Ancient Philosophy

Socrates, Plato, and Aristotle

Knowledge and Perception in Plato

Most of our contemporaries consider it self-evident that empirical knowledge is derived from perception. However, Plato and certain other philosophical schools espouse an entirely different theory: they assert that what is gained through the senses is unworthy of being called "knowledge," and that true knowledge should solely pertain to concepts. According to this view, "2 + 2 = 4" constitutes genuine knowledge, whereas a statement like "snow is white" is so fraught with ambiguity and uncertainty that it cannot find a place among philosophical truths.

This perspective may trace its roots back to Parmenides, but in its clear form, the philosophical world owes this view to Plato. In this chapter, I intend to examine only Plato's critique of the notion that knowledge is synonymous with perception, which constitutes the first half of the Theaetetus.

In this dialogue, an attempt is made to define "knowledge," which ultimately concludes with a negative result; several definitions are proposed and rejected, but none are put forth as satisfactory.

The first of the proposed definitions, and the only one I will consider, is articulated by Theaetetus as follows: "In my opinion, a person who knows something perceives that which they know, and, as it seems to me now, knowledge is nothing other than perception." Socrates identifies this theory with Protagoras’ assertion that "man is the measure of all things," meaning that "whatever seems to me to be, such it is for me, and whatever seems to you, such it is in turn for you." Socrates adds, "Thus, perception is always a perception of being, and as knowledge, it is infallible."

A significant portion of the subsequent argument concerns the characterization of perception; once this is established, it is not difficult to demonstrate that what we have come to know as perception cannot be considered knowledge.

To Protagoras’ theory, Socrates adds Heraclitus’ doctrine that everything is in constant flux, asserting that "all things to which we attribute the concept of being are in a state of becoming." Plato agrees with this regarding sensory objects but maintains that it does not apply to objects of true knowledge. However, throughout the dialogue, his positive theories remain in the shadows.

From Heraclitus’ theory, even if it applies only to sensory objects, follows a definition of knowledge as perception, leading to the conclusion that knowledge pertains to that which is in a state of becoming rather than to that which is.

There are certain elementary difficulties inherent in this matter. We are told that since 6 is greater than 4 but less than 12, it is simultaneously both large and small, which presents a contradiction. Socrates now stands above Theaetetus, who is still a somewhat immature youth; yet, in a few years, Socrates will be beneath Theaetetus. Thus, Socrates is both tall and short at once. The idea of relational statements seems to have puzzled Plato, as it has many great philosophers up to and including Hegel. However, these difficulties do not bear significant relevance to the argument at hand and may be overlooked.

Returning to perception, we find that it is considered conditioned by the interaction between an object and some sense organ, both of which, according to Heraclitus’ theory, are always changing and, in changing, alter the mental object of perception. Socrates notes that when he is healthy, he finds wine sweet, but when he is ill, he perceives it as sour. Here, the change in the perceiving subject induces a change in the mental object of perception.

Objections are raised against Protagoras’ theory, though some of them are later retracted. It is insisted that Protagoras must equally consider pigs and monkeys as measures of all things since they are also perceiving beings. Questions arise regarding the reality of perception in dreams and states of madness. The thought is presented that if Protagoras is correct, then one person knows no more than another: Protagoras is not only as wise as the gods but, what is even more serious, not wiser than a fool. Furthermore, if one person’s judgments are as correct as another’s, there are equal grounds to argue that the person who believes Protagoras to be wrong is indeed correct.

Socrates attempts to find answers to many of these objections by momentarily placing himself in Protagoras’ position. Regarding dreams, he posits that the mental objects of perception are true as such, and he dismisses the argument about pigs and monkeys as a gross insult; as for the argument that every person is the measure of all things and that one person is as wise as another, Socrates offers a very interesting response on Protagoras’ behalf, suggesting that while one judgment cannot be more true than another, it may be better in the sense that it leads to better consequences. This notion resonates with pragmatism.

However, this response, though devised by Socrates himself, does not satisfy him. For instance, he argues that when a doctor predicts the course of his illness, he indeed knows more about his future than Socrates does. And when people disagree about what laws a wise state should enact, the outcome will reveal that some individuals possessed greater knowledge of the future than others. Thus, we cannot escape the conclusion that a wise person serves as a better measure of things than a fool.

All these objections are directed against the theory that each person is the measure of all things and only indirectly against the "theory" that "knowledge" means "perception," since this theory leads to another. However, there is a direct argument, namely, that memory should be allowed just as perception is. This is accepted, and to this extent, the proposed definition is modified.

