Numbers are abundantly found in Plato's works but it seems (to me at least) that 5 plays a rather important role. The platonic solids are five, of course, even if they come rather later, the Timaeus being considered as one of the last dialogues. Also In the Critias there are five pairs of male twins. In the Sophist "the five greatest kinds" are discussed; in the Philebus four classes are considered with Socrates making the provision

if I want a fifth at some future time you shall allow me to have it.

There are probably some more, but is there a resource listing all such instances? And are there some more or less academic (not fringe) comments/references about this specific number in Plato?

  • You might add that five types of regime are identified in typology of decline in Republic, VIII-IV : (1) the kallipolis or ideal state, (2) timocracy, (3) oligarchy, (4) democracy, and (5) tyranny. Offhand I can't see why the number five should have any special significance for Plato or that its frequency actually does. But the point is interesting and well worth considering. Best : GLT
    – Geoffrey Thomas
    Dec 14, 2019 at 19:13
  • The five solids came from the Pythagoreans (the dodecahedron was constructed by Theaetetus), and the pentagram was also central in their mysticism, which Plato revered, so this is not very surprising. See On the pentagram as a Pythagorean emblem by Fossa and Greek Arithmology: Pythagoras or Plato? by Zhmud.
    – Conifold
    Dec 15, 2019 at 0:59
  • Plato repeatedly starts with 2 components, produces a "mix" and next applies a qualification that either obtains or not, e.g mixing vowels and consonants produces a word, either meaningful or not. Of course he might occasionally state that some items are just five. I am interested in both the logical and the analogical aspects but only in Plato texts and not as vague generalizations about symbolism and/or Pythagoreans. Thanks all the same.
    – sand1
    Dec 15, 2019 at 16:28

1 Answer 1


Diogenes Laërtius, bk.III contains a list of items that appear as sets in Plato's texts. It has been conjectured that Aristotle is its author, as the text asserts. The list is known with its latin name Divisiones quae vulgo dicuntur Aristoteleae (see Dorandi T., 2011, Mnemosyne, 64:4,p.632–8 ) and there are five sets of five elements mentioned in it:
(82) forms of civil government: one form is democratic, another aristocratic, a third oligarchic, a fourth monarchic, a fifth that of a tyrant.
(85) species of medicine : the first is pharmacy, the second is surgery, the third deals with diet and regimen, the fourth with diagnosis, the fifth with remedies.
(87) speech is either political, or rhetorical, or that of ordinary conversation, or dialectical, or technical.
(92) rule is either by law, or by nature, or by custom, or by birth, or by force.
(98) Welfare or happiness includes five parts. One part of it is good counsel, a second soundness of the senses and bodily health, a third success in one's undertakings, a fourth a reputation with one's fellow-men, a fifth ample means in money and in whatever else subserves the end of life.

  • Sometimes I come up with an idea tagged to/with a specific small finite number, and my numerological illusions kick in, so I try to tag other things with the same number, and... I wonder if Plato got five in a case he thought was crucial and then tried to find five in other cases? Sep 15, 2020 at 21:36
  • I'd like textual references for these putative Platonic septets. In the Republic, for instance, Plato identifies the kallipolis, or ideal polis, then a declension through timarchy, oligarchy, democracy, and tyranny. Where is 'monarchy' identified in the series of progressively imperfect poleis? It cannot be identified with the ideal polis since monarchy implies a single ruler; the kallipolis is ruled by a guardian class, not by a single individual
    – Geoffrey Thomas
    Sep 16, 2020 at 11:43
  • The Divisiones Aristoteleae is an undisputably old text and the Republic has for a template Hesiod's fivefold history. The rest is much too complicated, alas.
    – sand1
    Sep 18, 2020 at 10:17

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