Socrates' dream puts in generalized form the difficulty that plato saw in the mathematician's procedure of hypothesis, I.E., Of positing undemonstrated first principles ("prota") or elements ("stoicheia") as starting-Points of demonstration. If the elements are unknown, How can what is constructed from them be known?--A difficulty to which plato had earlier called attention in the 'republic' (510cd, 533cd.) this interpretation accords with the mathematical setting and personages of the dialogue, And explains why the explicit refutation of theaetetus' third proposal, That (...) knowledge be defined as true belief accompanied by a logos, Is so perfunctory and unconvincing. Furthermore, The dilemma thus brought to light is reflected in 'posterior analytics' (book i, Chap. 3), Which was presumably written during aristotle's residence in the academy in association with plato and the other mathematicians gathered around him. (shrink)

In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.

This is the first English translation of Proclus' commentary on Plato's Parmenides. Glenn Morrow's death occurred while he was less than halfway through the translation, which was completed by John Dillon. A major work of the great Neoplatonist philosopher, the commentary is an intellectual tour de force that greatly influenced later medieval and Renaissance thought. As the notes and introductory summaries explain, it comprises a full account of Proclus' own metaphysical system, disguised, as is so much Neoplatonic philosophy, (...) in the form of a commentary. (shrink)

The presence of slavery in the Laws has puzzled and distressed many of Plato's admirers. However, before passing judgment on Plato's attitude toward slavery, we must first have a clear idea of the legal status of the slave under Plato's law, and compare it with the slave's position under Greek law of Plato's day. This work sets out to do just that, as well as to provide a good account of Greek law, much of which has been lost over the (...) course of history. (shrink)