Ancient Philosophy

Socrates, Plato, and Aristotle

Theory of Ideas

The central part of Plato's dialogue The Republic, from the end of Book V to the conclusion of Book VII, is primarily dedicated to questions of pure philosophy, as opposed to politics. These questions are asserted quite emphatically in the following statement: "Until philosophers rule as kings in the cities, or those who are now called kings and rulers genuinely and adequately philosophize—until this union of political power and philosophy occurs, and until those individuals—many of whom currently strive either for power or for philosophy—are necessarily removed, the states will not be free from evils, nor will it be possible for the human race to behold the sunlit form of the state we have just described in words."

If this is true, we must determine what a philosopher is and what we mean by "philosophy." The reasoning that follows constitutes the most significant part of The Republic, and it has likely had the greatest influence in subsequent thought. At times, it possesses exceptional literary beauty; a reader may disagree (as I do) with its assertions, yet cannot help but feel their powerful impact.

Plato's philosophy is based on a distinction between reality and appearance, first established by Parmenides. In the reasoning we are currently examining, expressions and arguments from Parmenides are recurrent. However, the religious tone that permeates discussions of reality is more characteristic of Pythagoras than of Parmenides; much is said of mathematics and music, themes typically associated with Pythagorean disciples. This fusion of Parmenidean logic with the metaphysical world of Pythagoras and the Orphics engendered a theory that aimed to satisfy both the intellect and religious sentiment. The result was an impressive synthesis that, undergoing various transformations, influenced most great philosophers, up to and including Hegel. But Plato's impact extends beyond philosophers. Why did the Puritans oppose music, painting, and the ornate rituals of the Catholic Church? You will find the answer in Book X of The Republic. Why are children compelled to learn arithmetic in school? Justification for this is provided in Book VII of The Republic.

The following lines offer a summary of Plato's theory of ideas.

We posed the question: What is a philosopher? The first answer aligns with etymology: a philosopher is one who loves wisdom. However, this does not equate to one who loves knowledge in the sense that we might say a curious person loves knowledge; mere vulgar curiosity does not make one a philosopher. This definition, therefore, is refined: a philosopher is one who loves to "contemplate the truth." But what does contemplation entail?

Let us consider a person who loves beautiful things, who feels compelled to attend performances of new tragedies, to view new paintings, and to listen to music. Such a person is not a philosopher, for they love only beautiful things, while the philosopher loves beauty itself. The person who loves only beautiful things lives in a dream, whereas the one who knows the absolutely beautiful lives in reality. The former possesses only opinion, the latter knowledge.

What is the distinction between "knowledge" and "opinion"? A person with knowledge possesses understanding of something that exists, for that which does not exist is nothing (this echoes Parmenides). Thus, knowledge is infallible, as it is logically impossible for it to be erroneous. Opinion, however, may be mistaken. How is this possible? There can be no opinion about what does not exist, as that is impossible; nor can there be opinion about what is, for that would constitute knowledge. Therefore, opinion must simultaneously concern both what exists and what does not.

But how can this be? The answer is that individual objects invariably encompass opposing properties: that which is beautiful is also, in some respects, ugly; that which is just can, in some respects, be unjust, and so forth. All particular sensory objects, as Plato asserts, possess this contradictory nature; thus, they are intermediate between being and non-being and are suitable as objects of opinion, but not of knowledge. "And what shall we say of those who contemplate these [essences], eternally identical to themselves? For they know them, not merely think they do."

Thus, we arrive at the conclusion that opinion pertains to the sensory world, whereas knowledge relates to the supersensible eternal world; for example, opinion relates to individual beautiful objects, while knowledge pertains to beauty itself.

The sole argument posited is that it would be a contradiction in itself to suppose that a given phenomenon could simultaneously be beautiful and not beautiful or simultaneously just and unjust, and yet individual phenomena seemingly possess such contradictory properties. Therefore, individual things are unreal. Heraclitus said: "We both enter and do not enter the same river, we exist and do not exist." By synthesizing this with what Parmenides says, we arrive at Plato's conclusion.

