Theory of forms

The theory of Forms or theory of Ideas is a philosophical theory, concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggests that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Nonetheless, the theory is considered to be a classical solution to the problem of universals.
The early Greek concept of form precedes attested philosophical usage and is represented by a number of words mainly having to do with vision, sight, and appearance. Plato uses these aspects of sight and appearance from the early Greek concept of the form in his dialogues to explain the Forms and the Good.
Forms.
The original meaning of the term ("eidos"), "visible form", and related terms μορφή ("morphē"), "shape", and φαινόμενα ("phainomena"), "appearances", from φαίνω ("phainō"), "shine", Indo-European '*bʰeh₂-' or "*bhā-" remained stable over the centuries until the beginning of Western philosophy, when they became equivocal, acquiring additional specialized philosophic meanings. Plato used the terms "eidos" and "idea" (ἰδέα) interchangeably. 
The pre-Socratic philosophers, starting with Thales, noted that appearances change, and began to ask what the thing that changes "really" is. 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. What is the form really and how is that related to substance?
The Forms are expounded upon in Plato's dialogues and general speech, in that every object or quality in reality has a form: dogs, human beings, mountains, colors, courage, love, and goodness. Form answers the question, "What is that?" Plato was going a step further and asking what Form itself is. He supposed that the object was essentially or "really" the Form and that the phenomena were mere shadows mimicking the Form; that is, momentary portrayals of the Form under different circumstances. The problem of universals – how can one thing in general be many things in particular – was solved by presuming that Form was a distinct singular thing but caused plural representations of itself in particular objects. For example, in the dialogue Parmenides, Socrates states: "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." Matter is considered particular in itself. For Plato, forms, such as beauty, are more real than any objects that imitate them. Though the forms are timeless and unchanging, physical things are in a constant change of existence. Where forms are unqualified perfection, physical things are qualified and conditioned.
These Forms are the essences of various objects: they are that without which a thing would not be the kind of thing it is. For example, there are countless tables in the world but the Form of tableness is at the core; it is the essence of all of them. Plato's Socrates held that the world of Forms is transcendent to our own world (the world of substances) and also is the essential basis of reality. Super-ordinate to matter, Forms are the most pure of all things. Furthermore, he believed that true knowledge/intelligence is the ability to grasp the world of Forms with one's mind.
A Form is "aspatial" (transcendent to space) and "atemporal" (transcendent to time). In the world of Plato, atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether. Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location. They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word).
A Form is an objective "blueprint" of perfection. The Forms are perfect and unchanging representations of objects and qualities. For example, the Form of beauty or the Form of a triangle. For the form of a triangle say there is a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form "triangle" that allows us to know the drawing on the chalkboard is a triangle, and the Form "triangle" is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, time only affects the observer and not the triangle. It follows that the same attributes would exist for the Form of beauty and for all Forms.
Plato explains how we are always many steps away from the idea or Form. The idea of a perfect circle can have defining, speaking, writing, and drawing about particular circles that are always steps away from the actual being. The perfect circle, partly represented by a curved line, and a precise definition, cannot be drawn. Even the ratio of pi is an irrational number, that only partly helps to fully describe the perfect circle. The idea of the perfect circle is discovered, not invented. 
Etymology.
The words, εἶδος ("eidos") and ἰδέα ("idea") come from the Indo-European root or "*weid-" "see" (cognate with Sanskrit "vétti"). "Eidos" (though not "idea") is already attested in texts of the Homeric era, the earliest Greek literature. This transliteration and the translation tradition of German and Latin lead to the expression "theory of Ideas." The word is however not the English "idea," which is a mental concept only.
The theory of matter and form (today's hylomorphism) started with Plato and possibly germinal in some of the presocratic writings. The forms were considered as being "in" something else, which Plato called nature ("physis"). The latter seemed as carved "wood", ὕλη ("hyle") in Greek, corresponding to "materia" in Latin, from which the English word "matter" is derived, shaped by receiving (or exchanging) forms.
Terminology.
The English word "form" may be used to translate two distinct concepts that concerned Plato—the outward "form" or appearance of something, and "Form" in a new, technical nature, that never...assumes a form like that of any of the things which enter into her; ... But the forms which enter into and go out of her are the likenesses of real existences modelled after their patterns in a wonderful and inexplicable manner... The objects that are seen, according to Plato, are not real, but literally "mimic" the real Forms. In the Allegory of the Cave expressed in "Republic", the things that are ordinarily perceived in the world are characterized as shadows of the real things, which are not perceived directly. That which the observer understands when he views the world mimics the archetypes of the many types and properties (that is, of universals) of things observed.
Intelligible realm and separation of the Forms.
Plato often invokes, particularly in his dialogues "Phaedo", "Republic" and "Phaedrus", poetic language 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 ("Phd." 109a-111c). In the "Phaedrus" the Forms are in a "place beyond heaven" ("huperouranios topos") ("Phdr." 247c ff); 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 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 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).
Ideal state.
