As I understand it, Parmenides and Heraclitus were two pre-Socratic Greek philosophers whose views could not be farther apart. Parmenides believed that all change is illusory, and that there is just one indivisible entity which exists in reality. Heraclitus believed that change was the only thing constant in life, and that nothing maintains its existence or identity for longer than a moment. Yet it seems that they both had one belief in common.
In Plato's dialogue "Cratylus", the eponymous figure Cratylus, who was a follower of Heraclitus, claims that it's impossible to utter a falsehood:
Soc. Are you maintaining that falsehood is impossible? For if this is your meaning I should answer, that there have been plenty of liars in all ages.
Crat. Why, Socrates, how can a man say that which is not?- say something and yet say nothing? For is not falsehood saying the thing which is not?
Soc. Your argument, friend, is too subtle for a man of my age. But I should like to know whether you are one of those philosophers who think that falsehood may be spoken but not said?
Crat. Neither spoken nor said.
And in Plato's dialogue "Sophist", the Eleatic stranger, i.e. a foreigner from Elea who is a follower of Parmenides, makes mention of a Parmenidean argument that it's impossible to utter a falsehood:
Str. My dear friend, we are engaged in a very difficult speculation-there can be no doubt of that; for how a thing can appear and seem, and not be, or how a man can say a thing which is not true, has always been and still remains a very perplexing question. Can any one say or think that falsehood really exists, and avoid being caught in a contradiction? Indeed, Theaetetus, the task is a difficult one.
Str. He who says that falsehood exists has the audacity to assert the being of not-being; for this is implied in the possibility of falsehood. But, my boy, in the days when I was a boy, the great Parmenides protested against this doctrine, and to the end of his life he continued to inculcate the same lesson-always repeating both in verse and out of verse: "Keep your mind from this way of enquiry, for never will you show that not-being is" - Such is his testimony, which is confirmed by the very expression when sifted a little.
So my question is, was it common among Ancient Greek philosophers to believe that uttering a falsehood is impossible, given that two philosophers as different as Parmenides and Heraclitus apparently both believed it? Do we know of other philosophers who believed it? Or is this just a strawman that Plato attributes to various interlocutors in his dialogues so it can be knocked down?