Proclus Diadochus

Proclus Diadochus

Born: 8 Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey)

Died: 17 April 485 in Athens, Greece

Proclus's father, Particius, and his mother, Marcella, were citizens of high social position in Lycia. Particius was a senior law official in the courts at Byzantium. Proclus was brought up at Xanthus, on the south coast of Lycia, where he attended school.

It was intended that Proclus should follow his father and enter the legal profession. With this aim in mind he was sent to Alexandria but, while in the middle of his studies, he visited Byzantium and he became convinced that his calling in life was the study of philosophy. He returned to Alexandria where now he studied philosophy under Olympiodorus the Elder, in particular making a deep study of the works of Aristotle. He also learnt mathematics in Alexandria and in this subject his teacher was Heron (not the famous mathematician, Heron was a common name at this time).

Proclus was not entirely satisfied with the education he was receiving in philosophy in Alexandria so, while still a teenager, he moved from Alexandria to Athens where he studied at Plato's Academy under the philosophers Plutarch and Syrianus (a pupil of Plutarch). He progressed from being a student at the Academy to teaching there then, on the death of Syrianus, Proclus became head of the Academy. The title Diadochus was given to him at this time, the meaning of the word being successor.

At the Academy Proclus appears to have been well off and to have helped his friends and relations financially. He never married and lived a life which was, in certain respects, not unlike that proposed by Pythagoras. He did not eat meat and tried to live a religious life, composing hymns to the gods. His hymns were clearly highly thought of since seven of them have been preserved and are seen today as having considerable literary merit. Proclus was to remain as head of the Academy until his death.

A man of great learning, Proclus was regarded with great veneration by his contemporaries. He followed the neoplatonist philosophy which Plotinus founded, and Porphyry and Iamblichus developed around 300 AD. Other developers of these ideas were Plutarch and Syrianus, the teachers of Proclus. Heath writes:-

He was an acute dialectician and pre-eminent among his contemporaries in the range of his learning; he was a competent mathematician; he was even a poet. At the same time he was a believer in all sorts of myths and mysteries, and a devout worshipper of divinities both Greek and Oriental. He was much more a philosopher than a mathematician.

Of course, as one might expect, his belief in many religious sayings meant that he was highly biased in his views on many issues of science. For example he mentions the hypothesis that the sun is at the centre of the planets as proposed by Hipparchus but rejects it immediately since it contradicted the views of a Chaldean whom he says that it is unlawful not to believe.

Proclus wrote Commentary on Euclid which is our principal source about the early history of Greek geometry. The book is certainly the product of his teaching at the Academy. This work is not coloured by his religious beliefs and Martin, writing in the middle of the 19th century, says (see for example):-

... for Proclus the "Elements of Euclid" had the good fortune not to be contradicted either by the Chaldean Oracles or by the speculations of Pythagoreans old and new.

Proclus had access to books which are now lost and others, already lost in Proclus's time, were described based on extracts in other books available to Proclus. In particular he certainly used the History of Geometry by Eudemus, which is now lost, as is the works of Geminus which he also used. Heath, describing Proclus's Commentary on Euclid writes:-

Proclus deals historically and critically with all the definitions, postulates and axioms in order. The notes on the postulates and axioms are preceded by a general discussion of the principles of geometry, hypotheses, postulates and axioms, and their relation to one another; here as usual Proclus quotes the opinions of all the important authorities.

Another interesting part of Proclus's commentary is his discussion of the critics of geometry. He writes:-... it is against [the principles of geometry] that most critics of geometry have raised objections, endeavouring to show that these parts are not firmly established. Of those in this group whose arguments have become notorious some, such as the Sceptics, would do away with all knowledge ... whereas others, like the Epicureans, propose only to discredit the principles of geometry. Another group of critics, however, admit the principles but deny that the propositions coming after the principles can be demonstrated unless they grant something that is not contained in the principles. This method of controversy was followed by Zeno of Sidon, who belonged to the school of Epicurus and against whom Posidonius has written a whole book and shown that his views are thoroughly unsound.

Morrow in confirms the great debt that we owe to Proclus, and in particular his Commentary on Euclid when he writes in:-

Proclus was not a creative mathematician; but he was an acute expositor and critic, with a thorough grasp of mathematical method and a detailed knowledge of the thousand years of Greek mathematics from Thales to his own time.

The recent book gives a good description of the writings of Proclus found in his commentary on Book I of Euclid's Elements. The book [7] is an important contribution to the study of the philosophy of Proclus and in particular his philosophy of mathematics.