There are two aspects of opinion that are responsible for its inability to be true. The first is that it is based on sense-experience. For the pre-Socratic philosophers, the proper objects of sense-experience are qualities such as hot and cold, dry and wet, light and dark. These qualities tend to come in opposing pairs, so that what is hot is not cold, and what is cold is not hot. In forming opinions which describe sense-experience, we freely use language to name the opposing qualities. But Parmenides regarded this as an abuse of language.
Learn next about the opinions of men, as you listen to the deceptive ordering of my words. For men have established the habit of naming two thought-forms; therein they have erred, because one of the forms ought not to have been named. They have distinguished the thought-forms as opposed in character and as having properties that set them apart from each other. On the one hand there is the fire of the upper sky, gentle, rarefied, and everywhere identical to itself; on the other hand there lies opposed to it utter darkness, dense and heavy" (F9)The two thought-forms appear to be hot, bright, rare, light fire and cold, dark, dense, heavy earth. One might think that what should not be named is not-being or what is not-hot, not-bright, not-rare, not-light. But it seems wrong to claim that not-being is dense and heavy, or that the dense is merely the not-rare and the heavy merely the not-light. Aristotle claimed that, "he puts the hot on the side of Being, the cold on the side of Not-Being" (T10, cf. T13). There is some evidence that Parmenides admitted that hot, cold, and the rest can be sensed (T20, T21). At any rate, there is a problem with naming one of the thought-forms, and the problem lies in the fact that in some sense it is intended to refer to what is not.
Another way to interpret Parmenides's view is that names such as "hot" and "cold" do not designate anything at all. They are empty names. "Accordingly, all the usual notions that mortals accept and rely on as if true--coming-to-be and perishing, being and not-being, change of place and variegated shades of color--these are nothing more than names" (F8D). This interpretation raises a problem, however, since it seems reasonable to accept that something is named by these words, even if it is only sense-experience or appearances and not "what is." The use of the names seems at least meaningful, as is attested to the fact that Parmenides devoted a poem to the "way of opinion." However this issue gets resolved, it seems correct to say that the names do not express thoughts. In this way, Parmenides can claim that what is not cannot be thought, though it may be an ingredient in opinion. Conversely, what is thought cannot not be. This means that the "way of opinion" does not involve "thought" in its primary meaning. This appears paradoxical: what do they express? But it may be that this kind of paradox is unavoidable in the context of Parmenides's system.
Now we may turn to the relation between opinion and truth. It is safe to say that for Parmenides, something is true if and only if it is about what is, and something is false if and only if it is about what is not. A central Parmenidean thesis is that all thought is about what is, and no thought is about what is not: "you cannot know not-being and cannot express it" (F8). From the fact that all thought is about what is, it follows that all thought is true. From the fact that all opinion is intended to be about what is not, it follows that all opinion is false.
Protagoras is represented by Plato as holding the thesis: "It is not possible to think what is false" (T3). Given the above interpretation, Parmenides would have accepted this thesis. What is false is what is not, and what is not cannot, on Parmenides's view, be the object of thought. But Protagoras held the thesis for an entirely different reason: "because one can only think what he experiences, and what he experiences is true." This is in direct opposition to Parmenides's view that what one experiences is not true at all, but only false opinion. It is also in direct opposition to Parmenides's view that what is experienced is not thought. In fact, Protagoras does not respect any distinction between thought and opinion. Given these definitions, Protagoras holds in opposition to Parmenides that it is possible to think what is not.
What, then, is truth for Protagoras? We have no formal definition, but it is not hard to devise one. We are told that the individual human being is the "measure of all things, of what is, that it is, of what is not, that it is not." The specific "measure" of what is or is not is the way in which things seem or appear. One passage from Plato is quite suggestive in this regard, "whatever seems right and admirable to a particular city-state is truly right and admirable--during the period of time in which that opinion continues to be held" (T3). An opinion is true (while it is held) if and only if describes the way things appear to whoever has the opinion. Some opinions are about personal sense-experience, while others are about issues of right and wrong behavior, but both are subject to the same definition.
Now we can see more clearly why Protagoras held that it is impossible to think what is false. To do so, one would have to have an opinion that mis-describes the way things seem to him. But we can virtually identify an opinion with a description of the way things seem. If I sense a fire as being hot, how can I be of the opinion that it is not hot? Some philosophers would say that this is still possible, in that an opinion is a judgment and a judgment even about the way something appears to the senses can be mistaken. (See Keith Lehrer, Theory of Knowledge, Chapters 3 and 4). But Protagoras claims to the contrary that "one can only think what he experiences" (T3).
Now consider Aristotle's definition of truth:
To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true. (Metaphysics IV, 7 (1011b25-26)Aristotle allowed that truth can involve what is not. If I say that fire is not cold, then I may speak the truth, despite the negative character of what is asserted. This view is friendly (so far) to Protagoras's, in that it allows for true opinion. Parmenides, on the other hand, denies that we can truly say of what is not that it is not.
Protagoras claims that whatever one experiences is true. This is adaptable to Aristotle's definition, in that the experience is something that "is," so to say of an experience that one experiences it is true. If I say that honey tastes sweet to me, that is a true saying, so long as honey actually does taste sweet to me. Given that I cannot be mistaken in my judgment about how things taste to me, my thought must be a true one.
But there is a conflict between Aristotle's definition of truth and Parmenides's. Aristotle allows that we can say things about more than just our experiences. To say that fire burns wood is more than just to describe the way things appear to me. If I say that water burns wood, then I have thought something false, something Protagoras counts as impossible. Or a city-state might think that patricide (killing of one's father) is "right and admirable," a thought which Aristotle would say is false.
