Editing Analogy of the divided line (section)

== Metaphysical importance ==
The analogy of the divided line is the cornerstone of Plato's metaphysical framework. This structure illustrates the grand picture of Plato's metaphysics, epistemology, and ethics, all in one. It is not enough for the philosopher to understand the Ideas (Forms), he must also understand the relation of Ideas to all four levels of the structure to be able to know anything at all.<ref>Gail Fine, ''Knowledge and Belief in Republic V-VII'', in G. Fine (ed.) ''Plato I'' (1990), also in S. Everson (ed.) ''Cambridge Companions to Ancient Thought I: Epistemology'' (Cambridge University Press: New York, 1990), pp. 85–115.</ref><ref>Nicholas Denyer, ''Sun and line: the role of the Good'', in G. R. F. Ferrari (ed.) The Cambridge Companion to Plato's Republic (Cambridge University Press: New York, 2007), pp. 284–309.</ref><ref>''Republic'' [https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0168%3Abook%3D7%3Asection%3D520c 520c]: "For once habituated ... you will know what each of the 'idols' is and whereof it is a semblance, because you have seen the reality of the beautiful, the just and the good."</ref> In the ''Republic'', the philosopher must understand the Idea of Justice to live a just life or to organize and govern a just state.<ref>[http://rachelsingpurwalla.files.wordpress.com/2010/01/platos-defense-of-justice.pdf Rachel G.K. Singpurwalla, ''Plato’s Defense of Justice in the Republic''] "justice is a virtue appropriate to both cities and individuals, and the nature or form of justice is the same in both (''Republic'', 435a)."</ref>

The lowest level, which represents "the world of becoming and passing away" (''Republic'', 508d), is the metaphysical model for a [[Heraclitus|Heraclitean]] philosophy of constant flux and for [[Protagoras|Protagorean]] philosophy of appearance and opinion. The second level, a world of fixed physical objects,<ref name="Danaher">[http://www.the-philosopher.co.uk/lawsofthought.htm James Danaher, ''The Laws of Thought''] "The restrictions Plato places on the laws of thought (i.e., "in the same respect," and "at the same time,") are an attempt to isolate the object of thought by removing it from all other time but the present and all respects but one."</ref><ref>''Cratylus'' [https://www.perseus.tufts.edu/hopper/text?doc=Plat.+Crat.+439d&fromdoc=Perseus%3Atext%3A1999.01.0172 439d-e] "For if it is ''ever'' in the same state, then obviously ''at that time'' it is not changing (Plato's realism); and if it is ''always'' in the same state and is always the same, how can it ever change or move without relinquishing its own form (Aristotle's realism)"</ref> also became [[Metaphysics (Aristotle)|Aristotle's metaphysic]]<nowiki/>al model. The third level might be a [[Pythagoreanism|Pythagorean]] level of mathematics. The fourth level is Plato's ideal [[Parmenides|Parmenidean]] reality, the world of highest level Ideas.