According to Plato, Socrates postulated a world of ideal Forms, which he admitted were impossible to know. Nevertheless, he formulated a very specific description of that world, which did not match his metaphysical principles. Corresponding to the world of Forms is our world, that of the shadows, an imitation of the real one. Just as shadows exist only because of the light of a fire, our world exists as, "the offspring of the good". Our world is modeled after the patterns of the Forms. The function of humans in our world is therefore to imitate the ideal world as much as possible which, importantly, includes imitating the good, i.e. acting morally.
Plato lays out much of this theory in the "Republic" where, in an attempt to define Justice, he considers many topics including the constitution of the ideal state. While this state, and the Forms, do not exist on earth, because their imitations do, Plato says we are able to form certain well-founded opinions about them, through a theory called recollection. Combined with the form of the Good, the recollection allows for a kind of karma. Recalling the Good initiates good actions, which then allows for others to recall the Good and initiate good actions.
The republic is a greater imitation of Justice:Our aim in founding the state was not the disproportional happiness of any one class, but the greatest happiness of the whole; we thought that in a state ordered with a view to the good of the whole we should be most likely to find justice.
The key to not know how such a state might come into existence is the word "founding" ("oikidzomen"), which is used of colonization. It was customary in such instances to receive a constitution from an elected or appointed lawgiver; however in Athens, lawgivers were appointed to reform the constitution from time to time (for example, Draco, Solon). In speaking of reform, Socrates uses the word "purge" ("diakathairountes") in the same sense that Forms exist purged of matter.
The purged society is a regulated one presided over by philosophers educated by the state, who maintain three non-hereditary classes as required: the tradesmen (including merchants and professionals), the guardians (militia and police) and the philosophers (legislators, administrators and the philosopher-king). Class is assigned at the end of education, when the state institutes individuals in their occupation. Socrates expects class to be hereditary but he allows for mobility according to natural ability. The criteria for selection by the academics is ability to perceive forms (the analog of English "intelligence") and martial spirit as well as predisposition or aptitude.
The views of Socrates on the proper order of society are certainly contrary to Athenian values of the time and must have produced a shock effect, intentional or not, accounting for the animosity against him. For example, reproduction is much too important to be left in the hands of untrained individuals: "... the possession of women and the procreation of children ... will ... follow the general principle that friends have all things in common, ..." The family is therefore to be abolished and the children – whatever their parentage – to be raised by the appointed mentors of the state.
Their genetic fitness is to be monitored by the physicians: "... he (Asclepius, a culture hero) did not want to lengthen out good-for-nothing lives, or have weak fathers begetting weaker sons – if a man was not able to live in the ordinary way he had no business to cure him ..." Physicians minister to the healthy rather than cure the sick: "... (Physicians) will minister to better natures, giving health both of soul and of body; but those who are diseased in their bodies they will leave to die, and the corrupt and incurable souls they will put an end to themselves." Nothing at all in Greek medicine so far as can be known supports the airy (in the Athenian view) propositions of Socrates. Yet it is hard to be sure of Socrates' real views considering that there are no works written by Socrates himself. There are two common ideas pertaining to the beliefs and character of Socrates: the first being the Mouthpiece Theory where writers use Socrates in dialogue as a mouthpiece to get their own views across. However, since most of what we know about Socrates comes from plays, most of the Platonic plays are accepted as the more accurate Socrates since Plato was a direct student of Socrates.
Perhaps the most important principle is that just as the Good must be supreme so must its image, the state, take precedence over individuals in everything. For example, guardians "... will have to be watched at every age in order that we may see whether they preserve their resolution and never, under the influence either of force or enchantment, forget or cast off their sense of duty to the state." This concept of requiring guardians of guardians perhaps suffers from the Third Man weakness (see below): guardians require guardians require guardians, ad infinitum. The ultimate trusty guardian is missing. Socrates does not hesitate to face governmental issues many later governors have found formidable: "Then if anyone at all is to have the privilege of lying, the rulers of the state should be the persons, and they ... may be allowed to lie for the public good."
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 simply referred to as something the participants are already familiar with, 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 for the validity of the theory itself or to explain precisely what Forms are. Commentators have been left with the task of explaining what Forms are and how visible 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 interpret 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 there is a little beauty in one person, a little beauty in another—all the beauty in the world put together is the Form of Beauty. Plato himself was aware of the ambiguities and inconsistencies in his Theory of Forms, as is evident from the incisive criticism he makes of his own theory in the Parmenides.
Evidence of Forms.
Plato's main evidence for the existence of Forms is intuitive only and is as follows.
Human perception.
We call both the sky and blue jeans by the same color, blue. However, clearly a pair of jeans and the sky are not the same color; moreover, the wavelengths of light refracted by the sky at every location and all the millions of blue jeans in every state of fading constantly change, and yet we somehow have a consensus of the basic form Blueness as it applies to them. Says Plato: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 that long before our bodies ever existed, our souls existed and inhabited heaven, where they became directly acquainted with the forms themselves. Real knowledge, to him, was knowledge of the forms. But knowledge of the forms cannot be gained through sensory experience because the forms are not in the physical world. Therefore, our real knowledge of the forms must be the memory of our initial acquaintance with the forms in heaven. Therefore, what we seem to learn is in fact just remembering.
