SOCRATES: For he [Protagoras] says, you know, that ‘Man is the measure of all things: of the things which are, that they are, and of the things which are not, that they are not.’(Theaetetus, 152a)
…
Well then, in that case are we going to say that the wind itself, by itself, is cold or not cold? Or shall we listen to Protagoras, and say it is cold for the one who feels cold, and for the other, not cold? (Theaetetus, 152b)

In the ‘man is the measure of all things’ doctrine1, Protagoras sets out a claim that serves as the foundation for sophistic relativism. Given that every man’s perception about phenomena in the world is as respectable as the perception of any other man; judging whether something is true or false becomes only a matter of subjective preference. Having this sophistic relativism set in place, a question then arises as to by what means is it possible to derive some sort of knowledge and to what degree will it entail some form of objectivity and universality? If any given phenomena can be judged differently according to different perceivers, what does that say about the nature of knowledge? In this essay it will be demonstrated how some form of logos persists even if all statements are deemed to be equally true. Lastly, a few contentions that Plato expresses will also be demonstrated.

One of the underlying ideas of the ‘man is the measure of all things’ doctrine is also the primacy of the ‘two-_logoi_’ rule. This doctrine proposed by Protagoras encompasses the premise that there will always be two opposite arguments for any given proposition. These two arguments are always contrary to one-another, but both can nonetheless be argued for or against equally well; both arguments therefore are true but none of them are deemed to be absolutely true.2 However, the two apposing logos are frequently given a moralistic and judgmental connotation, such that one is deemed to be a ‘just argument’ and the other as an ‘unjust argument’. By accounting this aspect of the ‘two-_logoi_’ doctrine, one might point out a contradiction that it has with the relativist ‘man is the measure of all things’ doctrine, which posits that there are as many logoi as there are men capable of making an argument. If everything is reduced to binary oppositions: just and unjust, good and bad, true or false; then it appears that there can only be two opposite logoi in any given proposition, contrary to a innumerable multiplicity of truths and interpretations about a given proposition. However, this conclusion might be derived if one assumes that each of the two arguments under the ‘two-_logoi_’ doctrine is immutable and unchangeable. This assumption is precisely what is put under question by the antiologoi doctrine, which posits that any two-_logoi_ arguments can both become contradictory once they confront one-another, bringing them to a state of aporia, an impasse with no resolution3. This poses as a problem, “since if each man’s perception are true and these constitute logoi it might seem that concerning every thing there would be not two logoi, but a number very much greater, namely as many as there were perceptions by different people”4. In this case, the number of logos that lie in opposition with one another would go beyond just two arguments. Moreover, in relation to the moralizing aspect mentioned above, does not each person have their own moral judgment as to what constitutes the just and the unjust, the good and the bad, the true or the false?

It is at this point that the problem of language comes in. According to Protagoras, it is not that there is an A and non-A statement for each proposition that necessary makes the former true and the later false, but that each of these statements are equally true because both are about different things that have little or nothing to do with the actual thing that is being referenced5. This observation largely resonates with Wittgenstein’s theory of ‘language games’: for Gorgias, the claim that all logoi are true rests on the fact that all logoi never really appertain to the thing-in-itself of the object in question, but are always external to the object, and therefore cannot be contradicted and therefore can only be true6. To this claim, a contention voiced by Democritus and Plato will be mention below. However, given that every statement is true, it can be seen how logical statements just like language, do not have a one-one relationship with the thing they are referring to, but rather, a purely semantical relationship that refers to things only in their appearance7. It is here that Gorgias’ famous three arguments pose as a foundation for the epistemology of sophistic relativism:

  1. Nothing is.
  2. Even if it is, it cannot be known to human beings.
  3. Even if it is and is knowable, it cannot be indicated and made meaningful to another person.

Here it is suggested that (1) there is no such thing as an absolute thing-in-itself, (2) but even if there is such a thing as an absolute thing-in-itself it cannot be grasped by the human faculties of knowledge. Although this problem has already been formulated and debated quite sufficiently by Ancient Greek thinkers, it is a problem that was also central to two important modern thinkers: René Descartes and Immanuel Kant. Descartes claimed that all absolute knowledge of external phenomena can be accessed by the mind thanks to a God who directs and grounds its capacities to grasp the world absolutely. Kant on the other hand, claimed that the thing-in-itself cannot be known through the finite capacities of human reason, but does maintain that it is “thinkable”.8 For the sophists, the things-in-itself is also unknowable and falls somewhat in line with the Kantian doctrine although the doctrine of sophistic relativism goes less assuredly towards making a claim about thinkability and truths since every man remains ‘the measure of all things’. However, lets hypothetically suppose that a person has managed through some miraculous way, attain absolute knowledge about a thing, then according to (3), it becomes impossible to communicate it due to the intrinsic limitations of language that make it impossible to convey a statement while not at the same time abstracting from the thing that the statement refers to. Another feature of the external world that makes grasping absolute knowledge about it ever more difficult, is the fact that a phenomena changes its nature the very next moment one references it. Here, one can recall Heraclitus’s claim that “No man ever steps in the same river twice, for it is not the same river and he is not the same man”. In Theaetetus, Plato expounds an addition to this thought by demonstrating that everything is in the state of becoming from one moment to the next, which makes the possibility of absolute truth questionable:

SOCRATES: But, I say, look here. Was Protagoras one of those omniscient people? Did he perhaps put this out as a riddle for the common crowd of us, while he revealed the Truth as a secret doctrine to his own pupils?
THEAETETUS: What do you mean by that, Socrates?
SOCRATES: I’ll tell you; and this, now, is certainly no ordinary theory—I mean the theory that there is nothing which in itself is just one thing: nothing which you could rightly call anything or any kind of thing. If you call a thing large, it will reveal itself as small, and if you call it heavy, it is liable to appear as light, and so on with everything, because nothing is one or anything or any kind of thing. What is really true, is this: the things of which we naturally say that they ’are’, are in process of coming to be, as the result of movement and change and blending with one another. We are wrong when we say they ‘are’, since nothing ever is, but everything is coming to be. (Theaetetus, 152e)

Given that all things are in constant becoming and cannot be refereed by an absolute truth, the question then arises regarding as to what knowledge is and how can it be obtained and shared among others. Due to the inherent difficulties in Gorgias’s three arguments, the sophists attempt to define a more moderate definition of knowledge. A form of this method is to pose questions that attempt to understand truth relativistically and not positivistically. One of the exemplars for this method was Classen, who instead of posing the usual Socratic and early Platonic question of ‘what is x?’, posed the question of ‘in what respect is x different from y?’9. In this sense, knowledge is established based on a correlational case to case basis that is inherently relativistic. In contrast, Plato in Theaetetus entertains the idea of grounding knowledge of things based on mathematical relations that particulars have to their universals, which is inherently positivistic. One of these examples include what is known as the ‘Spiral of Theodorus’ which consist of multiple triangles with incremental hypotenuse lengths (√3, √5, … √17) that together constitute a spiral (Theaetetus, 147c). What this geometric demonstration provides is the possibility of formulating an absolute ideal of a spiral that is constituted out of particular triangles that share a commonality with one another—a geometric rule where that makes every particular triangle constitutes a spiral. The question then arises regarding whether a universal notion of knowledge can be derived in the same way that a ‘Spiral of Theodorus’ can be derived from the particular triangles that constitute it. Since the definition of ‘knowledge of’ is based on a case to case definition of this term, e.g. “knowledge of the making of shoes” or “knowledge of the making of wooden furniture”; Plato begs a more universalizing definition of knowledge which can then bootstrap each particular example of knowledge to a universally defined concept of knowledge (Theaetetus, 146e). But under the guise of sophistic relativism, the possibility of accessing the universal definition of knowledge, or an absolute definition of anything for that matter, is itself put in question since as Heraclitus claims, phenomena changes the very next moment after a concept of it has been derived.

Another way in which Plato attempts to counteract the doctrine of two-_logoi_ that are always in contradiction with one another, is through his theory of Forms. In the same way that there can be many instances of triangles that relate to an overarching absolute idea of a triangle, for Plato, there can be a similar universal idea of a chair, beauty, virtue, and knowledge. Since for Plato, contradictions between two-_logoi_ occurs because one is dealing with the phenomenal representations of these logoi, and not their static, absolute idea of Forms.10 Once all things become correlated to their adjacent Forms, contradictions cease to arise, since by their very definition, there can be no contradictions among Forms because they are absolute universals. Further, both Plato and Democritus challenge Protogoras’s claim that all statements are true, which is a crucial aspect of his ’man is the measure of all things’ doctrine. They object: “if every representation is true, the judgement that not every representation is true, being based on a representation, will also be true, and thus the judgment that every representation is true will become false”.11

Given that Protogoras and other sophists raised certain philosophic questions that remain unresolved even until this day12; namely, is there such a thing as an absolute truth or are there as many truths as there are observing individuals. It is not surprising to see thinkers like Plato and Socrates attack these sophistic arguments in an attempt to ground some form of rationality and epistemology when talking about phenomena in the world. But what these sophistic questions ultimately demonstrate is the difficulty of escaping relativism without resolving into some dogmatic and naive counter-theory. Even Plato’s and Democritus’s objection against Protagoras’s statement that all “representations are true”, itself relies on an anti- logoi—to which a sophist might reply: does this logoi really appertain to the statement it attacks or is it just another play of words? Gorgias’ proposition (1) “nothing is” begs a question: “how can we really know that something is and exists if we don’t have absolute access to it but only have access to an appearance of it”? A paranoid rationalist like Plato or Descartes would ruthlessly attempt to find some sort of way to ground absolute knowledge about a thing; a sophists on the other hand, might simply accept certain limits in epistemology and work within these limits.

  1. Socrates rhetorically mocks Protagoras’s claim that “man is the measure of all things”, for he asks, why is it that man is the measure of things and not a “Pig” or a “Baboon” given that these creatures also have the capacity to perceive (Theaetetus, 161c—d). ↩

  2. Kerferd G.B., The Sophistic Movement (Cambridge: Cambridge University Press, 1981), p. 81 ↩

  3. Kerferd, p. 82, 90 ↩

  4. Kerferd, p. 90 ↩

  5. Kerferd, p. 92 ↩

  6. Kerferd, p. 80 ↩

  7. Kerferd, p. 73 ↩

  8. Quentin Meillassoux, trans. Ray Brassier; After Finitude: An Essay on The Necessity of Contingency (New York: Bloomsbury, 2008), pp.31, 35 ↩

  9. Kerferd, p. 74 ↩

  10. Kerferd, p. 103 ↩

  11. Dillon, John & Gergel, Tanya; The Greek Sophists (New York: Penguin, 2003), p.15 ↩

  12. Meillassoux, 2008 ↩