We now turn to the critique of Heraclitus’ doctrine. Initially, it is taken to extremes, as we are told, in accordance with the practice of his pupils among the capable youths of Ephesus. A thing can change in two ways — through movement and through a change in quality, and it is believed that the doctrine of constant flux asserts that everything is always changing in both respects. And not only does everything undergo some qualitative change, but everything always alters all its qualities — thus, we are informed, the wise men of Ephesus think. This leads to inconvenient consequences. We cannot say "this is white," because if it was white when we began speaking, it will cease to be white before we finish our phrase. We cannot be correct in claiming that we see anything because sight continuously transitions into non-sight. If everything changes in everything, then sight has no right to be called more sight than non-sight, and any perception has no right to be called more perception than non-perception. And when we say "perception is knowledge," we might as well say "perception is ignorance."

This argument distills down to the following: whatever is in constant motion, the meanings of words must remain unchanged, at least temporarily, otherwise no statement will be definite and no statement will be more true than false. There must be something more or less permanent for reasoning and knowledge to be possible. I believe this should be accepted. A significant portion of all that pertains to flux is compatible with this acceptance.

In this passage, there is a refusal to discuss Parmenides on the grounds that he is too noble and grand. "He inspires me, much like Homer, with both reverence and awe." ... "I have come to appreciate the noble depth of this man in every respect." In these remarks, Plato expresses his love for the unmoving universe and his aversion to the constant flux of Heraclitus, which he permits only for the sake of argument. However, after this expression of respect, he refrains from elaborating on Parmenides’ views against Heraclitus’ theory.

We have now reached the final argument of Plato against the identification of knowledge with perception. He begins by stating that we perceive more through our eyes and ears than with our eyes and ears; further, he points out that some aspects of our knowledge are not tied to any sense organ. For example, we can know that sounds and colors are not alike, even though no single sense can perceive both. There is no specific organ for the perception of "being and non-being, likeness and unlikeness, identity and difference, nor are they defined by any particular number." The same applies to the noble and the shameful, the good and the evil. "... Some things the soul observes by itself, while others it observes through bodily faculties." We perceive hardness and softness through touch, but it is the soul that judges their existence and their mutual opposition. Only the soul can grasp existence, and we cannot comprehend truth without understanding existence. From this, it follows that we cannot know things solely through the senses, as we cannot ascertain the existence of things through one sense alone. Therefore, knowledge consists not in impressions but in inferences, and perception is not knowledge, for it is "in these [inferences] that we can grasp essence and truth; in that [in perception], we cannot."

It is by no means easy to distinguish what can be accepted from what must be rejected in this argument against the identification of knowledge with perception. Plato discusses three interrelated propositions, namely:

Knowledge is perception;

Man is the measure of all things;

Everything is in a state of constant motion.

• The first of these propositions, to which the aforementioned argument chiefly pertains, is scarcely discussed on its own, save for the last excerpt we have just provided. Here, it is argued that comparison, knowledge of existence, and understanding of numbers are necessary for knowledge, yet they cannot be included in perception, as they are not accomplished through any sense organ. They can be said to be distinct entities. Let us begin with likeness and unlikeness.

That two shades of color, which I observe, are alike or unalike depending on the circumstances represents something I ought to accept not as "perception," but as "judgment of perception." I must assert that perception is not knowledge but merely something that occurs and pertains equally to the realm of physics and the realm of psychology. Naturally, we consider perception, as does Plato, to be a relation between the perceiving subject and some object; we say, "I see a table." Yet here, "I" and "table" are logical constructions. The essence of the bare phenomenon is simply certain colored spots. They are associated with tactile images, can evoke words, and may become a source of memories. The mental object of perception, filled with tactile images, becomes the "object" believed to be physical; filled with words and memories, it becomes the "perception," which is part of the "subject" and is deemed spiritual. The mental object of perception is indeed a phenomenon; it is neither true nor false. When filled with words, it constitutes a judgment and can be true or false. This judgment I refer to as the "judgment of perception." The proposition "knowledge is perception" should be interpreted as meaning "knowledge is the judgment of perception." Only in this form can it be grammatically correct.

Let us return to likeness and unlikeness. When I simultaneously perceive two colors, due to their likeness and unlikeness, they can very well be part of the data, and one can assert them in the judgment of perception. Plato's argument that we lack a sense organ for the perception of likeness and unlikeness overlooks the cerebral cortex and assumes that all sense organs must reside on the surface of the body.

The argument for including likeness and unlikeness as potential perceptible data is as follows. Suppose we see two shades of color A and B and express the judgment: "A is like B." Further, let us assume, as Plato does, that this judgment is generally correct, and particularly correct in the case we are examining. Therefore, there exists a relation of likeness between A and B, not merely our judgment affirming likeness. If it were solely our judgment, it would be an arbitrary assertion, incapable of being true or false. Since it can evidently be true or false, there may exist a likeness between A and B, which cannot simply be something "mental." The statement "A is like B" is true (if it is true) by virtue of a "fact," just as the statement "A is red" or "A is round." The mind participates no more in the perception of likeness than in the perception of color.

