of highest level Ideas. Epistemological meaning Plato holds a very strict notion of knowledge. For example, he does not accept expertise about a subject, nor direct perception (see Theaetetus), nor true belief about the physical world (the Meno) as knowledge. 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. For this reason, in most of the earlier Socratic dialogues, Socrates denies knowledge both to himself and others. For the first level, "the world of becoming and passing away," Plato expressly denies the possibility of knowledge. Constant change never stays the same, therefore, properties of objects must refer to different Ideas at different times. Note that for knowledge to be possible, which Plato believed, the other three levels must be unchanging. The third and fourth level, mathematics and Ideas, are already eternal and unchanging. However, to ensure that the second level, the objective, physical world, is also unchanging, Plato, in the Republic, Book 4 introduces empirically derived axiomatic restrictions that prohibit both motion and shifting perspectives. See also Allegory of the Cave Allegorical interpretations of Plato Self-similarity Notes External links At MIT.edu: Plato's Republic: Translated by Benjamin Jowett At Perseus Project: Plato's Republic: Translated by Paul Shorey (1935) annotated and hyperlinked text (English and Greek) James Danaher, "The Laws of Thought", The Philosopher, Volume LXXXXII No. 1 Plato's Analogy of the Divided Line: A read at the Eastern Division Meetings of the American Philosophical Association, December 1988. Singpurwalla, Rachel G.K. "Plato’s Defense of Justice in the Republic", in Santas, Gerasimos (ed.). The Blackwell Guide to Plato's Republic (Oxford: Blackwell Publishing, 2006). Psychology, Philosophy, and Plato's Divided Line. Full text, analysis, and comprehensive hyperlinked bibliography on Plato's divided line. Articles containing proofs Concepts in epistemology Concepts in metaphysics Platonism Philosophical analogies Philosophical arguments