However, within Plato's theory lies something of great significance not found in his predecessors—his theory of "ideas" or "forms." This theory is partly logical and partly metaphysical. Its logical component deals with the meaning of general terms. There are many individual animals about which we can accurately say, "This is a cat." What do we mean by the term "cat"? Evidently, it signifies something distinct from each individual cat. An animal is deemed a cat because it shares a common nature characteristic of all cats. Language cannot function without such general terms as "cat," and such terms are evidently not meaningless. But if the word "cat" signifies anything, it signifies something that is not this or that cat, representing something akin to universal catness. It did not come into being when a particular cat was born, nor will it perish with the death of an individual cat. In fact, it occupies no place in space or time: it is "eternal." This constitutes the logical part of the theory. Arguments in its favor, whether ultimately irrefutably true or not, are robust and entirely independent of the metaphysical aspect of this theory.

According to the metaphysical part of this theory, the word "cat" signifies a certain ideal cat, the Cat, created by God and unique in its kind. Individual cats share the nature of the Cat, but more or less imperfectly. Only due to this imperfection can there be many cats. The ideal Cat is real; individual cats are merely apparent.

In the final book of The Republic, as an introduction to the condemnation of painters, there is a very clear exposition of the theory of ideas or forms. Here, Plato explains that when a number of individuals share a common name, they also share a common "idea" or "form." For example, although there may be many beds, there exists only one "idea" or "form" of a bed. Just as the reflection of a bed in a mirror is merely an appearance, not "real," so too are the various individual beds unreal, being merely copies of the "idea" that represents one real bed, created by God. Knowledge can pertain to this one bed, created by God, but regarding many beds made by carpenters, one can only possess opinion. The philosopher, as such, will concern himself only with one ideal bed, not with the many beds found in the sensory world. He will feel a certain indifference toward ordinary worldly matters. "If he possesses elevated thoughts and can mentally grasp the entirety of time and being, do you think that human life matters much to such a person?" The youth capable of becoming a philosopher will stand out among his peers as just and temperate, loving learning, endowed with a good memory and a naturally harmonious mind. Such a youth must be educated to become a philosopher and guardian.

At this point, Adeimantus interjects with a protest. When he attempts to argue with Socrates, Adeimantus expresses that he feels, at every turn, as though he is being led astray, so that by the end, all his previous notions appear to have been turned upside down. Yet, whatever Socrates may say, it remains a fact, as anyone can see, that those who dedicate themselves to philosophy become strange monstrosities, to say the least, if not complete charlatans. Even the best among them, philosophy renders useless to society.

Socrates concedes that this may be true in the world as it currently exists, but argues that the fault lies not with philosophers, but with others: in a wise society, philosophers would not appear foolish; only among fools are the wise considered devoid of wisdom.

How ought we to act in the face of this dilemma? There seem to be only two ways to establish our state: by transforming philosophers into rulers or rulers into philosophers. The former appears impossible as a starting point, for in a city that is not yet philosophical, philosophers lack popularity. Yet a natural sovereign might be a philosopher, and "…it suffices for one such individual to emerge, possessing dominion over the state, for this person to accomplish all that is currently disbelieved." Plato hoped he had found such a ruler in the young Dionysius, the tyrant of Syracuse, but this young man did not live up to his expectations.

In the sixth and seventh books of the "Republic," Plato contemplates two questions. The first inquiry is: What is philosophy? The second question is: How can we nurture a young man or woman with the suitable temperament to become philosophers?

For Plato, philosophy is a kind of contemplation, "the contemplation of truth." It is not purely intellectual; it is not merely wisdom, but rather a love of wisdom. Spinoza's "intellectual love of God" represents a nearly identical union of thought and feeling. Anyone engaged in any form of creative labor has experienced this state of spirit to a greater or lesser degree, wherein, after prolonged effort, truth or beauty is revealed, or seems to be revealed, in a sudden illumination—this may happen concerning a trivial question or regarding the universe. Such experiences can be immensely convincing; doubt may arise later, but in those moments, there exists a profound certainty. I believe that most of the most creative works in art, science, literature, and philosophy are the result of such moments. I cannot say whether others experience this as I do. As for me, I have discovered that when I wish to write a book on a particular subject, I must first absorb all the details until all the other aspects of the topic become familiar to me; then, on a certain day, if I am fortunate, I perceive the whole along with all its parts properly interconnected. After this, I need only to record what I have seen. A somewhat similar feeling arises when one walks through mountains shrouded in fog until every path, ridge, and valley is well-known individually, only then to see all these mountains clearly from a distance, illuminated by bright sunlight.