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 utilizes 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?
Criticisms of Platonic Forms.
Self-criticism.
Plato was well aware of the limitations of the theory, as he offered his own criticisms of it in his dialogue "Parmenides". There Socrates is portrayed as a young philosopher acting as junior counterfoil to aged Parmenides. To a certain extent it is tongue-in-cheek as the older Socrates will have solutions to some of the problems that are made to puzzle the younger.
The dialogue does present a very real difficulty with the Theory of Forms, which Plato most likely only viewed as problems for later thought. These criticisms were later emphasized by Aristotle in rejecting an independently existing world of Forms. It is worth noting that Aristotle was a pupil and then a junior colleague of Plato; it is entirely possible that the presentation of "Parmenides" "sets up" for Aristotle; that is, they agreed to disagree.
One difficulty lies in the conceptualization of the "participation" of an object in a form (or Form). The young Socrates conceives of his solution to the problem of the universals in another metaphor, which though wonderfully apt, remains to be elucidated:
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.
But exactly how is a Form like the day in being everywhere at once? The solution calls for a distinct form, in which the particular instances, which are not identical to the form, participate; i.e., the form is shared out somehow like the day to many places. The concept of "participate", represented in Greek by more than one word, is as obscure in Greek as it is in English. Plato hypothesized that distinctness meant existence as an independent being, thus opening himself to the famous third man argument of Parmenides, which proves that forms cannot independently exist and be participated.
If universal and particulars – say man or greatness – all exist and are the same then the Form is not one but is multiple. If they are only like each other then they contain a form that is the same and others that are different. Thus if we presume that the Form and a particular are alike then there must be another, or third Form, man or greatness by possession of which they are alike. An infinite regression would then result; that is, an endless series of third men. The ultimate participant, greatness, rendering the entire series great, is missing. Moreover, any Form is not unitary but is composed of infinite parts, none of which is the proper Form.
The young Socrates (some may say the young Plato) did not give up the Theory of Forms over the Third Man but took another tack, that the particulars do not exist as such. Whatever they are, they "mime" the Forms, appearing to be particulars. This is a clear dip into representationalism, that we cannot observe the objects as they are in themselves but only their representations. That view has the weakness that if only the mimes can be observed then the real Forms cannot be known at all and the observer can have no idea of what the representations are supposed to represent or that they are representations.
Socrates' later answer would be that men already know the Forms because they were in the world of Forms before birth. The mimes only recall these Forms to memory. The comedian Aristophanes wrote a play, "The Clouds", poking fun of Socrates with his head in the clouds.
Aristotelian criticism.
The topic of Aristotle's criticism of Plato's Theory of Forms is a large one and continues to expand. Rather than quote Plato, Aristotle often summarized. Classical commentaries thus recommended Aristotle as an introduction to Plato. As a historian of prior thought, Aristotle was 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. In examining Aristotle's criticism of The Forms, it is helpful to understand Aristotle's own hylomorphic forms, by which he intends to salvage much of Plato's theory.
In the summary passage quoted above Plato distinguishes between real and non-real "existing things", where the latter term is used of substance. The figures that the artificer places in the gold are not substance, but gold is. Aristotle stated that, for Plato, all things studied by the sciences have Form and asserted that Plato considered only substance to have Form. Uncharitably, this leads him to something like a contradiction: Forms existing as the objects of science, but not-existing as non-substance. Scottish philosopher W.D. Ross objects to this as a mischaracterization of Plato.
Plato did not claim to know where the line between Form and non-Form is to be drawn. As Cornford points out, those things about which the young Socrates (and Plato) asserted "I have often been puzzled about these things" (in reference to Man, Fire and Water), appear as Forms in later works. However, others do not, such as Hair, Mud, Dirt. Of these, Socrates is made to assert, "it would be too absurd to suppose that they have a Form."
Ross also objects to Aristotle's criticism that Form Otherness accounts for the differences between Forms and purportedly leads to contradictory forms: the Not-tall, the Not-beautiful, etc. That particulars participate in a Form is for Aristotle much too vague to permit analysis. By one way in which he unpacks the concept, the Forms would cease to be of one essence due to any multiple participation. As Ross indicates, Plato didn't make that leap from "A is not B" to "A is Not-B." Otherness would only apply to its own particulars and not to those of other Forms. For example, there is no Form Not-Greek, only "particulars" of Form Otherness that somehow "suppress" Form Greek.
Regardless of whether Socrates meant the particulars of Otherness yield Not-Greek, Not-tall, Not-beautiful, etc., the particulars would operate specifically rather than generally, each somehow yielding only one exclusion.
Plato had postulated that we know Forms through a remembrance of the soul's past lives and Aristotle's arguments against this treatment of epistemology are compelling. For Plato, particulars somehow do not exist, and, on the face of it, "that which is non-existent cannot be known". See "Metaphysics" III 3–4.
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, 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. English does not have such a word. 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?
Dialogues that discuss Forms.
The theory is presented in the following dialogues: