•  30
    The Mystery of Plato’s Receptacle in the Timaeus Resolved
    with Demetra Kalisperi
    In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 521-598. 2024.
    Plato, most unexpectedly, in the middle of the Timaeus (48e2-49a7) declares that the sensible bodies cannot be explained solely by their participation in the intelligible, as we were led to believe by reading the long succession of all his previous dialogues, but that it is now necessary to introduce, beside the intelligibles and the sensibles, a Third Kind, the Receptacle.We must, however, in beginning our fresh account of the Universe make more distinctions than we did before; for whereas then…Read more
  •  27
    This chapter aims to obtain a novel anthyphairetic interpretation of Knowledge as Recollection in Plato’s Meno 80d5-86c3 and 97a9-98b6, in a self-contained manner, in line with the anthyphairetic interpretation I have developed for the whole of Plato’s work.Plato sets out to explain his philosophical notion of Knowledge in the Meno, by explaining what he means by Knowledge in the concrete geometrical case of line a such that a2 = 2b2 for a given line b, in fact of the diameter a of a square with…Read more
  •  20
    The Theory of Ultrafilters
    with W. W. Comfort
    Journal of Symbolic Logic 41 (4): 782-783. 1976.
  •  4
    The Pell Equation in the Pythagoreans, Theaetetus, and Hindu Mathematics
    with Vassiliki Farmaki and Marina Brokou
    In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 915-1021. 2024.
    The reinterpretation of Plato’s philosophy in terms of periodic anthyphairesis, in fact of palindromically periodic anthyphairesis in the Politicus, and the reading of Book X of Euclid’s Elements under the new light, reveal deep mathematical contributions by Theaetetus, including a proof of the general Pell equation. Fascinating similarities of Theaeteus’ reconstructed proofs with the Hindus’ solution of the problem of Pell are noted.
  •  2
    In the present chapter, we provide a novel interpretation of the concept of Plato’s and Xenocrates’ indivisible line, in fact, we show that indivisibility is just another description of the Platonic intelligible true Being. Our claim and arguments are based on our earlier interpretation of Plato’s intelligible Being as the philosophic analogue of a dyad of opposite kinds in periodic anthyphairesis (as revealed primarily in the Meno, the second hypothesis of the One in the Parmenides, and the Sop…Read more