The Pythagorean-Epicurean Succession

Diogenes Laertius claims that Epicurus stands at the end of a succession of philosophers he called the Italian tradition, whose main pioneer was Pythagoras.

But philosophy, the pursuit of wisdom, has had a twofold origin; it started with Anaximander on the one hand, with Pythagoras on the other. The former was a pupil of Thales, Pythagoras was taught by Pherecydes. The one school was called Ionian, because Thales, a Milesian and therefore an Ionian, instructed Anaximander; the other school was called Italian from Pythagoras, who worked for the most part in Italy. And the one school, that of Ionia, terminates with Clitomachus and Chrysippus and Theophrastus, that of Italy with Epicurus.

The Ionian tradition, originating with Thales and Anaximander passes through Socrates, and then splits into three main streams:

1. The Academic lineage, from Plato down to Clitomachus
2. The Peripatetic lineage, from Plato’s student Aristotle down to Theophrastus
3. The Cynic-Stoic lineage, from Antisthenes, via Diogenes of Sinope, down to Chrysippus

This was allegedly completely separate from the Epicurean tradition.  It was commonly claimed that Epicurus was mainly inspired by the atomist physics of Democritus (and also the hedonist ethics of the Cyrenaics).  Diogenes Laertius therefore summarises the “Italian” succession leading from Pythagoras to Epicurus as follows:

In the Italian school the order of succession is as follows: first Pherecydes, next Pythagoras, next his son Telauges, then Xenophanes, Parmenides, Zeno of Elea, Leucippus, Democritus, who had many pupils, in particular Nausiphanes [and Naucydes], who were teachers of Epicurus.

This contrasts with the Ionian tradition, which Diogenes Laertius identified with Socrates, and which lead, through him, to the Platonic and Cynic-Stoic successions.  The Epicurean tradition did not descend from Socrates, and was apparently more aligned with other, pre-Socratic, philosophers.

The following list contains links to the philosophers in this lineage…

1. Pherecydes
2. Pythagoras
3. Telauges
4. Xenophanes
5. Parmenides
6. Zeno of Elea
7. Leucippus
8. Democritus
9. Nausiphanes
10. Epicurus

What ideas might some of them hold in common?