I am convinced that such experiences are necessary for good creative work, but they alone are insufficient. In fact, the subjective certainty they provide can lead one astray fatally. William James describes a man who experienced the effects of laughing gas; whenever he was under its influence, he knew the secret of the universe, but when he returned to his senses, he forgot it. Ultimately, he managed, through immense effort, to record this secret before the vision vanished. Fully awake, he hurried to see what he had written. It was: "Everywhere smells of oil." What seems like a sudden insight can be misleading, and it is essential to soberly verify it when the divine intoxication subsides.

Plato’s contemplation, which he fully trusted when writing the "Republic," ultimately required the assistance of a parable, the allegory of the cave, to convey to the reader the nature of this contemplation. Yet he leads the reader to this understanding through various preliminary reflections intended to make them see the necessity of the world of ideas.

Firstly, the world of intellect differs from the world of the senses; then, intellect and sensory perception—each in turn—are divided into two kinds. The two kinds of sensory perception do not concern us. The two kinds of intellect are called, respectively, "mind" and "reason." Among these, the mind is of a higher order: it deals with pure ideas, and its method is dialectic. Reason is a type of intellect employed in mathematics; it is inferior to the mind because it uses hypotheses that cannot be verified. For instance, in geometry, we say: "Let ABC be a right triangle." It would be against the rules to ask whether ABC is indeed a right triangle, although if that is the figure we have drawn, we can be certain that it is not right, for we cannot draw perfectly straight lines. Consequently, mathematics can never tell us what is but only what would be if… In the world of the senses, there are no straight lines; therefore, if mathematics is to possess more than hypothetical truth, we must find proof of the existence of supersensory straight lines in the supersensory world. This cannot be done through reason, but, according to Plato, it can be accomplished through the intellect, which shows that in the heavens there exists a right triangle whose geometric properties can be confirmed categorically rather than hypothetically.

Here lies a difficulty that, evidently, did not escape Plato's notice and was apparent to his contemporary idealist philosophers. We have seen that God created only one bed, and it would be natural to suppose that He made only one straight line. But if there is a heavenly triangle, then God must have created at least three straight lines. Geometric objects, though ideal, must exist in many examples: we require the possibility of two intersecting circles, and so forth. This suggests that, according to Plato's theory, geometry ought not to be capable of providing ultimate truth but should be condemned as part of the study of phenomena. Nonetheless, we must overlook this question, as Plato himself answers it somewhat ambiguously.

Plato attempts to explain the distinction between clear intellectual contemplation and unclear perception of the senses through an analogy with visual sensation. Sight, he states, differs from the other senses in that it requires not only an eye and an object but also light. We see clearly those objects illuminated by the sun; in twilight, we see indistinctly, and in complete darkness, we see nothing at all. Thus, the world of ideas is what we see when objects are illuminated by the sun, while the world of transient things is the unclear, twilight realm. The eye is akin to the soul, and the sun, as the source of light, is akin to truth or the good. "…So it is with the soul: whenever it reaches out to where truth and being shine, it perceives and knows them, which demonstrates its rationality. But when it inclines toward the realm of confusion, darkness, becoming, and decay, it dulls, becomes susceptible to opinions, alters them this way and that, and seems to lose its mind… Thus, what lends truth to knowable things and endows a person with the capacity to know, that you should consider the idea of the good—the cause of knowledge and the knowability of truth."

This leads to the famous image of the cave, whereby those devoid of philosophy may be likened to prisoners in an underground cave who can see only in one direction, as they are bound; behind them burns a fire, and before them is a wall. Between them and the wall, there is nothing; all they see are their own shadows and the shadows of the objects behind them cast upon the wall by the light of the fire. They inevitably take these shadows for real objects and have no concept of the things that create these shadows. Finally, one of them manages to escape the cave into the sunlight; for the first time, he sees real objects and realizes that he has been deceived by shadows all along. If he is of the kind of philosopher capable of becoming a guardian, he will consider it his duty toward his former companions in captivity to return to the cave, explain the truth to them, and show them the way upward. Yet he will find it difficult to convince them, for after experiencing sunlight, he will perceive the shadows less clearly than they do and will seem to them more foolish than before his escape.

