How did philosopher Plato react to relativism?
The standard formulation of relativism in ancient philosophy was the homo-mensura statement of Protagoras:
"Man is the measure of all things, of those that are that they are and of those that are not that they are not."
Plato's dialogue, Theaetetus, is an extended refutation of the homo-mensura doctrine and its epistemological consequences. First, he argues that the individual judgement can be deranged. If a person has a fever, he may perceive the temperature as hot that an unfevered man would perceive as cold. But it cannot be hot and cold, and thus we cannot accept as the criterion the judgement of the individual, i.e. the possibility of individuals having distorted judgements precludes the possibility that each thing is as the individual judges it. Next, in the dialogue, the discussion moves to a refutation of knowledge as perception. Then it argues that since the object of knowledge must remain stable the Heraclitean theory of flux implies that perception can only lead to opinion not knowledge.
In many of the dialogues and in The Republic, especially in the allegory of the cave, Plato develops the idea that the realm of Ideas or Forms exists apart from the world of time and space. The world we perceive with our physical senses is the world of "relativism." Everything we perceive with our senses is limited and transitory. The realm of Forms is absolute and unchanging. We can draw triangles on paper or in the sand but those began existing at one moment and will cease existing at a later moment. The drawn triangles will also of necessity be a certain type of triangle--a right triangle, an equilateral triangle, etc. But the concept of Triangle, which can be perceived only by the intellect, the Reason, is absolute and eternal. The concept is a closed three-sided figure whose internal angles equal 180 degrees. That concept is not relative to anything, according to Plato. A particular triangle drawn or made in the world of time and space is relative to the particulars of its physical existence.