Now suppose that a person is of the opinion that water burns wood, which by Protagoras's definition is true because it is his opinion. Later he abandons that opinion in favor of the new opinion that fire burns wood. Protagoras would say (if Plato's account of him is correct) that the first opinion is "unsound" and the second is "sound," and that the second opinion is "better" than the first. "The resulting appearances are sometimes ignorantly spoken of as 'true'; I, however, do not call them truer than the earlier ones but simply better" (T3). They are better in that they are the issue of a healthy soul, while the original opinion reflects the operations of a sick soul. Protagoras is said to have claimed that, "It is the wise man's task, when the people are afflicted with unsound beliefs, to substitute others so that they seem true and therefore are true" (T3).
A problem with this view is that Protagoras seems to be asserting that the state of being sick or healthy is more than mere seeming. He makes the assertion to justify his charging "a large fee" for converting opinion though the exercise of his wisdom. Would the fee be justified if the student just seemed to have a healthier mind? Moreover, there would be no real sense in which the condition of being healthy is better than that of being sick, it would just seem better. So Protagoras seems to be making practical claims that are not backed up by his theory. In his defense, it might be argued that it is true that the condition of being healthy is better than that of being sick because it seems so to Protagoras and whoever agrees with him. It is true, that is, for them, and perhaps there are few who would disagree with Protagoras. If Protagoras is trying to persuade someone that his high fees are justifed, he can appeal to the way things seem to that person.
How can anyone assert seriously that the opinion that water burns wood is true? The answer must be that the opinion expresses the sense-experience of the person at the time, perhaps resulting from hallucination. There are two ways of explaining this. One is that Protagoras is departing from the usual meanings of terms. The thought "water burns wood" must be taken to mean "it appears to me that water burns wood." This is indeed a true opinion, by Aristotle's definition. The other is that Aristotle (and his posterity) have incorrectly described the nature of truth. This seems more likely the way in which Protagoras would have seen it, and it is how Aristotle interpreted Protagoras. This way is difficult. A hint of the problems it involves is that on Protagoras's definition, Aristotle's opinion about truth is true for him!
There is a possible middle way between the account of truth that has here been attributed to Protagoras and that of Aristotle. According to Sextus Empiricus, Protagoras held that, "There are intelligible principles inherent in the matter of every phenomenon; because matter is essentially the sum of all the seemings that it has for any and all persons" (F3). On this interpretation, there is objectivity in truth after all. If it seems to me that water burns wood, it is true that water burns wood, and this is part of what it is to be water and wood. A more plausible view is that it is part of what it is to be water and wood that water seems to me to burn wood. But on that view, it is not asserted that it is true that water burns wood. It should be noted that a strong argument can be made that this "objective" interpretation imposed on Protagoras by later philosophers and conflicts with his real view. (See Gregory Vlastos's Editor's Introduction in the Library of Liberal Arts edition of Plato's Protagoras.)
Aristotle objected to Parmenides's account of truth on the grounds that it allows the same thing to have a quality and its opposite.
If such a position is adopted, then it follows that the same thing is and is not, that it is both good and bad, and simlarly for other contradictions; because, after all, a given thing will seem beautiful to one group of people and ugly to another, and by the theory in question each of the conflicting appearances will be "the measure." (T4)A similar criticism is that "If it is equally possible to affirm and to deny anything whatever on any subject, then a given thing will be at once a ship, a wall, and a man" (T6). Presumably this would arise when different people (or the same person at different times) has expriences of a single object as each of these things, perhaps due to hallucination or illusion.
Protagoras could respond in various ways. He could "bite the bullet" and accept that the same thing is both beautiful and ugly, perhaps on the grounds that these words mean "beautiful to someone" and "ugly to someone." In that case, he would be following Aristotle's definition of truth. Or he could say that the fact that one has a true opinion that an object is beautiful does not imply that the object is beautiful. All it means is that the object appears beautiful to someone. In that case, he would be denying a fundamental property of "detachment" philosophers have attributed to truth, that "It is true that X" implies "X."
Aristotle would no doubt respond that in either case, the concept of truth is used promiscuously, so much so as to be useless. The point of language is to distinguish things and to describe them as they are, and the concept of truth indicates the fact that some of our descriptions succeed and some fail. If they all are successful, then there is no point in distinguishing between truth and falsehood. To this, Protagoras might reply that there is still a point. At least the notion of truth is applicable to the way things appear. An object will not be described as a ship, a wall, and a man, unless there are the appearances of a ship, a wall, and a man. As was noted above, Protagoras thought that these differences reflect the workings of healthy or sick minds.
For a long time, Aristotle's view was the only one taken seriously. The Epicureans held that all opinions about sense-experience are true, acknowledging that opinions about what lies beyond appearances are often false. Even the ancient skeptics accepted the Aristotelian definition of truth, only denying or refusing to accept that the truth can be known. Protagorean relativism was given a boost in the late nineteenth century by the German philosopher Friedrich Nietzsche. One of his primary goals was to undermine conventional morality. He claimed that philosophers from Socrates onward had built up a notion of "moral truth" as expressing an objective moral reality. Niezsche credited the Sophists with having attacked this notion: "they postulate the first truth that a 'morality-in-itself,' a 'good-in-itself' do not exist, that it is a swindle to talk of 'truth' in this field" (The Will to Power, Section 428). More generally, Nietzsche tried to break down the distinction Parmenides had erected between appearance and reality, which is the basis for the Aristotelian definition of truth. Nietzsche's views have become quite popular, especially among European philosophers.
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