"After this," I said, "you can liken our human nature concerning enlightenment and ignorance to a certain condition... Look here: people seem to be situated in an underground dwelling, much like a cave, where a wide opening extends along its length. From a young age, they have shackles on their legs and necks, so they cannot move from their place and see only what is directly in front of them, for they cannot turn their heads due to these chains. They are turned away from the light that comes from a fire burning far above, while between the fire and the prisoners there runs a raised path, protected—just look—by a low wall, similar to the screen behind which conjurers place their assistants when showing puppets over the screen.

"I can picture that."

"Then imagine also that behind this wall other people are carrying various objects, holding them in such a way that they are visible above the wall; they pass by with statues and all sorts of images of living beings, made of stone and wood. As is customary, some of those bearing these objects converse, while others remain silent.

"You paint a strange image and strange prisoners!"

"Similar to us. Firstly, do you think that, being in such a condition, people see anything—whether their own or someone else's—besides the shadows cast by the fire on the wall situated before them?"

The significance of the Good in Plato's philosophy is peculiar. Knowledge and truth, he says, are akin to the Good, but the Good must be placed above. "The Good is not existence; it lies beyond existence, surpassing it in dignity and power." In the perception of absolute Good, dialectic leads to the end of the intellectual realm. Through the Good, dialectic can dispense with the hypotheses of mathematics. The underlying assumption is that reality, in contrast to appearance, is the complete and perfect Good; thus, to perceive the Good means to perceive reality. Throughout Plato's philosophy, there runs a similar blend of the intellectual and the mystical as found in Pythagorean philosophy; yet at this culminating point, mysticism clearly predominates.

Plato's theory of ideas contains numerous obvious errors. Nevertheless, it represents a significant advance in philosophy, as it is the first theory to highlight the problem of universals, a concern that has persisted in various forms up to the present. Initiatives often present themselves in a rough form at first, but this should not detract from their originality. Some of what Plato articulated remains valid even after all necessary corrections have been made. The absolute minimum that endures, even from the most hostile perspective towards Plato, is this: we cannot express our thoughts in a language composed entirely of proper names; we must also have general terms such as "human," "dog," "cat"; or, if not such terms, then words expressing relations, such as "similar," "previous," etc. These words are not meaningless sounds, but it is difficult to understand how they can carry meaning if the world consists entirely of individual entities denoted by proper names. There may be ways to circumvent this argument, but in any case, it allows for an initial favorable expression regarding universals. For the time being, I shall accept it as somewhat valid. However, when so much is allowed, it does not necessarily follow that everything else Plato asserts is valid.

Firstly, Plato possesses no conception of philosophical syntax. I can say: "Socrates is mortal," "Plato is mortal," and so on. In all these propositions, one may suppose that the word "mortal" has absolutely the same meaning. But whatever it signifies, it denotes something that is not the same as Socrates, Plato, or the other individuals constituting the human race. "Mortal" is an adjective. It would be meaningless to say "mortal is mortal." Plato commits an error akin to saying "mortal is mortal." He believes that beauty is beautiful; he holds that the universal "human" is the name of an ideal human created by God, and that actual humans are its imperfect and to some extent unreal copies. He cannot fully grasp how vast the distance is between universals and individual objects. His "ideas" are in reality other individual objects, superior in ethical and aesthetic regard to ordinary individual objects. Later, he began to understand this difficulty, as evidenced in the "Parmenides," which contains one of the most remarkable examples in the history of self-criticism by a philosopher. It is presumed that "Parmenides" was recounted by Antiphon (Plato's half-brother), who alone remembered this dialogue; he later became solely interested in horses. He was seen carrying a bridle and was hardly persuaded to recount the famous dialogue involving Parmenides, Zeno, and Socrates. This, it is said, occurred when Parmenides had already grown old (he was about 65 years old), Zeno was middle-aged (around 40), and Socrates was quite young at that time. Socrates expounds the theory of ideas. He is convinced that there are ideas of similarity, justice, beauty, and goodness. He is unsure whether there exists an idea of humanity; yet he indignantly rejects the suggestion that there could be ideas of such things as hair, dirt, or filth—though he adds that he sometimes thinks that nothing can exist without a corresponding idea. But he avoids this viewpoint for fear of sinking into an abyss of empty talk.

