In the Theaetetus, Socrates helps Theaetetus test an idea he’s inherited from Protagoras – the idea that "man is the measure of all things" – against ideas accepted by its proponents. His view seems to be, "The only way I can really test my ideas is against ideas accepted by me."
What does Protagoras mean, and what are possible viewpoints on Protagoras's claim?
Construct and explain an argument that you think is a fair representation of the thinking that lies behind this view.
Develop and explain what you think is ones principal objection to this argument. and how would one argue their objections.
In one of Plato's dialogues, Plato records Socrates as having a conversation with Theaetetus, an Athenian mathematician who was also a devout follower of Protagoras of Abdera, a Sophist. It is Protagoras who is quoted in the dialogue as claiming that man "is the measure of all things, of the existence of things that are, and of the non-existence of things that are not" (Great Philosophers, "Protagoras: Plato's Critique"). To claim that man is "the measure of all things" is to say that knowledge of truth rests on the opinions of man as individuals, which is another way of saying that truth is relative, an argument that Socrates adamantly opposed, preferring instead the idea of absolute truth ("Protagoras: Plato's Critique"). Truth becomes relative when, like Protagoras, we equate truth with perception. If truth is only perception, then any person's perception of what is true is of course going to be different, or relative to that person. More specifically, in the phrase man is "the measure of all things," Protagoras seems to be using the term measure to mean comparison or judgement; in other words, he is saying that man judges all things to be true based on a comparison. If we also see Protagoras as claiming that truth is perception, then, yes, he would be saying that man judges truth by comparing it to his own perceptions of what is true. Hence, yes, it can be said Protagoras seems to be claiming, "The only way I can really test my ideas is against ideas accepted by me."
While many accept the philosophy of relative truth, others have shown the argument of relativism can "often lead to implausible conclusions" (Standford Encyclopedia of Philosophy, "Relativism"). The above statement particularly presents a logical fallacy. If one only tests ideas based off of one's own ideas, then knowledge can never really truly be obtained. To obtain knowledge, one must search outside of one's self. It can be said we can only gain knowledge from others rather than from ourselves. Therefore, we would learn new knowledge or new ideas by testing our own ideas against someone else's ideas rather than against our own ideas. True, one can only test ideas that have been internalized, meaning that we can only test ideas we are thinking about, making them a part of our own internal thought process. But one can internalize ideas without actually, fully accepting them. One can internalize ideas simply on the basis of knowing that the other person with the idea has done a great deal more research on the topic than we have. Once we internalize the ideas, we then compare them against our own to figure out weaknesses and strengths in both our own ideas and the other person's. But testing doesn't have to stop there. We can even test someone else's ideas against a brand new person's ideas, another scholar's ideas altogether. Once we make a decision about which ideas are weak or strong, we then fully internalize them by using them to change our own conceptions. However, as it can be seen, testing ideas is not merely a process of testing our own ideas against our own ideas. To fully gain new knowledge, we must test our ideas against ideas outside of ourselves.
Socrates himself pointed out a logical fallacy in Protagoras's argument. If knowledge of truth is only perception, then what's keeping Protagoras from only arguing that man is "the measure of all things"? Why not argue that anything with sensory perception is the measure of all things, like a "pig or dog-faced baboon"--why can't they equally make judgements based on perception about what is true?
Hence, as we can see, while the relativism argument sometimes does have merit, it can also be shown to lead to "implausible conclusions."