Theory of forms

Pre-Socratic philosophy

The pre-Socratic philosophers, ancient Greek thinkers who predated Plato and his mentor (Socrates), noted that appearances change, and they began to ask what the thing that changes "really" is. If something changes, what is it that remains to ground the thing's identity? The answer was substance, which stands under the changes and is the actually existing thing being seen. The status of appearances now came into question, including how the appearance is related to the substance. For instance, the earliest known pre-Socratic philosopher, Thales, argued that the fundamental substance of which all things are made is water.

Scriptures written by Pythagoras, another pre-Socratic philosopher, suggest that he developed an earlier theory similar to Plato's Forms. For Pythagoras, like Plato, the substance or essence of all things was not something physical (like water) but rather something abstract. However, Pythagoras' theory was much narrower than Plato's, proposing that the non-physical and timeless essences that compose the physical world are specifically numbers, whereas Plato conceived of his Forms as a vast array of intangible ideals.

Theory

The Forms are expounded in Plato's dialogues, wherein it is proposed that every kind or quality—goodness, justice, equality, beds, horses, etc.—has a corresponding Form; these Forms are held to be that which is "really real", whereas sensible phenomena (i.e., those perceived through the senses) are merely their "shadows" or imitations: momentary portrayals of the Form, as realized under various circumstances. Thus, for Plato, Forms are more real than the objects of our everyday experience: though Forms are timeless and unchanging, physical things are in constant flux; where Forms are unqualified perfection, physical things are qualified and conditioned.

Form answers the question, "What is that, essentially?" That is, a Form is something like the essence of a thing or quality: that without which the thing would not be the kind of thing that it is. For example, there are countless and disparate tables in the world, but the "Form of Table" is that essence of "tableness" in virtue of which each particular table is a table. Alternatively, or in addition, a Form may be understood as a sort of objective "blueprint": the perfect and unchanging paradigm for some kind, quality, or mathematical object.

Given that such Forms are exactly the same whenever anyone chooses to consider them (as it is difficult to imagine what it would even mean for there to be a change in the very geometrical ideal of, say, the isosceles triangle)—i.e., time only affects the observer, not the ideal—and are similarly unaffected by location, Plato obtained what was perhaps his most original result, qua Forms: that they are aspatial (transcendent to space) and atemporal (transcendent to time). Neither sempiternal (enduring for all time) nor mortal, they transcend time altogether; similarly, they have no spatial dimensions—and thus neither any orientation in space—nor (like the point) do they possess locations.

Though Forms are non-physical, neither are they merely within the mind (i.e., they are real in the strictest sense of the word). Indeed, according to the Platonic understanding, the world of Form is—as well as transcendent to the sensible world—the essential basis both thereof, and of true (stable, enduring) knowledge. Conversely, sensible particulars—being changeable, subject-relative, and tied to unreliable perception—provide an apt basis for only opinion.

For example, consider a triangle drawn upon a blackboard: such a triangle, as drawn by a human hand, is necessarily imperfect—as will be all earthly triangles—so whence the recognition thereof as approximations of mathematically ideal triangles (which we have never seen)? For Plato, it is the intelligibility of the "Form of Triangle" that allows us to know the drawing on the chalkboard as a triangle. Similarly, the Form of the circle enables us to draw, define, speak, and write about particular circles—and to recognize and understand the ways in which they fall short of the ideal—though a perfect circle cannot be encountered or perceived by the senses.

For the Platonist, then, the idea of the perfect circle is discovered, not invented—the Form itself exists eternally, regardless of whether it is instantiated or cognized. It follows that the same would go for the Form of Beauty, and indeed for all Forms.

Intelligible realm and separation of the Forms

Plato often invokes poetic language—particularly in the Phaedo, Republic, and Phaedrus—to illustrate the mode in which the Forms are said to exist. Near the end of the Phaedo, for example, Plato describes the world of Forms as a pristine region of the physical universe located above the surface of the Earth. In the Phaedrus, the Forms are in a "place beyond heaven" (hyperouranios topos); and in the Republic, the sensible world is contrasted with the intelligible realm (noēton topon) in the famous Allegory of the Cave.

It would be a mistake to take Plato's imagery as positing the intelligible world as a literal physical space apart from this one. Plato emphasizes that the Forms are not beings that extend in space (or time), but rather subsist apart from any physical space whatsoever. Thus we read in the Symposium of the Form of Beauty: "It is not anywhere in another thing, as in an animal, or in earth, or in heaven, or in anything else, but itself by itself with itself" (211b). And in the Timaeus, Plato writes: "Since these things are so, we must agree that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything anywhere, is one thing." (52a; emphasis added.)

