This is probably the Eleatics. The big dialectic that drives Plato's Parmenides is trying find a via media between the silence of a single, undifferentiated "ohm" (Parmenides, there is just one thing) and inchoate, meaningless noise (Heraclitus, everything is always changing, including the meanings of our words, and so it is impossible to say anything true about anything).*

*Note: Heraclitus arguably avoids this charge through the role of the Logos, but in what comes down to us its role is extremely unclear and seems rather ad hoc.

Thanks for the tip! on tracing this thing further, I have found it associated with the name of Antisthenes, who has been associated with the Eleatics as well as a couple other schools. Aristotle says
"Hence Antisthenes was too simple-minded when he claimed that nothing could be described except by the account proper to it, -- one predicate to one subject; from which the conclusion used to be drawn that there could be no contradiction, and almost that there could be no error" (metaph. V.29)