Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

32 results

Page 1 of 2

  • Plato's Astronomy

  • Ivor Bulmer-Thomas
  • Journal:
    The Classical Quarterly / Volume 34 / Issue 1 / May 1984
    Published online by Cambridge University Press:
    11 February 2009, pp. 107-112
    Print publication:
    May 1984

  • In one of the most disputed passages of Greek literature Plato in the Republic, 7. 528e–530c prescribes astronomy as the fourth study in the education of the Guardians. But what sort of astronomy? According to one school of thought it is a purely speculative study of bodies in motion having no relation to the celestial objects that we see. While this interpretation has rejoiced the hearts of Plato's detractors, who regard him as an obstacle to the progress of science, it has dismayed his admirers. Another school of thought holds that what Plato meant was that astronomers must get to know the real motions of the heavenly bodies as opposed to their apparent motions as seen by us on earth. The opposed interpretations may be set out in the following representative citations from Sir Thomas Heath and John Burnet.

  • Plato's Theory of Number

  • Ivor Bulmer-Thomas
  • Journal:
    The Classical Quarterly / Volume 33 / Issue 2 / December 1983
    Published online by Cambridge University Press:
    11 February 2009, pp. 375-384
    Print publication:
    December 1983

  • In a well-known passage Aristotle ascribes to Plato, or as some think to his followers, the dictum, ⋯ γ⋯ρ ⋯ριθμóς ⋯στιν ⋯κ ⋯νòς κα⋯ τ⋯ς ⋯ορίστον (Met. 1081a, 14), ‘Number is (formed) from the one (unit, monad) and the undetermined (indefinite, unbounded) dyad (duality)’, but what this apparently simple statement means has remained a mystery until modern times. In other passages Aristotle expands it to explain that the indefinite duality is a duality of the great and small, e.g., ὡς μ⋯ν οὔν ὕλην τò μ⋯γα κα⋯ τò μικρòν εἶναι ⋯ρχ⋯ς, ὡς δ' οὐσίαν τò ἔν. ⋯ξ ⋯κείνων γ⋯ρ κατ⋯ μ⋯θεξιν το⋯ ⋯νòς εἶναι τοὺς ⋯ριθμο⋯ς (Met. 987b20–22). ‘As the matter (of number) he posits the great and small for principles, as substance the one; for by the mixture of the one with them he says numbers (arise).’ This identification of the dyad with the great and small, elsewhere called τò ἄνισον (‘the unequal’) and τò ἄπειρον (‘the unbounded’), gives a first clue to its nature. In a notable article in Mind 35 (1926), 419–40, continued in vol. 36, (1927), 12–33, and amplified by D' Arcy Wentworth Thompson in vol. 38 (1929), 43–55, A. E. Taylor first suggested a connexion between the indefinite duality and the modern theory of continued fractions. In the light of subsequent research in the history of Greek mathematics it may now be asserted with a high degree of confidence that his conjecture was almost certainly correct; but it was then no more than a conjecture, and when he looked for confirmation he looked in the wrong direction.

Page 1 of 2