Now I turn to existence, which Plato particularly emphasizes. He asserts that we have a thought regarding sound and color that encompasses both simultaneously, namely, that they exist. Existence belongs to all and lies among the things that the mind encompasses; without grasping existence, one cannot grasp truth.

The argument against Plato here differs fundamentally from the argument concerning likeness and unlikeness. It consists in the following: everything Plato says about existence represents poor grammar or, more accurately, poor syntax. This question holds significant importance not only concerning Plato but also regarding other issues, such as the ontological proof of the existence of God.

Suppose you tell a child: "Lions exist, while unicorns do not"; you can demonstrate this regarding lions by taking the child to the zoo and saying, "Look, this is a lion." You would not add, unless you are a philosopher: "And you can see that it exists." If, being a philosopher, you do add this, you would be speaking nonsense. To say "lions exist" means "lions are present," that is, the proposition "x is a lion" is true for an appropriate "x." But you cannot state that an appropriate "x" "exists": we can only apply this verb to a description, regardless of whether it is complete or incomplete. "Lion" is an incomplete description because it applies to many objects: "the largest lion in the zoo" is a complete description because it applies only to one object.

Now, looking at a bright red spot, I may say: "This is my current mental object of perception"; I may also say: "My current mental object of perception exists"; but I must not say: "This exists"—because the word "exists" has meaning only when it relates to a description, not to a name. This releases existence from being one of the things the mind perceives.

Let us now turn to the understanding of numbers. Here it is necessary to consider two quite distinct matters: on one hand, arithmetic propositions, and on the other, empirical propositions of enumeration. "2 + 2 = 4" pertains to the first category; "I have ten fingers" belongs to the second.

I must agree with Plato that arithmetic and pure mathematics, in general, are not derived from perception; pure mathematics consists of tautologies, akin to the statement "men are men," albeit usually more complex. To ascertain the correctness of a mathematical statement, we need not examine the world, but only the meanings of the symbols involved; and these symbols, when we proceed without definitions (which exist merely for the sake of brevity), turn out to be such words as "or," "not," "all," and "some," which, like "Socrates," signify nothing in the actual world. A mathematical equation asserts that two groups of symbols hold the same meaning; and as long as we confine ourselves to pure mathematics, this meaning must be one that can be understood without knowledge of what may be perceived. Therefore, mathematical truth, as Plato asserts, is independent of perception; yet it is a truth of a very particular kind, concerned solely with symbols.

Enumerative statements, such as "I have ten fingers," belong to an entirely different category and, clearly, at least partially, depend on perception. It is evident that the concept of "finger" is abstracted from perception; but what of the concept of "ten"? It may seem that here we approach a true universality, or Platonic idea. We cannot claim that "ten" is abstracted from perception, for any perceptual object that can be considered ten of some kind of thing may also be viewed entirely differently. Suppose I designate all the fingers of one hand as "fingers"; then I may assert, "I have two fingers," which describes the same perceptual fact I previously described using the number ten. Thus, in the statement "I have ten fingers," perception plays a lesser role, while the concept assumes greater significance than in a statement like "this is red." The question, however, is only one of degree.

The complete response regarding statements that contain the word "ten" reveals that, when these statements are properly analyzed, they contain no component corresponding to the term "ten." Explaining this in the case of a large number like ten would be complex, so let us consider the statement "I have two hands." This means:

"There exist such a and such b that a and b are not identical, and for any x, the statement 'x is my hand' is true if and only if x is a or x is b."

Here, the word "two" is absent. Indeed, two letters, a and b, appear, but we need not know that there are two, just as we need not know whether they are black, white, or of any other color.

Thus, numbers are, in a precise sense, formal. The facts that verify different statements asserting that various sets, each containing two numbers, have in common not a component, but a form. This distinguishes them from statements about the Statue of Liberty, the Moon, or George Washington. Such statements pertain to a specific part of space and time; this is what is common among all assertions that may be made regarding the Statue of Liberty. However, there is nothing common between statements like "there are two such things," apart from their shared form. The relationship of the symbol "two" to the meaning of the statement in which it occurs is significantly more complex than the relationship of the symbol "red" to the meaning of the statement in which it appears. We may assert that in a certain sense the symbol "two" signifies nothing, for when it occurs in a true assertion, there is no corresponding component in the meaning of that assertion. We may continue, if we wish, to say that numbers are eternal, immutable, and so on, but we must add that they are logical fictions.

