Crombie, I. M. (2012). An Examination of Plato's Doctrines: Plato on Knowledge and Reality, Volume 7. Oxon: Routledge. مخونه91. د کتاب نړيواله کره شمېره9780415632171.منځګړی |CitationClass= له پامه غورځول شوی (لارښود)
Let the length of AE be equal to and that of AC equal to , where (following Socrates, however, ; insofar as the equality of the lengths of BC and CD is concerned, the latter restriction is of no significance). The length of CE is thus equal to . It follows that the length of BC must be equal to , which is seen to be equal to the length of CD.
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.
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.
Republic520c: "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."
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."
Cratylus439d-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)"
Republic520c "For once habituated you will discern them infinitely better than the dwellers there, and 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."
Republic4.436b "It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time"
Republic4.437a "let us proceed on the hypothesis that this is so, with the understanding that, if it ever appear otherwise, everything that results from the assumption shall be invalidated"
It is interesting to note that modern logical analysis claims to prove that the potentially falsifiable "empirical content of a theory is exactly captured by ... axiomatization ... that uses axioms which are universal negations of conjunctions of atomic formulas" (C. Chambers, The Axiomatic Structure of Empirical Content)Archived 27 June 2010 at the Wayback Machine.
Plato's Principle of Non-Contradiction (Republic, 4.436b) for the objective, physical world is presented with three axiomatic restrictions: The same thing ... cannot act or be acted upon ... in contrary ways ... (1) in the same part (2) in relation to the same thing (3) at the same time.