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Why Can’t We Step Twice Into A River?

The implicit argument:

  1. The minute parts of what we regard as a self-same river are subject to continuous flux.
  2. So what regard as a self-same river is in fact a numerically distinct object from one moment to another.

So reconstructed, the argument is pretty clearly invalid.

Question #1: What’s the missing premise?

Something like this would do the trick: Qualitative difference entails numerical difference.

More formally:    For any objects x and y: if x and y are qualitatively different, then x ≠ y

Equivalently:      For any objects x and y: if x = y, then x and y are qualitatively identical

Question #2: Does (or would) Heraclitus endorse the suppressed premise?

Surely not!  (See CCR passages 55 and 56, among many others.)  Not only does Heraclitus deny that qualitative identity is a necessary condition for persistence over time, he goes rather farther and claims that qualitative difference (in the form of motion, dynamic forces, etc.) is necessary for the persistence of many kinds of things – perhaps, even, for every kind of thing.

Conclusion: the quip for which Heraclitus is most famous is almost certainly not something he said or believed; Plutarch substantially misrepresented his view, and the misrepresentation took on a life of its own.