The phrase πάντα ῥεῖ (panta rhei) “everything flows” either was spoken by Heraclitus or survived as a quotation of his. This famous aphorism used to characterize Heraclitus’ thought comes from Simplicius, a neoplatonist, and from Plato’s Cratylus. The word rhei (cf. rheology) is the Greek word for “to stream”, and is etymologically related to Rhea according to Plato’s Cratylus.
The philosophy of Heraclitus is summed up in his cryptic utterance:
ποταμοῖσι τοῖσιν αὐτοῖσιν ἐμβαίνουσιν, ἕτερα καὶ ἕτερα ὕδατα ἐπιρρεῖ.
Potamoisi toisin autoisin embainousin, hetera kai hetera hudata epirrei
“Ever-newer waters flow on those who step into the same rivers.”
τὰ ὄντα ἰέναι τε πάντα καὶ μένειν οὐδέν
Ta onta ienai te panta kai menein ouden
“All entities move and nothing remains still”
and in 402a
“πάντα χωρεῖ καὶ οὐδὲν μένει” καὶ “δὶς ἐς τὸν αὐτὸν ποταμὸν οὐκ ἂν ἐμβαίης”
Panta chōrei kai ouden menei kai dis es ton auton potamon ouk an embaies
“Everything changes and nothing remains still … and … you cannot step twice into the same stream”
Instead of “flow” Plato uses chōrei, “to change place” (χῶρος chōros).
The assertions of flow are coupled in many fragments with the enigmatic river image:
Ποταμοῖς τοῖς αὐτοῖς ἐμβαίνομέν τε καὶ οὐκ ἐμβαίνομεν, εἶμέν τε καὶ οὐκ εἶμεν.
“We both step and do not step in the same rivers. We are and are not.”
Compare with the Latin adages Omnia mutantur and Tempora mutantur (8 CE) and the Japanese tale Hōjōki, (1200 CE) which contains the same image of the changing river, and the central Buddhist doctrine of impermanence.
However, the German classicist and philosopher Karl-Martin Dietz interprets this fragment as an indication by Heraclitus, for the world as a steady constant: “You will not find anything, in which the river remains constant. … Just the fact, that there is a particular river bed, that there is a source and a estuary etc. is something, that stays identical. And this is … the concept of a river”