There is another question. Concerning sound and color, Plato states that "both are two, but either is one." We have examined two; now we must consider one. There exists an error akin to that regarding existence. The predicate "one" applies not to things, but only to singular classes. We can say, "the Earth has one satellite," but it would be a syntactical error to say, "the Moon is one." For what could such a statement mean? You could just as well assert, "the Moon is many," since it has many parts. To say, "the Earth has one satellite" means to attribute the property of the concept "satellite of the Earth," specifically the following property:

"There exists such a c that the statement 'x is a satellite of the Earth' is true if and only if x is c."

This is an astronomical truth; but if you replace "satellite of the Earth" with "the Moon" or any other proper name, the result will either be nonsensical or merely tautological. "One," therefore, is a property of certain concepts, just as "ten" is a property of the concept "my finger." To argue that "the Earth has one satellite—the Moon; therefore, the Moon is one" is as erroneous as claiming that "there were twelve apostles, Peter was an apostle; therefore, Peter was twelve," which would be valid if we replaced the word "twelve" with "white."

These considerations reveal that while there exists a formal type of knowledge—namely, logic and mathematics—which does not arise from perception, Plato's arguments concerning all other forms of knowledge are flawed. This, of course, does not prove that his conclusion is incorrect; it merely demonstrates that he failed to provide a valid basis for assuming the truth of his conclusion.

Now I turn to Protagoras's assertion that man is the measure of all things, or, as it is often interpreted, that each individual is the measure of all things. It is essential to determine at what level we should conduct this discussion. Clearly, we must first distinguish between the mental objects of perception and the inferences drawn from them. Regarding the former, each person is inevitably confined to their own mental objects of perception; what one knows about the mental objects of other individuals is known through inference from one's own during conversations and reading. The mental objects of perception for those dreaming or hallucinating are, in essence, almost identical to those of others; the only objection to this is that, due to their unusual context, they may lead to false conclusions.

But how do we fare with inferences? Are they equally personal and private? In a certain sense, we must concede that they are. In what I believe, I must hold this belief based on some emerging reason. Indeed, my reason may be an assertion made by another person, but it could serve as a perfectly adequate basis, for instance, when I am a judge listening to witness testimonies. And no matter how much I may adhere to Protagoras's view, it is reasonable to accept the opinion of an expert regarding a number of individuals as more preferable than my own, since I may arrive at the conclusion that, if I initially disagree with them, a more careful consideration of the matter reveals that they were indeed correct. In this sense, I may concede that another person is wiser than I. The position of Protagoras, when properly interpreted, does not assert that I never make mistakes, but merely that evidence of my errors should be presented to me. My former "self" can be evaluated just as one evaluates another person. However, all of this presupposes that regarding inferences, in contrast to the mental objects of perception, there exists some impersonal criterion for correctness. If any inference I make is as good as any other, then indeed there would follow the intellectual anarchy that Plato derives from Protagorean views. Thus, concerning this crucial matter, Plato is seemingly correct. Yet, an empiricist would argue that perceptions serve as the verification of the correctness of inferences derived from empirical material.

The doctrine of universal flux is presented by Plato in a caricatured form, and it is difficult to assume that anyone ever adhered to it in the extreme way he portrays. Suppose, for instance, that the colors we see are in constant flux. A term such as "red" refers to many shades of color, and when we say "I see red," there is no basis to suggest why this statement should not remain true for as long as it takes to articulate it. Plato arrives at his conclusions by applying to processes of constant change such logical oppositions as perception and non-perception, knowing and unknowing. Such oppositions, however, are ill-suited to describe the processes in question. Imagine that on a foggy day you observe a person walking away from you down the road: their figure becomes increasingly indistinct, and there comes a moment when you are certain you can no longer see them, yet there exists an intermediate period of doubt. Logical oppositions were invented for our convenience, but continuous change necessitates a quantitative apparatus, the possibility of which Plato overlooks. Consequently, what he states in this regard largely misses the mark.

At the same time, we must concede that if words did not possess, within certain limits, fixed meanings, conversation would be impossible. However, it is equally easy to fall into the opposite extreme. Words do change their meanings. Take, for example, the word "idea." It is only through significant education that we learn to ascribe to this word a meaning somewhat akin to that which Plato attributed to it. It is necessary for changes in word meanings to occur more slowly than the changes these words describe; yet it is not required that there be no changes in meanings at all. Likely, this does not apply to abstract terms in logic and mathematics, but as we have seen, these words pertain solely to form rather than to the content of statements. Here, once more, we see how peculiar logic and mathematics are. Under the influence of the Pythagoreans, Plato excessively equated all other knowledge with mathematics. He shared this error with many of the greatest philosophers, yet it remains an error nonetheless.