Ambiguities of the theory

What are Forms?

Plato's conception of Forms actually differs from dialogue to dialogue, and in certain respects it is never fully explained, so many aspects of the theory are open to interpretation. Forms are first introduced in the Phaedo, but in that dialogue the concept is taken as something with which the participants are already familiar, and the theory itself is not developed. Similarly, in the Republic, Plato relies on the concept of Forms as the basis of many of his arguments, but feels no need to argue at length for the validity of the theory itself. Commentators have been left with the task of explaining what Forms are and how physical objects participate in them, and there has been no shortage of disagreement.

Some scholars advance the view that Forms are paradigms, perfect examples on which the imperfect world is modeled; others place emphasis upon the Forms as universals, so that the Form of Beauty, for example, is that quality that all beautiful things share. Yet others interpret Forms as "stuffs", the conglomeration of all instances of a quality in the visible world; under this interpretation, we could say that there is a little beauty in one person, a little beauty in another, and so on—thence, all the beauty in the world put together is the Form of Beauty.

What things get Forms?

Plato himself was clearly aware of those ways in which his own theory was ambiguous or underspecified; in the Parmenides, for example, the titular character engages in incisive criticism thereof (see "Self-criticism", below), and Socrates expresses doubt as to whether there are Forms for all things, or for only some things. As Cornford points out, though the young Socrates is given as admitting that he has "often been puzzled about these things", in reference to whether or not there are Forms of Man, Fire, and Water, these nevertheless do appear as Forms in later works; however, others—such as hair, mud, and dirt—do not. Of these latter, Socrates is made to assert that "it would be too absurd to suppose" that they have Forms, though his interlocutor Parmenides seems to disagree: "Yes, for you are still young, and philosophy has not yet taken hold upon you, Socrates, as I think it will later."

Many interpret Parmenides (who is depicted, throughout the dialogue, as taking the philosophical lead) to here be voicing Plato's own judgment on the matter; and—more generally—it is likewise commonly supposed that Plato held there to be a Form for every (positively-defined) kind and property; but both positions have their dissenters.

Evidence of Forms

Human perception

In Cratylus, Plato writes:

But if the very nature of knowledge changes, at the time when the change occurs there will be no knowledge, and, according to this view, there will be no one to know and nothing to be known: but if that which knows and that which is known exist ever, and the beautiful and the good and every other thing also exist, then I do not think that they can resemble a process of flux, as we were just now supposing.

Plato believed—or, at least, has his Socrates hypothesize—that long before our bodies ever existed, our souls existed and inhabited heaven, whereat they became directly acquainted with the Forms themselves. Real knowledge, in the Platonic sense, is knowledge of the Forms; such knowledge cannot be gained through sensory experience alone, however, because Forms are not to be found within the sensible world. Our true knowledge of the Forms must thus arise from the faint memory of an initial heavenly acquaintance therewith; and so what we seem to have learned, we have in fact recollected instead.

Perfection

No one has ever seen a perfect circle, nor a perfectly straight line, yet everyone knows what a circle and a straight line are. Plato uses the tool-maker's blueprint as evidence that Forms are real:

... when a man has discovered the instrument which is naturally adapted to each work, he must express this natural form, and not others which he fancies, in the material ...

Perceived circles or lines are not exactly circular or straight, and true circles and lines could never be detected since by definition they are sets of infinitely small points. But if the perfect ones were not real, how could they direct the manufacturer?

Universals

A given quality (e.g., sphericity) often appears to be possessed alike by multiple distinct entities at once (e.g., ball-bearings as well as tennis balls); the question as to what exactly (if anything) is shared therebetween, and how it is that one thing in general could yet be many things in particular, is known as the problem of universals. Plato is usually taken to be the originator of the conundrum, and he advanced the theory of Forms as providing a solution: when the same general quality can be predicated of many particular objects, it is because the particulars partake of the same Form; e.g., a beautiful flower, a beautiful face, and a beautiful building—though beautiful in entirely different ways—all participate in the Form of the Beautiful; it is this that enables us to speak of their common beauty, and "beauty" in general (rather than being able only to speak, separately, of particular beautiful things).

Thus, the Form—though itself a distinct singular entity—causes, or explains, the plurality of its sensible instances in particular objects, and there is no need to suppose that one and the same thing be both one and many simultaneously. As Socrates states, in the dialogue Parmenides: "Nor, again, if a person were to show that all is one by partaking of one, and at the same time many by partaking of many, would that be very astonishing. But if he were to show me that the absolute one was many, or the absolute many one, I should be truly amazed."