"You are still young, Socrates," said Parmenides, "and the love of wisdom has not yet wholly seized you, as I believe it will over time, when no such thing will seem trivial to you..."

Socrates agrees that, in accordance with his view, "...there are certain ideas, the names of which are imparted to other things partaking in them; for example, those who partake in similarity become similar, those who partake in greatness become great, those who partake in beauty become beautiful, and those who partake in justice become just."

Parmenides continues to raise obstacles: a) does each individual thing partake in the whole idea or in a part of it? There are objections to both views. In the first case, one thing is in many places at once; in the second case, the idea is divisible, and the thing possessing a part of the small will be less than absolute smallness, which is absurd; b) when an individual object partakes in some idea, then both that individual object and this idea are similar; thus, there must exist another idea encompassing both the individual objects and the original idea. There must exist yet another idea that encompasses these individual objects and the already noted ideas, and so forth to infinity. Thus, each idea, instead of being one, becomes an infinite series of ideas. (This is the same as Aristotle's argument concerning the "third man."); c) Socrates expresses the thought that perhaps ideas are merely thoughts, but Parmenides points out that thoughts must be about something; d) ideas cannot be similar to the individual objects that have partaken of them, due to the reason stated above (in); e) if ideas exist, they must be unknown to us because our knowledge is not absolute; f) if God possesses absolute knowledge, then he would not know us and, consequently, would be unable to govern us.

Nevertheless, the theory of ideas is not wholly rejected. Without ideas, says Socrates, there would be nothing on which the mind could rest, and therefore reasoning would be destroyed. Parmenides tells him that his difficulties arise from his lack of preliminary preparation, but no definitive conclusions have been reached.

I do not believe that Plato's logical objections to the reality of individual sensory objects withstand scrutiny. He asserts, for instance, that any beautiful object is, in some respect, also ugly; what is double is also half, and so forth. However, when we discuss a particular work of art, stating that it is beautiful in some respects and ugly in others, analysis invariably (at least theoretically) allows us to articulate: "This part or aspect is beautiful, while that part or aspect is ugly." As for "double" and "half," these are relative concepts; there is no contradiction in the fact that 2 is the double of 1 and half of 4. Plato consistently encounters difficulties due to his misunderstanding of relative concepts. He believes that if A is greater than B and less than C, then A is simultaneously both large and small, which he perceives as a contradiction. Such difficulties represent a childish ailment of philosophy.

The distinction between reality and appearance cannot yield the consequences attributed to it by Parmenides, Plato, and Hegel. If appearance is indeed merely phenomenon, then it is nothing and thus already constitutes part of reality; this is a correct argument in the Parminedean sense. If appearance is not truly phenomenon, why should we concern ourselves with it? Yet, someone might assert, "Appearance is not truly phenomenon, but seems to be phenomenon." This does not resolve the matter, for we must ask again: "Does it truly seem to us that it is phenomenon, or does it merely appear to us as if it is phenomenon?" Sooner or later, even if it appears that appearance is phenomenon, we must arrive at something that genuinely is phenomenon and thus represents part of reality. Plato would not have denied that many beds present a phenomenon, although there exists but one real bed, namely, the bed created by God. Yet he seemingly failed to consider the implications of the fact that there are many appearances, and that this multiplicity is part of reality. Any attempt to divide the world into parts, one of which is more "real" than the other, is doomed to fail.

This is connected to another curious aspect of Plato's thought, namely, that knowledge and opinion must pertain to different subjects. We should say: "If I think it will snow, that is opinion; if later I see that it is snowing, that is knowledge; but the object of consideration in both cases is the same." However, Plato maintains that what may at any time be the subject of opinion can never be the subject of knowledge. Knowledge is definite and infallible; opinion is not only susceptible to error but is necessarily erroneous, since it admits the reality of what is merely appearance. All this reiterates what Parmenides had stated.

