What difficulties ensue from the Heraclitean theory of flux?
Perhaps the two most famous statements attributes to Heraclitus are "everything flows" and "you cannot step in the same river twice, for different and different waters will flow over you." Both of these fragments suggests that in some way the world is in constant flux. Plato's Cratylus and Theaetetus are both extended responses to the consequences of Heraclitean physics.
How can we know or speak of a world in which there is no being but only becoming? The knowledge one gains from perception is constantly obsolete as the perceived object will have changed by the time perception is crystallized in memory. One cannot know what an object is, but only what it was at the moment of perception. One cannot make general claims, such as “humans are featherless bipeds” because that presumes stability. Nor can one speak at all, for meaning in language presumes stable objects of reference or signification for words.