Criticisms of Platonic Forms

Self-criticism

Participation

An immediate difficulty, and perhaps one of the most fundamental, arises when one attempts to conceptualize just how exactly it is that an object "participates" in a form (or Form). The young Socrates explains his solution to the problem via a metaphor:

Nay, but the idea may be like the day which is one and the same in many places at once, and yet continuous with itself; in this way each idea may be one and the same in all at the same time.

This solution calls for a distinct Form, in which the particular instances participate while retaining their separate identities; i.e., the Form is somehow "shared out", like the day, to many places. Plato hypothesized that distinctness meant existence as an independent being—thus leaving his theory open to attack via the famous Third Man argument of Parmenides, which many have held to prove that Forms cannot both exist independently and yet be participated in by particulars.

The Third Man argument

The argument, in outline, proceeds as follows. Suppose that the members of a set E are all possessed of a certain quality—canonically, "largeness"—in virtue of their participating in the Form of Largeness (sometimes also termed "Largeness Itself"), F₁; suppose, further, that F₁ is itself large (else, in what way might participation therein confer or explain largeness?). A new collection of large entities may then be considered—the original members of E, plus F₁—all of which must, as before, be large in virtue of participating in some Form of Largeness F₂. Given a few fairly natural premisses (e.g., that a Form is not identical to any of its participants / nothing participates in itself), an infinite regress now becomes inevitable: since F₁ and F₂ must be distinct, there is another set of large things—comprising F₁, F₂, and the members of E—all of which must participate in a third distinct "Form of Largeness"; and so on, ad infinitum. That is: an endless series of "third men".

Plato's Socrates and his titular interlocutor take for granted that the regress is fatal to Socrates' initial theory of Forms: the infinity of distinct Forms-of-Largeness might—as well as being intuitively unappealing, and conflicting with the desideratum that there be only one unique Form per predicate—be considered to fail as an explanation for largeness (the largeness of the entities in E is never grounded in a final principle), which some take to be Plato's intended interpretation; others understand the argument to rest upon the fact that, given a model wherein a "piece" of a Form is in whatever partakes thereof, the Forms of the regress are not unitary but rather must be composed of infinite parts.

The "Likeness Regress" and other arguments of Parmenides

The young Socrates did not give up the Theory of Forms over the Third Man but took another tack: that Forms are paradigms, of a sort, which their participants resemble; since resemblance is a symmetrical relation, this necessarily means that the Forms also resemble their participants. Parmenides immediately destroys this suggestion, as well, with the "Likeness Regress"—an argument variously interpreted as being either a retread of the Third Man, or different thereto in a crucial respect. Whichever interpretation may be correct, the argument is successful, and Parmenides thence goes on to raise a further pair of difficulties with Socrates' version of the Forms.

Despite Parmenides' characterization of this latter pair as, together, the greatest difficulty the theory had yet faced, scholars are divided upon the interpretation and validity thereof; similarly, whether the Third Man and Likeness regresses are truly fatal to the theory depends upon the axioms from which one begins, and various opinions exist as to what these should be.

Aristotelian criticism

The topic of Aristotle's criticism of Plato's theory of Forms is vast, and continues to expand. Rather than quote Plato, Aristotle often summarized. Classical commentaries thus recommended Aristotle as an introduction to Plato, even when in disagreement; the Platonist Syrianus used Aristotelian critiques to further refine the Platonic position on Forms in use in his school, a position handed down to his student Proclus. As a historian of prior thought, Aristotle is invaluable; however, this was secondary to his own dialectic, and in some cases he treats purported implications as if Plato had actually mentioned them, or even defended them. For examining Aristotle's critiques, it is helpful to understand his own hylomorphic forms, by which he intended to salvage much of Plato's theory.

Aristotle argues that on the standard Platonic assumptions, as he sees them, it seems that Forms ought exist only for substances: Forms—being entities that exist separately and independently—are clearly (Aristotelian) substances, and whatever participates in such a Form must share in this substantiality. But many Platonic arguments, such as the "arguments from the sciences", appear to militate in favor of Forms for many non-substantial entities as well—e.g., health is an object of study in the science of medicine, yet it is certainly not a substance.

Given that Aristotle has accurately interpreted his predecessor's claims, Plato seems to have been caught in a contradiction: only substances have corresponding Forms, yet there are Forms that correspond to the (often non-substantial) objects of science. Aristotle's critiques proved, and remain, highly influential, though scholars have differed as to whether—and to what degree—this criticism and its fellows are truly problematic for (Platonic) Forms; Scottish philosopher W. D. Ross, for example, objects that this is a mischaracterization of Plato, whereas Gail Fine finds Aristotle to be broadly correct.

Aristotle outlines another, related criticism: that, if Forms correspond to universals, this leads to the existence of (purportedly) non-Platonic forms—not only the Form of Difference (or of "Otherness"), but also the Not-Tall, the Not-Beautiful, etc. As Ross indicates, however, Plato himself did not make the leap from "A is not B" to "A is Not-B"; as far as the dialogues go, Plato's own view could easily be that Otherness only applies to various particulars, which need not each correspond to actual "Not-Forms". For example, there would then be no "Form of Not-Greek", since "not Greek" groups together sundry peoples by only the lack of a feature—i.e., "not being (or speaking) Greek"—in common; it is not a natural division, in other words. Under this interpretation, there is—rather than a "Form of Not-Greek"—just the Form of Difference from, or in relation to, Greekness; and likewise for tallness, beauty, and so on.

Aristotle also developed arguments against Plato's epistemology, in regard to the latter's hypothesis that we know Forms through a remembrance of existing—along with the Forms—in "a place beyond heaven".

Scholastic criticism

Nominalism (from Latin nomen, "name") says that ideal universals are mere names, human creations; the blueness shared by sky and blue jeans is a shared concept, communicated by our word "blueness". Blueness is held not to have any existence beyond that which it has in instances of blue things. This concept arose in the Middle Ages, as part of Scholasticism.

Scholasticism was a highly multinational, polyglottal school of philosophy, and the nominalist argument may be more obvious if an example is given in more than one language. For instance, colour terms are strongly variable by language; some languages consider blue and green the same colour, others have monolexemic terms for several shades of blue, which are considered different; other languages, like the Mandarin qing denote both blue and black. The German word "Stift" means a pen or a pencil, and also anything of the same shape. The English "pencil" originally meant "small paintbrush"; the term later included the silver rod used for silverpoint. The German "Bleistift" and "Silberstift" can both be called "Stift", but this term also includes felt-tip pens, which are clearly not pencils.

The shifting and overlapping nature of these concepts makes it easy to imagine them as mere names, with meanings not rigidly defined, but specific enough to be useful for communication. Given a group of objects, how is one to decide if it contains only instances of a single Form, or several mutually exclusive Forms?

Primary sources

Dialogues that discuss Forms

• Meno: 71–81, 85–86: The discovery (or "recollection") of knowledge as latent in the soul, pointing forward to the theory of Forms
• Phaedo

73–80: The theory of recollection restated as knowledge of the Forms in soul before birth in the body,109–111: The myth of the afterlife, 100c: The theory of absolute beauty

• Symposium: 210–211: The archetype of Beauty.
• Phaedrus: 248–250: Reincarnation according to knowledge of the true, 265–266: The unity problem in thought and nature.
• Cratylus: 389–390: The archetype as used by craftsmen, 439–440: The problem of knowing the Forms.
• Theaetetus: 184–186: Universals understood by mind and not perceived by senses.
• Sophist: 246–259: True essence a Form. Effective solution to participation problem. The problem with being as a Form; if it is participatory then non-being must exist and be being.
• Parmenides: 129–135: Participatory solution of unity problem. Things partake of archetypal like and unlike, one and many, etc. The nature of the participation (Third man argument). Forms not actually in the thing. The problem of their unknowability.
• Republic

• Book III: 402–403: Education the pursuit of the Forms.
• Book V: 472–483: Philosophy the love of the Forms. The philosopher-king must rule.
• Books VI–VII: 500–517: Philosopher-guardians as students of the Beautiful and Just implement archetypical order, Metaphor of the Sun: The sun is to sight as Good is to understanding, Allegory of the Cave: The struggle to understand forms like men in cave guessing at shadows in firelight.
• Books IX–X, 589–599: The ideal state and its citizens. Extensive treatise covering citizenship, government and society with suggestions for laws imitating the Good, the True, the Just, etc. Metaphor of the three beds.

• Timaeus: 27–52: The design of the universe, including numbers and physics. Some of its patterns. Definition of matter.
• Philebus: 14–18: Unity problem: one and many, parts and whole.
• Seventh Letter: 342–345: The epistemology of Forms. The Seventh Letter is possibly spurious.