theaetetus’s. So also the eminent Iranian [babylonian?] mathematician likely also Maryam Mirzakhani of Century XXI AD, dead at 40 after she had won the highest honor in the world, a kind of Nobel Prize in mathematics.
All of this puts me in mind of a general sort of soul, call him Archytoides, familiar with the specialist term ‘dimoiron’ meaning our ‘two thirds’ which appears in the Theaetetus-Mirzakhani ‘only 5 such solids are possible’. This is the theorem 18a, postscripted to the end of Euclid Book — right where the young mathematician finishes his co-construction of Plato’s 5th and final solid. He complete’s his Platonic duty by comprehending the icosahedron in the sphere.
Curiously, a man named Amphinomus is reported in Proclus’s Commentary on Euclid I to have raised an issue, likely at Proclus’s Academy, raised this against Aristotle’s view, the view namely that no mathematician – just qua mathematikos – can ask the question ‘Why’. That would require him to be of a higher platonic rank, a Philosopher namely. Amphinomus reportedly retorted to Aristotle countering with ‘Why can’t I, and and yet save myself as pure mathematikos – for example what’s wrong with a mathematician, even whilst saving his rank and status, his asking WHY ONLY 5 REGULAR SOLIDS AND NOT INFINITELY MANY, — LIKE REGULAR POLYGONS, SAY A MYRIAGON, IN THE CIRCLE? [Of course Proclus makes no reference to Descartes’s myriagon — enough to have his philosophic Noumenality intact, and continue, — just like Philip of Opus — to restrict his doing geometry ‘insofar as it furthered Platonic philosophy’. The SUDA was busy with its item about ‘philosophus’ when it oddly starts describing Philippus of Opus.]
Back to my epithetic-named Archytoides: the octave-tunings that have come down to us (thanks to Prof Barber) from Archytas, pythagorean friend of Plato’s, include the familiar standard ‘diatonic’ with its elementary sounds which we may locate on ‘middle C’. This means in turn that it has the major ditone, Do – Me and also the next higher octave, Archytoides needs no back-metaphrastic to understand our notation C’ – E’, in some way hyper-aurally ‘the same interval (diathesis)’ as that earlier Do – Me but in fact it is doing a Me’ – Do’ vice versa.
The EPIMORIC exponent, which is the ‘improper’ fraction 3/2, requires both a subduplicative and a triplicative operation, if cube root 4 or its vice versa term cube root 2 were to be reckoned out. All of this starting from the Do-Re-Me diatonic scale inside what Aristotle calls the octave’s Essence.
Please see this from GH Hardy of Oxford, 1921
Hardy’s cube root 4, pure mathematics p 34 r3
Here you will find something of a ‘roadmap’ leading from Theaetetus’s mathematical work now lodged in Book X of Euclid’s Elements and his co-constructions of (including inscriptions into the sphere) all 5 of the so-called Five Platonic Solids — Book XII of that same work:
[03.v.20]
Do try a search, O Reader, in this test file from Republic, inside TLG0059,
try searching this following 3-character string: 475
This MS Word file is alas in a difficult old code, but the best I now have available: beta-code of the TLG’s text of REPUBLIC. This file pointedly makes an inclusion of my scholarly insertions [I overlay the strikeover marking to signal to you, an initiate, that I intend by ‘scholarly’ merely my personal low-level claim, differing as the ‘quasi-X’ differs from the mere X !] The quasi-Socrates or new ‘Socrates’ whom I detect between the lines in of Rep. VII: in particular I detect him just above line 527e3 and yet just below e2. Adam wondered about Antisthenes. We make a near-fetched rejoinder here: I am advancing my candidate, a Thesleffian ‘ Mr. NewSocrates.’ You will find him Present everywhere at this present site, though under many names, a polycratic agent he surely was, the polyonymously named Amphinomus .
Also known as Socrates Alternate.
This strike-through marking is newly coined by myself today, viz. 5 May 2020
Aristotle is likely pointing a quasi-YoungPlatonist finger at his teacher Philip in the following text [or perhaps only the revised-Bekker text, — you be the judge, O Reader] of Ethica Nicomachea I,9:
philo-theamoni in 2 variant mss of EN I, 9 r2
In the below moderately user-friendly form of a MS Word listing of textual lines. Do click on it if you have ‘WORD’ in some recent version; then kindly follow these 6 steps :
- after seeing the numbered file, beginning from start of Euthyphro at line 1, then–
- type (cntrl) + f, or the standard way of saying ‘I am trying to find all occurrences of this following word or phrase…’ then–
- try to get a good response by first looking in upper left corner of your screen for an open rectangular box, which will be awaiting your reply, below the word Navigation then–
- try as a first example typing into this box these 4 characters: a)ei This, as you know, is Plato’s favorite way of saying our ‘always’ or ‘forever’. Presto change-o then–
- see if you don’t get a response, where all of this first page of results are highlighted for you, and finally then–
- See if you can scroll down through successive pages, until
- you have seen all 37 specimens in Symp. of [the OCT 1995- their variant of ‘always’, which is identical to this TLG variant of] Plato’s word for ‘always’, h.e. A)EI.
In Greek this 3-letter variant looks like this, (after the final grave-accent has been re-added):
ἀεὶ
Here is my own — much boosted and much TAL-modified — rendition of their TLG text, with my line numbering and some of the likely page numbers from OCT’ s forthcoming Tomus II, inserted by myself:
We need to move forward from Od. Book XVIII to Book III where At line 26
Athena introduces Telemachus the Thoughtful early in Odyssey Mr. πεπνυμένος
Telemachus wisely called by Athena, PEPNUMENOS Od iii.21
This epithet is hyper-special. He shares it with — of all persons, AMPHINOMUS ! The Homeric text is also the very word there (18.125): πεπνυμένος
Telemachus wisely called by Athena, PEPNUMENOS Od iii.21
It requires more than the typical space for commentary, this near-final chapter of Republic’s Book VII. I am in the belief that this astronomy chapter requires at least two special extras: (1) a detailed discussion of a certain singular scholion to the mixing bowl chapter of Timaeus and (2) a detailed analysis of the line in the ‘astronomy-geometry’ sections of Chapt 10, with particular attention to the ‘myriad eyes’ image at 527e2. The scholion to Timaeus fastens itself in a curious and intimate way onto the line at Stephanus 42b1 with multiple uses of the same verb ‘kratein’.
allo up’ allou and multiple kratein’s, Rep 4, end
Craters were explored by direct inspection “if someone were to look [at True Earth] from above,” ei tis anwthen thewrito‘, Phaedo 113. Here is a public broadcaster’s transcript of the exact seconds of the joint search by Lovell and Anders, both generals, a few days short of the end of calendar 1968:
apollo 8 Lovell, Anders, earthrise image 24-xii-68
That portion of Timaeus is adjacent to the references to instruments of measuring time measurements and assorted mixing processes are brought forward. Also the way of comparing the numbers of souls, some above and others he has as companions herebelow.
Tiresias factored out gender, was blinded for it — Thesleff
Hubble’s epic myriad eyes, with notes
Telemachus vs Amphinomus Odyssey 18 149 and 156
Younger Socrates 