Editing Law of noncontradiction (section)

=== Plato's synthesis ===
[[Plato]]'s version of the law of non-contradiction states that "The same thing clearly cannot act or be acted upon in the same part or in relation to the same thing at the same time, in contrary ways" (The ''[[Republic (dialogue)|Republic]]'' (436b)). In this, Plato carefully phrases three [[axiom]]atic restrictions on ''action'' or reaction: in the same part, in the same relation, at the same time. The effect is to momentarily create a frozen, timeless [[state of affairs (philosophy)|state]], somewhat like figures frozen in action on the frieze of the Parthenon.<ref>[http://www.the-philosopher.co.uk/2004/05/the-laws-of-thought-2004.html 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>

This way, he accomplishes two essential goals for his philosophy. First, he logically separates the Platonic world of constant change<ref>Plato's [[Analogy of the divided line|Divided Line]] describes the four Platonic worlds</ref> from the formally knowable world of momentarily fixed physical objects.<ref>''Cratylus'', starting at [https://www.perseus.tufts.edu/hopper/text?doc=Plat.+Crat.+439e&fromdoc=Perseus%3Atext%3A1999.01.0172 439e]</ref><ref>"A thing which is F at one time, or in one way, or in one relation, or from one point of view, will be all too often not-F, at another time, in another way" ("Metaphysical Paradox" in Gregory Vlastos, ''Platonic Studies'', p.50)</ref> Second, he provides the conditions for the [[dialectic]] method to be used in finding definitions, as for example in the ''[[Sophist (dialogue)|Sophist]]''. So Plato's law of non-contradiction is the empirically derived necessary starting point for all else he has to say.<ref>"Two Principles of Noncontradiction" in Samuel Scolnicov, ''Plato's Parmenides'', pp.12-16</ref>

In contrast, Aristotle reverses Plato's order of derivation. Rather than starting with ''experience'', Aristotle begins ''a priori'' with the law of non-contradiction as the fundamental axiom of an analytic philosophical system.<ref>Similarly, Kant remarked that Newton "''by no means dared to prove this law a priori, and therefore appealed rather to experience''" (''Metaphysical Foundations'', 4:449)</ref> This axiom then necessitates the fixed, realist model. Now, he starts with much stronger logical foundations than Plato's non-contrariety of action in reaction to conflicting demands from the three parts of the soul.