Podcast episode
December 20, 2017
Episode 17: The Enigma of Pythagoreanism
The sources about Pythagoras seem to tell us everything and nothing; we have a wealth of information from classical and late-antique sources, but, as we saw last week, when we try to sift through it all, we come up with very few writings about Pythagoras himself which we can confidently say tell us about him as he was historically, before the overlay of Platonistic interpretation which coloured nearly all post-Platonic reading of Pythagoras and led to the later currents known as ‘Neopythagorean’. The same is not true for Pythagoreanism. We have the fragmentary writings of one of the philosophic Pythagoreans of the fifth century BCE, Philolaos of Croton, who really was more or less what we think of when someone says ‘Pythagorean philosopher’: he saw mathematical ratios as key constituents of reality, privileging number and harmony as ontological principles. He investigated musical harmony, mathematics, and cosmology. Great.
But how do we get from Pythagoras and his earliest followers, whose way of life seems to have had very little to do with mathematics and everything to do with magic and mystery, to later thinkers like Philolaos, with their mathematical and harmonic concerns? That is the story we try to tell in this episode. It is a story with some holes in it, because our evidence is patchy, but the good news is that it involves a political takeover in southern Italy by the Pythagorean sect, followed by a massacre, which is more than you can say for most history of philosophy.
Works Discussed in this Episode:
Primary
If you are unclear about DK numbering, see the notes to episode 15 of the podcast.
- Iamblichus: a good edition of Iamblichus’ De vita Pythagorica is Dillon, J. and Hershbell, J. P. (1991). Iamblichus: On the Pythagorean Way of Life, Scholars’ Press. Iamblichus, Comm. Math. 76.19, citing a lost Aristotelean original, on the split between the Pythagorean schools.
- Philolaos of Croton: DK 44 B1-7, 13, 17 are generally thought to be the authentic fragments.
- Plato Republic X 6ooa9-b5.
- Polybius: I have used the translation found in Walbank, F. (Ed.), 1979. Polybius: The Rise of the Roman Empire. Penguin, London.
Secondary
- Burkert, W., 1972. Lore and Science in Ancient Pythagoreanism. Harvard University Press, Cambridge, MA. Page 119 quoted on the Pythagorean hegemony in southern Italy.
Recommended Reading:
- Delatte, A., 1922. La vie de Pythagore de Diogène Laërce. M. Lamertin, Brussels.
- Fritz, K. v. (1945). ‘The Discovery of Incommensurability by Hippasus of Metapontum’, The Annals of Mathematics, Second Series 46 : 242-64.
- Huffman, C.A., 1993. Philolaus of Croton: Pythagorean and Presocratic: A Commentary on the Fragments and Testimonia with Interpretive Essays. Cambridge University Press, Cambridge.
- Huffman, C. A. (Ed.), 2014. A History of Pythagoreanism. Cambridge University Press, Cambridge.
- Kirk, G. S.; Raven, J. E. and Schofield, M., 1983. The Presocratic Philosophers. Cambridge University Press, Cambridge.
- Lévy, I., 1926. Recherches sur les sources de la légende de Pythagore. Éditions Ernest Leroux, Paris.
- O’Meara, D., 1989. Pythagoras Revived : Mathematics and Philosophy in Late Antiquity. Oxford University Press, Oxford.
- Philip, J. A., 1966. Pythagoras and Early Pythagoreanism. University of Toronto Press, Toronto.
- Rohde, E. (1871). ‘Die Quellen des Jamblichus in seiner Biographie des Pythagoras’, Rheinisches Museum für Philologie 26 : 554-76.
- Thesleff, H., 1961. An Introduction to the Pythagorean Writings of the Hellenistic Period. Abo Akademi, Abo.
- Von Fritz, K., 1940. Pythagorean Politics in Southern Italy. Columbia University Press, New York, NY.
Themes
Pre-Socratic Philosophy, Pythagoras, Pythagoreanism, Secret Societies
Bernie Lewin
September 13, 2019
That Aristotle might be the best source of pre-Platonic Pythagoreanism is not a new idea. It seems to have some currency among the mathematical astronomy types in the late Renaissance, and certainly by the time of Leibniz. And yet Leibniz (others?) interpreted Aristotle’s account differently from you. Which makes me wonder who is right.
I recall you said something to the effect that Aristotle said the Pythagoreans said that numbers are the essence of everything. I also recall one of your interviewees earlier say something similar and to the effect that ‘things are numbers’. So there seems to be some agreement that this is likely to be their view. And the obvious source is Aristotle. But Aristotle gives both views.
These are found in Aristotle’s prologue to his Metaphysics which gives famous accounts of the Pythagoreans and of (the esoteric mathematical) Plato. When Aristotle launches into his account of the Pythagoreans (at 985b20) he says that the ‘principles’ (arche) of mathematics are the principles of everything, and then that the ‘elements’ of numbers are the elements of everything. This is the presumed source of the slogan appropriated by Leibniz ‘essentiae rerum sunt ut numeri’. It was pretty clear to Leibniz that the goal was not numbers but beyond numbers – if you found the essence of numbers then your found the essence of being. That’s pretty clear to me. But that is not the end of it.
The support for your view comes later when Aristotle says (987a20) ‘…hence number is the essence of all things’. But here he is referring to the original-one itself as the essence of all that is predicated. (987a20). But there is more. By this stage he is signalling that he is interpreting. In this mode he goes on to contrast the Pythagoreans to Plato, where they say that the ‘things themselves are numbers’, while Plato finds number to be distinct from things.
So what are we to make of this? We should remember this is Aristotle. And that he was about to introduce a new view in rejection of all this mathematical reductionism – something he was hostile to, and didn’t really understand. And so he might have seen differences where there were none.
Why is it important that it might be the ‘essence’ or the ‘element’ of number that is the essence of things? Well, in the first place we can make sense of this. Indeed, it is in sympathy with modern mathematised physics. But more importantly it finds accords with Platonism without contradicting other sources of early Pythagoreans (e.g., fragments of Philolaus). Afterall, Aristotle himself says that in most respects Plato was in accord with them. Let’s take a shortcut and recite a Platonic doctrine that goes something like this: the form of beauty, the form of the good and the form of numbers all have their essence in the form of forms, the original one. There is thus something beyond number that is the essence or element of number. The Platonic revolution was in the account of this origin–i.e., that Monad/Dyad replaces limit/unlimited–which is in fact Aristotle’s main point.
In other words, I would suggest there is some truth hidden in Aristotles account, where there was a shift away from number to ratio (i.e., towards the Dyad as the essential logos). But if we can’t work out what the Pythagoreans meant when they said ‘things-are-numbers’, then it might be because they never said it.
Bernie Lewin
September 13, 2019
I am sorry, I confused the argument at the beginning of the above comment. My strong argument is against the claim that the evidence supports the early Pythagorean dogma: ‘things are numbers’. The Pythagorean view is likely more subtle than a literal reading of that, and it is likely closer to what became esoteric Platonism. As for Leibniz, he gave assent to their view obtained via Aristotle that ‘the essences of things are like numbers’ (essentiae rerum sunt sicut numeri) My recollection was a bit faulty when I made the comment. But, if this is the Pythagorean view, then it is not unsympathetic to modern physics.
Seth charles
May 5, 2020
I’m curious where in Iamblichus’ Life of Pythagoras he claims that the Pythagoreans went underground, disappearing completely to the eyes of the world. I am very interested in following this thread but am not finding that statement in my version of that book. Or perhaps I misunderstood and that is not actually the source text for this idea?
Earl Fontainelle
May 13, 2020
Iamb. V.P. 35. 252-3.