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We hope to have this discussion page active soon. SUN TE DU' ERXOMENW ... (WHEN TWO OF US PROCEED TOGETHER ...) March 22, 2008 What portions of Euclid's Elements did Theaetetus write? I answer that Yes, parts of what Heiberg now has as Books III, X and XIII of ‘Elements’, now under Euclid’s name, came from the original writing of Theaetetus. I argued (in my Sprague Lecture of April 2004) that seven or more passages, especially from Books X and XIII -- and from separately preserved material added onto Book III -- are due to Theaetetus. Further material may also be reliably traced back to him, especially some of the scholia in Euclid's margins, usefully edited by Heiberg. Three additional questions, about the Academy where Theaetetus seems to have been active and writing:
(1) Did Eudoxus write expansions of, or alternate versions of, his Bks V and XII? (what of his student Helicon, pictured by his side in the ‘philosophenmosaik’ in Naples -- what of Philip, pictured stage-right in that same mosaic -- antagonist to Eudoxus and Helicon ?) (2) Can we reliably attribute the ps-platonic Sisyphus to Dicaearchus? (what of Aristotle's role here?) (3) Can we reconstruct more of these debates in mathematics, such as about 'The Angle'? (what of Philip's part in this?) I propose to defend a qualified 'Yes' answer to all three of these questions.
Some investigation of these topics went on at Center for Hellenic Studies in 1969-70, where I presented a paper on the non-eudoxan version of Book XII. I have carried on a sporadic private correspondence with various scholars on these matters in recent decades since. Here at www.theaetetus.net I can host some back_and_forth on these three questions, and on the major question about Theaetetus.
There may well be further questions, such as: (4) Can we reliably attribute the ps-aristotelian "De Mundo" to Philip of Opus? On this topic also I have had private scholarly exchanges in recent years. Some new fragments of Philip lend support to the 'yes' answer. The larger subject is the pre-euclid era in mathematical research, especially at Early Academy. It seems that Plato's mathematical colleagues suffered from nicknaming behavior. For example Eudoxus got nicknamed 'endoxos', possibly because he was 'famous', possibly because he adopted what Aristotle considers the unreasonable endoxon (debating position) of Hedonism. I have published my argument that the name 'athenaeus cyzicenus' was a lightly generalised nickname for Helicon of Cyzicus. Other names amongst debaters inside the Early Academy may also need interpretation. 'Amphinomus' is a leading example of this. There are reasons for thinking Philip’s in-Academy antagonists put him in this role, the seemingly righteous ‘suitor’, ever flattering Plato and ambitious to be the Successor. He will have been rival to Speusippus there, as the mythical Amphinomus was rival to Telemachus in Ithaca. Stage-names ('masks') will have been natural on the scene of those vigorous in-Academy debates in the years shortly after -354. That was the year of the famous Seventh Letter, which anticipates controversies. The Letter issues exhortations, likely to junior colleagues at the Academy, about holding to a high level of collegial and unjealous behavior in disputation. It also offers a vivid mathematical topic for debate and discussion, the nature of The Circle. The battle described in Sophist as Olympian Gods vs. Titanic Elders (i.e. 'Heaven's Own Idealists' vs. 'Earthloving physicists') is likely to be an intra-Academic quarrel. Similarly the tug-of-war between those who venture to 'move that on which it is forbidden to move' and the reactionary defenders of (as they thought this) Platonism.
It will have been perfectly natural if claimants to inherit the Platonic mantle had been coming forward for some years since Plato's return from his third and final voyage to Syracuse (-360). Plato's warnings and exhortations will have been intended for debaters in general, but particularly those disputing the pro's and con's of Platonism right there after Plato's third homecoming to Athens.
Is it a self-indulgence to fancy that Plato would be charmed by the concept of an aether-borne "theaetetus.net" ? More likely yes, – so runs the plausible narrative I am hoping to present in due course – if such a thing were to include a discussion board. This is intended as following after Socrates-the-Elder, thus an open intellectual exchange, jealousies and petty rivalries not allowed. Consider the case of Aristotle, in his DeCaelo I, 3. His topic is opinions about the cosmic rim, its ever-flowing aether. His critical review of the opinions of predecessors (elsewhere he calls this practice 'peirastic'). In this case he traces opinions back to the time of remote ancestors, but brings it up to 'today', where followers will be 'updating' Anaxagoras [likely at the Academy].
The discussion page here at theaetetus.net: topics should be centred on mathematics at the Early Academy, and how best give them the right historical setting. Did Hippasus and his colleagues construct the dodecahedron and other ideal cosmic figures a few generations before Theaetetus? Did Amphinomus precede Aristotle in some intellectual advance or did Aristotle get there first? Who was Amphinomus? Is there any 'Boeotian' or pythagorean material behind him ? Behind the nickname 'Amphinomus' do we rightly find Plato’s secretary Philip ? Did Dicaearchus sometimes counter Theophrastus concerning the 'bios praktikos', or Aristotle onfuture contingency ?
Research will forever be causing fresh questions to arise, and arise yet once again, the more recent results having reset the starting points. Such sifting of opinions, says Aristotle (perhaps making facetious reference to Anaxagoras' Apeiron) must happen 'apeirakis' ('endlessly often'). Let the resetting continue. Until this page becomes active, please address your comments to
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