Justice requires that, before moving on, I say something about Mary Margaret MacKenzie's interpretation of the river fragments in her paper "Heraclitus and the Art of Paradox".
In my improvisations, I had suggested that "You would not step in the same river twice" was proposed dialectically by Heraclitus, and that it looks forward to or invites some kind of reply or resolution. It was on this point that my thought coincided with MM's interpretation. Here is how she puts it:
The outrageous 91 directly challenges common sense; and it requires no philosophical effort to understand it. It appears, of course, immediately absurd to deny us the ability to go on getting our feet wet--so that we immediately respond, 'No, it is possible to step into the same river twice'. Let us call this response to the paradox the doxa.That is what I had thought also. MM continues:
This is the correlate of the paradox, the truth which the paradox denies; any paradox has a corresponding doxa, just because seeing a paradox to be surprising or paradoxical involves us in the judgement that it appears to be false.But here I would want to dissent. I don't think that, in fact, every paradox functions in the same way: not all paradoxical claims are intended dialectically, and not all of them invite us to reply with the obvious. (That's why to refute the Dichotomy by walking away from someone who explains it is ingenious, not obvious.)
I had thought that the statement as reported by Plato, "You would not step into the same river twice" invites such a response precisely because it uses the potential optative (relying for the moment, as I was, on Vlastos' judgment that it can stand). Naturally if one thinks that all paradoxical claims are dialectical, then the mood employed must be irrelevant, and MM follows the usual view in dismissing it as archaic.
MM then argues: The initial paradoxical claim invites the listener to articulate (perhaps only to himself) the doxa; but then paradox and doxa together may be combined in a single statement that takes the form of a contradiction (perhaps generalized or formalized slightly, precisely to call attention to the contradiction); but then this contradiction is resolved by Heraclitus, when he supplies the needed (but previously implicit) qualifiers:
It is impossible to step into the same river twice. (paradox)According to this sort of interpretation, Heraclitus states paradoxes only provocatively, to get a line of argument started. MM concludes:
We do step into the same river. (doxa, implicitly thought)
We both step and do not step, are and are not in the same rivers. (contradiction, formed by a synthesis of paradox and doxa)
To those who step into the same rivers, different and different waters flow. (a non-paradoxical and non-contradictory resolution)
So all three of the river fragments are in some way true; but for different reasons, and at different stages of discourse. The connection between the three fragments that I have offered shows how the fragments could be retained, and arranged in an argumentative sequence, moving from pre-philosophical assumptions to a formal grasp of the dangers of contradiction. From 91 to 49a we move from common sense to reflection; at 49a we shift from material issues to formal considerations (away from banks and water to the worry about contradiction); and at 12 we can account for and resolve the formal difficulty in a non-paradoxical truth.