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Glancing through a recent newsletter for Pythagorean studies, it's interesting to see how many of the articles concern Empedocles. I've never exactly thought of Empedocles as a Pythagorean, though he's obviously part of a broader "Pythagorish" tendency, as it were. Perhaps the thing which unifies "Pythagoreans" is not so much the ethical prescriptions and metempsychosis, or mathematics, in a narrow sense, but rather the effort to deliver an account of multiplicity that meets Eleatic strictures. This can be through the arithmetization of relations, or, as in Empedocles, through a substance pluralism with a focus on the moving causes. Empedoclean Love and Strife are ontological and epistemic principles at once.
Memory, metempsychosis, the ethical disposition toward the other animals, the mathematics, the mythological exegesis, are all of a piece. On the widest ontological scope, what all these Pythagoreans and Orphics and Platonists have in common is the reality of relations. The Orphics, for instance, are trying to close the circle between ritual and cosmogony.
The most important thing with respect to Pythagoreanism is that it isn't just numerology, it's arithmology in a wider sense.
Porphyry (VP 19) states that the Pythagorean doctrines which "gained general notoriety" were: 1) Immortality of the soul; 2) Transmigration, esp. into other species; 3) Cyclical nature of time; 4) One genus of all living things. Now, this doesn't at all rule out mathematics being important to the Pythagoreans; he's just speaking of what got people's attention.
What these ideas all do, and the math as well, is to create vehicles for securing diverse relations as knowable. They posit certain continua—a Deleuzean might say "planes of immanence"?—within which these relations become concrete. The relation to other animals becomes concrete in the single genus of Animality. The relation to time becomes concrete in cycles. The relation to Gods becomes concrete in the whole Orphic toolkit. The role of arithmetic is to make relation as such concrete, as multiplicities suspended in unity. The Platonic doctrine of anamnêsis serves to make the relation to ideas concrete.
Memory, metempsychosis, the ethical disposition toward the other animals, the mathematics, the mythological exegesis, are all of a piece. On the widest ontological scope, what all these Pythagoreans and Orphics and Platonists have in common is the reality of relations. The Orphics, for instance, are trying to close the circle between ritual and cosmogony.
The most important thing with respect to Pythagoreanism is that it isn't just numerology, it's arithmology in a wider sense.
Porphyry (VP 19) states that the Pythagorean doctrines which "gained general notoriety" were: 1) Immortality of the soul; 2) Transmigration, esp. into other species; 3) Cyclical nature of time; 4) One genus of all living things. Now, this doesn't at all rule out mathematics being important to the Pythagoreans; he's just speaking of what got people's attention.
What these ideas all do, and the math as well, is to create vehicles for securing diverse relations as knowable. They posit certain continua—a Deleuzean might say "planes of immanence"?—within which these relations become concrete. The relation to other animals becomes concrete in the single genus of Animality. The relation to time becomes concrete in cycles. The relation to Gods becomes concrete in the whole Orphic toolkit. The role of arithmetic is to make relation as such concrete, as multiplicities suspended in unity. The Platonic doctrine of anamnêsis serves to make the relation to ideas concrete.
