In Timaeus we find much detail about contemporaries’ theory of tuning the octave, i.e. inserting whole tones, half tones and even sometimes quarter-tones,
inside of the 1:2 ratio. Archytas goes a step further than the ‘just’ tuning when he brings in a new and larger prime, larger than 2,3,5 (this final 5 was used in ‘just’ tuning).
If we avail ourselves of the very next prime — i.e. 7 — we are precisely in step with Archytas’s so-called ‘enharmonic’ scale. This includes the Archytas-defined example of an ‘epimoric’ ratio. Twenty eight twenty sevenths ratio is sometimes called the quarter-tone, slightly shaved down from the 16:15 half-tone of the Just Tuning. F.Murray Barbour has presented and analysed the various near-Timaeus tunings, and has preserved an interesting graphic. It depicts Pythagoras or a follower of his, one a man near Younger Socrates in the Napels mosaic of the first Academy:
Please see some humorous reflections on ‘haecceity’ and ‘quiddity’ from the OED. Peter Geach, who would have called himself a ‘Logitioner’ as used in OED’s 16th cent. ‘quiddity’ case:
a typo needs fixing in this slide’s title, the third ‘n’ needs to be a ‘t’ as it appears herebelow in Alexander of Aphrodisias’s word ‘ekeininotES’ [sic et non], — but you can easily fix this in your mind, O over-attentive reader !
30.ix.20 Kindly look at our Venetus ms. which has traces of Young Socrates at 42b1 . along with an ascerbic remark — against Plato ! — likely from Philip of Opus: Tim 42 b1, f two modifications not reported by Burnet frm Venetus T r4
This following textual peculiarity from the Paris ms. A catches attention — for our late-Plato preference for AIEI over AEI:
In the philologically rich Chap 14 of Timaeus (41D – 42E), there jump up a pair of notable phrasings in our Venetus T, one a flag seemingly inserted by the scholiast, the other an alternate reading. Please look at T here: Tim 45 b1, f two light modifications not reported by Burnet frm T Bonitz list just 2 specimens of the usage of EUDOXUS, de-occultation or anaphainein, a title for him Tim 45 b1, f two light modifications not reported by Burnet frm T 9.viii.20 A dissertation of nearly a centenary ago now spotlighted a habit of ancient style: ‘alliteration bei den Drei Tragikern’ It will have required an effort for the researcher to find a better case than this following in Philip of Opus, a kind of “fourth tragedian” It is an exaggerated example perhaps, its DeMundo 399a “akosmia/kosmos/akoloutheia/akolasia” — truly a pile-up of poetic puns: please look, especially if you are or if you are deeply disbelieving, at this following slide: akosmia calling the Pan by the name ‘Mundo’ i e Kosmos v.20 r5 13.vii.20 this clip from Aristotle’s fragment 313 has some remaining fixes needed. Please be patient while this fixing proceeds… I judge that frag. 313 contains various significant pointers. toward the idea of using ‘athroisma’ as metaphor for a foregathering of — or an anticipation of –universalisation as in the Posterior Analytics , work going on at Early Academy. This exemplifies the Early Academy’s ‘joint search dialectic’ on cases we may call ‘amia’ or ‘deprived of its loner status’: work towards a new view, echoed in Timaeus repeatedly, of the meaning of ‘katholou’ This puts the new amia- or the athroisis-concept into an unfamiliar place from a logical point of view —- a non-singular, alongside others within items logically more generic, but in a way opposite to the ‘One’ and ‘Singular’. But this in turn puts the Amia and universality forward as the ‘always or for the most part’ formula so common in Aristotle, thus a ‘flocking’ universal, like so many summer swallows. Logically, then, it forms a part of the ‘ Dyad of greater-or-lesser’ and is a non-loner alongside its flock, the newly formed near-Universal. Are the origins Pythagorean ? Perhaps even Theban, relayed by Philip from Opus ? In Timaeus, Politicus there are repeated clustering of terms like ‘athoisma’ or ‘sunathroisma’ elsewhere in the corpus-in-the-making [see Fink, ed., 2012] they are rarities — even loners. amiai in Aristotle fragment 313. and EN ‘s loner Pythag swallow proverb r2 10.vii.20 Use of a ‘chisel’ is connected — not very indirectly — with 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 rather a universal in every ‘shaving’ or ‘comma’, their foundational feature being ‘like every other shaving, and like the whole gold coin, it is pure gold.’ Anaxagorean form of ‘abstraction’ under surveillance 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 the ‘unperceivably small’ or 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. 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 this very direction 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 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 31.v.20 Who exactly is behind the pointed reference to ‘my’ way of speaking [or arguing] ? Not the same ‘me’ of Seventh Letter ! Holger, Epin 989E dunamin thn emhn tou legontos 31-v-20 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. 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 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 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 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’ in Chapt 22, –flock of αἰεὶ
AIEI, clustering in Ch 22 of Euthyd ++++++ akosmia not so when I call the sum-Pan by the name ‘Mundo’ i e Kosmos v.20 de-occultation or de-hiding and re-hiding in nature of Ideas – Amphinomus r2 Consider Bury’s fine note to Symp 209C near Diotima speech, with Tim 26 d and joint search urbanely invited by optatives there: Bury’s note on Symp 209C see Tim 26d with its euporoien logwn met emou Timaeus Chapt 1: 17 a1 Chapt 2: 19 b3 Chapt 3: 21 a7 4-8-3-tim-17a1-19c2-21b2-begin-timaeus-256r 4-8-3-tim-21b3-22d8-24c4-256v Chapt 4: 25 d7 Chapt 5: 27 c1 +++++++++++++++++++++++++++++++ It is quite natural if we call Pythagoras of Samos a direct ancestor of the ancient group or society whom Plato is soon to call Friends of Forms. Certainly he is more strongly associated with these than with those called Ionian, or Ionians, — Friends of Earth, Plato calls them. In Timaeus Ch. V, Plato launches his discourse on the world’s body and its sensible and tangible aspect. This recognises the all-but-complete dominion of a cosmic Nous over this lower world’s necessity. Here is a brief discussion of ‘heaven’ and ‘earth’ and how scientists of Plato’s day (post Pythagoras, but prior to Aristotle) dealt with ‘the nature of things’. It is a curious lexical sidelight on this that the De rerum Natura recognises ‘swerve’ or ‘parenklisis‘ [παρέγκισις] amongst the world’s atoms, its basic bodies. Further, possibly tracing back as far as Aristotle or even his ancestors near the time of Pythagoras, thus well before Euclid and Epicurus themselves, put forward the definition of Right Angle different from how Euclid defines it. They made their definition specify ‘exemption from parenklisis’. Heiberg relayed this seemingly old-elementarian’s [an academician’s ?] definition from our best ms. of Euclid, — its scholia, or marginalia. The Stamatis edition keeps this seemingly old definition, which also embodies a lexical rarity, the word DICHOTOMHMA. It is adjacent parcels of such half-pieces that exhibit their orthogonal quality, by being ‘without parenklisis’. Here you will find some of my observations on Plato, Aristotle and Younger Socrates, particularly on pre-Epicurean thinking about the world’s (created) body : heavenly-vs.-sublunar-science-5 http://www.internetculturale.it/jmms/iccuviewer/iccu.jsp?id=oai%3A22.214.171.124%3A18%3AVE0049%3ACSTOR.241.10700&mode=all&teca=marciana ++++++++++++++++++++++++++++++++ 4-8-3-tim-24c4-26b4-28b3-257r Chapt 6: 29 d7 Chapt 7: 31 b4 4-8-3-tim-28b3-30c6-33c3-257 Bury’s note on Symp 209C see Tim 26d with its euporoien logwn met emou Chapt 8: 34 a8 Chapt 9: 36 d8 Chapt 10: 37 c6 Chapt 11: 38 b6 4-8-3-tim-33c4-36c4-38b8-258r Chapt 12: 39 e3 Chapt 13: 40 d6 4-8-3-tim-38b8-39e6-41c5-258v
Chapt 14: 41 d4 scholion to Tim 42b1, O Supremely Wise Plato (259r), r4
Chapt 15: 42 e5 Chapt 16: 44 d3 4-8-3-tim-41c5-43b1-44d4-259r Chapt 17: 47 e3 4-8-3-tim-44d4-46c6-48c1-259v Chapt 18: 48 e2 Chapt 19: 52 d2 4-8-3-tim-48c1-50d4-53a2-260r Chapt 20: 53 c4 Chapt 21: 55 c7 Chapt 22: 56 c8 4-8-3-tim-53a2-55a2-56e2-260v Chapt 23: 57 d7 Chapt 24: 58 c5 Chapt 25: 60 b6 4-8-3-tim-56e2-58d2-60c7-261r Chapt 26: 61 c3 Chapt 27: 64 a2 4-8-3-tim-60c7-62d5-64e3-261v Chapt 28: 65 b4 Chapt 29: 66 d1 Chapt 30: 67 c4 4-8-3-tim-64e3-67a2-68e3-262r Chapt 31: 69 a6 Chapt 32: 70 d7 4-8-3-tim-68e3-70c2-72a6-262v Chapt 33: 72 d4 4-8-3-tim-72a6-73e5-75c2-263r Chapt 34: 76 e7 Chapt 35: 77 c6 Chapt 36: 79 a5 4-8-3-tim-75c2-77b5-79b6-263v Chapt 37: 79 e10 Chapt 38: 80 d1 Chapt 39: 81 e6 4-8-3-tim-79b6-81b2-83a1-264r Chapt 40: 84 c8 4-8-3-tim-83a1-84d1-86a6-264v Chapt 41: 86 b1 Chapt 42: 87 c1 4-8-3-tim-86a6-87d8-89c2-265r Chapt 43: 89 d2 4-8-3-tim-89c2-91b4-92c9-265v-end-of-timaeus-only-33-ll-in-col-b