In the dialogue between Socrates and Theaetetus, as recorded by Plato, Theaetetus is presented as holding the opinion of Protagoras. Theaetetus explained to Socrates that “he who knows anything perceives that which he knows, and, as it appears at present, knowledge is nothing else than perception.”( Plat. Theaet. 151e)
Protagoras, according to Socrates, said “that man is ‘the measure of all things, of the existence of the things that are and the non-existence of the things that are not.’”(Theaet. 152a) Socrates interpreted Protagoras to mean that “individual things are for me such as they appear to me, and for you in turn such as they appear to you – you and I being ‘man’”(ibid). Socrates presented peritropê case against that opinion in 159a-171e.
Some doctrines of relativism hold that what we mean by saying proposition p is true is that p is true for an individual i who believes p. When I assert something like: “it is true that that grass is green”, what I mean is that, “it is true that that grass is green for me”.
Following that chain of reasoning, all truth, we are led to believe, is relative to its believer in a given context. A proposition is not “truth” in and by itself, but only “truth for” its believer.
Now, like Socrates would have said, “come now, let us examine [this] utterance together, and see whether it is a real offspring or a mere wind-egg.” (151e) I think this form of relativism is a mere wind-egg. When I say to you that p is true, I am expected to give reasons why I think p is true or why I think you should also think that p is true. But if I say to you, p is true for me, I would not be surprised if your answer is: “good on ya’ Prayson, that is good for you, so what?”
If we reduce truth to truth for an individual, including a relativist holding such view, then the proposition “all truth are relative” is also true for its believer (i.e. a relativist holding such a view). If that is true, we can simply answer that relativist with, “good on ya’ that is good for you, so what?” If she wishes us to also believe that it is true that truth is relative not only for her but also for us, then she would have peritropê her own case against herself.
Plato. Plato in Twelve Volumes, Vol. 12 translated by Harold N. Fowler. Cambridge, MA, Harvard University Press; London, William Heinemann Ltd. 1921.