In one respect, Plato's metaphysics likely differs from Parmenides'. According to Parmenides, there exists only the One, whereas Plato posits many ideas. There are not only the beautiful, the true, and the good, but, as we have seen, there exists also the heavenly bed created by God; there is a heavenly man, a heavenly dog, a heavenly cat, and so on—a veritable Ark of Noah. However, this appears not to have been sufficiently pondered in the "Republic." The Platonic idea or form is not a thought, although it can be an object of thought. It is difficult to understand how God could create it, since its existence is timeless, and he could not have resolved to create a bed if his thought, at the moment of that decision, did not have as its object that very Platonic bed that we are told he created. What is timeless must be uncreated. Here we encounter a difficulty that has troubled many philosophical theologians. Only a contingent world, a world in space and time, can be created; yet this is the ordinary world, condemned as illusory and as evil. Hence, one might suppose that the creator has only created an illusion and evil. Some Gnostics were so consistent that they embraced this viewpoint; yet in Plato, this difficulty does not yet manifest, and it must be assumed that in the "Republic" he was entirely unaware of it.

The philosopher who becomes the guardian, according to Plato, must return to the cave and live among those who have never seen the sun of truth. It would seem that God Himself, if He wished to amend His creation, would have to act similarly; thus, a Platonic Christian might interpret the Incarnation. Yet it is entirely impossible to explain why God was dissatisfied with the world of ideas. The philosopher discovers an already existing cave and returns to it, prompted by benevolence. But the Creator, if He created everything, could have, as it may seem, altogether avoided the cave.

This difficulty likely arises solely from the Christian conception of the Creator and cannot be attributed to Plato, who asserts that God created not everything, but only that which is good. The multiplicity of the sensory world, according to this perspective, has some other source, rather than God. And ideas, perhaps, could exist without being created by God as components of His essence. The visible pluralism suggested by the multiplicity of ideas would thus not be final. Ultimately, there exists only God or the Good, in relation to whom ideas may be used as adjectives. This, in any case, is a possible interpretation of Plato.

Plato further presents an interesting sketch regarding the education necessary for the young man who is to become a guardian. We have seen that the young man is chosen for this honorable position based on a combination of intellectual and moral qualities: he must be just and gentle, love learning, possess a good memory, and have a harmonious mind. The young man, selected for these virtues, will spend the age between 20 and 30 studying four subjects of Pythagoras: arithmetic, geometry (plane and solid), astronomy, and harmony. These pursuits should not aim at any utilitarian goals but should serve solely to prepare his mind for the contemplation of eternal things. For example, in the field of astronomy, he should not worry excessively about existing celestial bodies, but rather engage with the mathematics of the movement of ideal celestial bodies. This may seem absurd to the modern person, but strangely, this perspective proved fruitful in empirical astronomy. This curious fact deserves attention.

The visible movements of the planets, if not subjected to very deep analysis, appear irregular and complex, far from how the Pythagorean Creator would have conceived them. It was clear to every Greek that the heavens ought to exemplify mathematical beauty, which could only be realized if the planets moved in circles. This would have been especially evident to Plato, as he emphasizes the good. Thus arose the problem: is there any hypothesis that could lead the apparent disorder of planetary movements to order, beauty, and simplicity? If such a hypothesis exists, then the idea of the good would confirm our insistence on this hypothesis. Aristarchus of Samothrace proposed the following hypothesis: all planets, including the Earth, revolve in circles around the Sun. This view was rejected for two millennia, partly based on Aristotle's authority, who ascribes a similar hypothesis to the Pythagoreans. This hypothesis was restated by Copernicus, and it may seem that its success justifies Plato's aesthetic inclination in astronomy. Unfortunately, however, Kepler discovered that the planets move in ellipses rather than circles, and that the Sun lies at their focus, not at their center. Thus, the geometric simplicity that Plato sought and which Aristarchus of Samothrace seemingly found turned out, in the end, to be illusory.

This part of scientific history illustrates a general rule: any hypothesis, no matter how absurd, can be useful to science if it enables the discoverer to think of things in a new way; but when it serves this purpose accidentally, it will likely become an obstacle to further progress. The belief in the good as the key to scientific understanding of the world was beneficial at a certain stage of development in astronomy, but at each later stage, it proved harmful. The bias towards ethics and aesthetics, observed in Plato and even more so in Aristotle, significantly contributed to stifling Greek science.

It is noteworthy that modern Platonists, with few exceptions, are ignorant in the realm of mathematics, despite the immense significance Plato assigned to arithmetic and geometry, and despite the profound influence they exerted on his philosophy. This serves as an example of the detrimental consequences of specialization: if a person has spent so much time in their youth studying the Greek language that they have had no time to study the things Plato deemed important, they ought not to write about Plato.