Friday, March 28, 2014

Divided lines

The plan is for us to read some of Plutarch's Quaestiones platonicae at our Thursday seminar next term.  I've been looking at no. 3 (1001C-1002E), in which he wonders whether the smallest of the four segments of the 'divided line' in Republic 6 is supposed to stand for eikasia and its objects (as Proclus has it: In Rem Pub. Plat. or for noēsis and its objects (a view to which Plutarch is at least prepared to give some serious consideration: 1001D-1002B).

I've gone to my bookshelf to see what other people make of it.  Mostly they don't register that there is a decision to be made, though a notable exceptions are: Nicholas Denyer's 'The Sun and Line: the role of the good' in G. R. F. Ferrari (ed.) The Cambridge Companion to Plato's Republic (Cambridge, 2007), at 292-4 (Nick turns this into a rather nice point about the nature of this as a diagrammatic representation of something intelligible), and J. Adam's 1902 commentary ad 509d6.  (Adam plumps for eikasia corresponding to the smallest section: see the diagram on p. 65 of vol.2.)

Otherwise, everything I can lay my hands on from where I sit has it that the smallest section stands for eikasia and its objects: 

R. C. Cross and A. D. Woozley, Plato's Republic: a Philosophical Commentary (London, 1964) at 203-5 and 230.
I. A. Richards, Plato's Republic (Cambridge, 1966), at 119.
J. Annas, An Introduction to Plato's Republic (Oxford, 1981), at 247.
C. D. C. Reeve, Philosopher-Kings: the Argument of Plato's Republic (Indianapolis, 1988), diagram on Frontispiece.
S. Scolnicov, Plato's Metaphysics of Education (London, 1988), at 91.
T. Penner, 'The forms in the Republic' in G. Santas ed. The Blackwell Guide to Plato's Republic (Oxford, 2006), 234-62, at 235.

It's not hard to see why: Socrates says that the ratios track 'clarity and unclarity' (σαφηνείᾳ καὶ ἀσαφείᾳ 509d9) and 'truth and untruth' (ἀληθείᾳ τε καὶ μή 510a9) and so I suppose a natural inference is that this means: the larger the line, the greater the clarity.

But has anyone in recent scholarship gone for the un-Proclan view and assigned eikasia and its objects to the largest section?

UPDATE: On 'clarity' here see J. Lesher,  'The meaning of "saphēneia" in Plato's Divided Line', in M. L. McPherran, Plato's Republic: A Critical Guide (Cambridge, 2010), 171-87.

A Google image search for 'plato divided line' throws up some interesting variants.  Quite a few diagrams do not divide the line unequally.  And although the Proclan version is the most common, there are examples of the alternative.  For example:

I found that one at: (from the 'Eidisi Academy of Higher Learning'...)

Here's another from:

And a third from:


Interlocutor said...

Don't know of anyone unequivocally plumping for the un-Proclan view, but there's some interesting discussion of Denyerian themes in Richard Foley's "Plato’s Undividable Line: Contradiction and Method in Republic VI", Journal of the History of Philosophy, vol. 46, no. (2008) –24.

Nicholas d. Smith, “Plato’s divided Line”, Ancient Philosophy 6 [ 996]: 25–46) has an interesting discussion of the literature.

James Warren said...

Great! Thanks. So: add Smith to those who raise the q. explicitly (he then endorses the Proclan interpreation), together with G. Fine, 'Knowledge and belief in Republic V-VII' in S. Everson ed. Epistemology (Cambridge, 1990), 85-115, at 98 n.26.