We critically reconsider an old hypothesis of the role of the dekad in Pythagorean philosophy. Unlike Zhmud, we claim that: 1) the dekad did play a role in Philolaus’ astronomical system, and 2) Aristotle did not project Plato’s theory of the ten eidetic numbers onto the Pythagoreans. We claim that the dekad, as the τέλειος ἀριθμός, should be understood in Philolaus’ philosophy as completeness and the basis of counting in Greek – as in most other languages – in a decimal (...) system. Additionally, we argue that the number ten is not even a candidate for the τέλειος ἀριθμός in Plato’s philosophy. As a final result of our discussion, we compare and contrast Philolaus’, Plato’s, and Speusippus’ accounts of completeness in relation to numbers. (shrink)

The Aristotelian Πολιτεῖαι collected information on the history and organization of reportedly 158 city-states. Of these only the Ἀθηναίων πολιτεία survives almost in its entirety on two papyri. All that remains of the other constitutions is the epitome by Heraclides Lembus (second centuryb.c.e.) and about 130 fragments. This article will look at the transmission of Heraclides’ epitome (itself preserved as excerpts) and explore the possibility of identifying further fragments of the original text.

Diogenes Laertius' list of Aristotle's works includes a Homeric Puzzles in six books, as does the list in the biography of Aristotle attributed to Hesychius. This latter also includes a Homeric Problems in ten books, which appears to be the same as an item in the biography attributed to Ptolemy al-Gharib. The later and more derivative Vita Marciana attributes to Aristotle a Homeric Questions. The only other reference to the title of such a work by Aristotle is from the anonymous (...) Antiatticista, a second-century a.d. lexicon : ‘They say Alcaeus the comic poet and Aristotle in Homeric Puzzles said this.’ Finally, Poetics 25 – which begins περὶ δὲ προβλημάτων καὶ λύσεων – is a summary, with examples, of just such a work, and a description of how to undertake such an inquiry. (shrink)

The author deals with the lost works of Empedocles, an often neglected subject, in the frame of the discussion concerning the number of the poems and their main features. He reviews the traces of the Passage of Xerxes, of the Medical Discourse, and of the Proem to Apollo among the fragments and witnesses, taking his cue from textual aspects and dealing with the contents, the significance of each of these writings in Empedocles’ culture and thought and their multifarious relationships with (...) his times. As to the Passage, he tries to reconcile the contrasting interpretations so far proposed (historical or religious poem). Concerning B111, the only relic from the Medical Discourse, he explains why its contents are incompatible with the Physical Poem and the Purifications. He analyzes the Proem to Apollo in several perspectives (text, witnesses, contents also from the epistemological point of view, literary genre). He assigns fragments 131–134 and 142 to the Proem, drawing one of his arguments from the comparison with the third Homeric Hymn to Apollo, and also suggesting a relationship with an intellectual cult of the sun. Formal features help to ascribe each fragment to the relevant poem. Close similarities between fragments do not necessarily mean that they come from the same writing: Empedocles is wont to allude to one poem of his while composing another. The author concludes that the striving for a reductio ad unum of the Acragantine’s output, also evident in the attempt by a number of scholars to make only one poem out of the Περὶ φύσεως and the Καθαρμοί, has often led researchers to take for granted that none of the fragments preserved might belong to the lost works. (shrink)