Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Pythagoras Revived: Mathematics and Philosophy in Late Antiquity

Synopsis

The Pythagorean idea that number is the key to understanding reality inspired philosophers in the fourth and fifth centuries to develop theories in physics and metaphysics using mathematical models. These theories were to become influential in medieval and early modern philosophy, yet until now, they have not received the serious attention they deserve. This book marks a breakthrough in our understanding of the subject by examining two themes in conjunction for the first time: the figure of Pythagoras as interpreted by the Neoplatonist philosophers of the period, and the use of mathematical ideas in physics and metaphysics.

Excerpt

In the preceding two chapters the overall intentions and structure of Iamblichus' work On Pythagoreanism have been examined as they appear in the first four extant books and in so far as they can be discovered in Psellus' excerpts from Books V-VII. It remains to review briefly the results achieved and to attempt some assessment of the significance of the work as a whole, in relation both to Iamblichus' other works and interests and to the earlier versions of Pythagoreanism sketched above in Chapter I. The importance of Iamblichus' Pythagoreanizing programme for the later history of Greek philosophy will be the subject of Part II of this book.

But have we reached, even with the help of Psellus' excerpts, an adequate view of the work On Pythagoreanism as a whole? There were after all three further books (Books VIII-X) concerning which next to nothing is known. Might they not, were they to resurface some day, alter our general picture of the work? The last three books concerned geometry, music, and astronomy 'according to the Pythagoreans'. In the general scheme of the work they occupied positions comparable to that of Book IV, the Nicomachean introduction to arithmetic. We can therefore expect that they would have been similar in function and character: elementary introductions to the remaining three mathematical sciences, using 'Pythagorean' sources.

But I think we can go further than this. Iamblichus might have composed, for Books VIII-X, new elementary introductions to geometry, music, and astronomy, on occasion citing 'Pythagorean' authorities. It is more likely, however, that he would have reissued 'Pythagorean' introductions to these sciences if such were available, as he did in the case of Nicomachus' Introduction to Arithmetic (=Book IV). And certainly such introductions were available to him. But one can only speculate about precisely which ones he would have used. Given his high standing as a Pythagorean in Iamblichus' eyes, Nicomachus would seem the most likely author he would have chosen and there is . . .

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