Theory Of Forms

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Plato's Theory of FormsThe name of this syndrome of Plato's thought is not modern and has not been extracted from certain dialogues by modern scholars. The term was used at least as early as Diogenes Laertius, who called it (Plato's) "Theory of Forms:" ...., asserts that Forms, and not the material world of change Plato's allegory of the cave, possess the highest and most fundamental kind of reality. Plato spoke of forms (sometimes capitalized in translations: The Forms) Page 528 states that Form or Idea get capitalized according to this convention when they refer "to that which is separate from the characteristics of material things and from the ideas in our mind." in formulating Platonic realism to the problem of universals.

Forms Terminology: The Forms and the forms The English word "form" may be used to translate two distinct concepts with which Plato was concerned—the outward "form" or appearance of something (Greek eidos and idea in their conventional, nontechnical senses, or other terms such as morphē), and "Form" in a new, technical sense, apparently invented by Plato (esp. eidos, idea). These are often distinguished by the use of uncapitalized "form" and capitalized "Form," respectively. In the following summary passage, the two concepts are related to each other:Timaeus (dialogue) Paragraph 50 a-c, Jowett translation. Suppose a person were to make all kinds of figures (schēmata) of gold...—somebody points to one of them and asks what it is (ti pot'esti). By far the safest and truest answer is say that it is gold; and not to call the triangle or any other figures which are formed in the gold "these" (tauta) as though they had existence (hōs onta)... And the same argument applies to the universal nature (phusis) which receives all bodies (sōmata)—that must always be called the same; for, while receiving all things, she never departs at all from her own nature, and never...assumes a form (morphē) 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 (mimēmata) of real existences (tōn ontōn aei) modelled after their patterns (tupōthenta) in a wonderful and inexplicable manner.... The forms that we see, according to Plato, are not real, but literally mimic the real Forms. In the Allegory of the cave expressed in The Republic (Plato) they are called the shadows of real things. That which the observer understands when he views the mimics are the archetypes of the many type (metaphysics) and property (metaphysics) (that is, of universal (metaphysics)) of things we see all around us. They are not located in the object, which as far as Plato is concerned, is mere smoke and mirrors situated in space (which also is real).

What are the Forms? The Greek concept of form precedes the attested language and is represented by a number of words mainly having to do with vision: the sight or appearance of a thing. The main words, (eidos) and (idea)This transliteration leads to the unfortunate misnomer "theory of Ideas." The word is not the English "idea," which is a mental concept only, and the famous theory has nothing at all to do with the "ideas" of English speakers. come from the Indo-European root *weid-, "see". Both words are in the works of Homer, the earliest Greek literature. Equally as ancient is μορφή (morphē), "shape", from an obscure root. The φαινόμενα (phainomena), "appearances", from φαίνω (phainō), "shine", Indo-European *bhā-, was a synonym.

These meanings remained the same over the centuries until the beginning of philosophy, when they became equivocal, acquiring additional specialized philosophic meanings. The Pre-Socratic philosophy, starting with Thales, noted that appearances change quite a bit and began to ask what is the thing "really" that is doing the changing. The answer was Substance theory, 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?

Thus the theory of matter and form (today's hylomorphism) was born. Starting with at least Plato and possibly germinal in some of the presocratics the forms were considered "in" something else, which Plato called nature (phusis). The latter seemed as a "mother" (Matter (philosophy) from mater) of substances by receiving (or losing) forms.

But what were the forms? In Plato as well as in general speech there is a form for every object or quality in reality: forms of 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 is Form itself. 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 the 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, Parmenides (dialogue) 129: "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 was considered particular in itself.

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.Cratylus (dialogue) 389: "For neither does every smith, although he may be making the same instrument for the same purpose, make them all of the same iron. The form must be the same, but the material may vary ...." Plato held that the world of Forms is separate from our own world (the world of substances) and also is the true basis of reality. Removed from matter, Forms are the most pure of all things. Furthermore, Plato believed that true knowledge/intelligence is the ability to grasp the world of Forms with one's mind.For example, Theaetetus (dialogue) 185: "... the mind, by a power of her own, contemplates the universals in all things."

A Form is aspatial (outside the world) and atemporal (outside time). Atemporal means that it does not exist within any time period. It did not start, there is no duration in time, and it will not end. It is neither eternal in the sense of existing forever or mortal, of limited duration. It exists outside time altogether.The creation of the universe is the creation of time: "For there were no days and nights and months and years ... but when he (God) constructed the heaven he created them also." - Timaeus (dialogue) paragraph 37. For the creation God used "the pattern of the unchangeable", which is "that which is eternal." - paragraph 29. Therefore "eternal" - to aïdion, "the everlasting" - as applied to Form means atemporal. 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.Space answers to matter, the place-holder of form: "... and there is a third nature (besides Form and form), which is space (chōros), and is eternal (aei "always", certainly not atemporal), and admits not of destruction and provides a home for all created things ... we say of all existence that it must of necessity be in some place and occupy space ...." - Timaeus (dialogue) paragraph 52. Some readers will have long since remembered that in Aristotle time and space are accidental forms. Plato does not make this distinction and concerns himself mainly with essential form. In Plato, if time and space were admitted to be form, time would be atemporal and space aspatial. They are non-physical, but they are not in the mind. Forms are extra-mental.These terms produced with the English prefix a- are not ancient. For the usage refer to They are however customary terms of modern metaphysics; for example, see and see

A Form is an objective "blueprint" of perfection.For example, Timaeus (dialogue) 28: "The work of the creator, whenever he looks to the unchangeable and fashions the form and nature of his work after an unchangeable pattern, must necessarily be made fair and perfect ...." The Forms are perfect themselves because they are unchanging. For example, say we have 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, the time is that of the observer and not of the triangle.

The pure land The Forms exist in a rarefied sector of the universe. For everything on earth there is a formal counterpart:Phaedo paragraph 109.But the true earth is pure (katharan) and situated in the pure heaven (en katharōi ouranōi) ... and it is the heaven which is commonly spoken by us as the ether (aithera) ... for is any man could arrive at the extreme limit ... he would acknowledge that this other world was the place of the true heaven (ho alethōs ouranos) and the true light (to alethinon phōs) and the true earth (hē hōs alēthōs gē).

In comparison to it our earth is "spoilt and corroded as in the sea all things are corroded by the brine."Paragraph 110. There the colors are "brighter far and clearer than ours; there is a purple of wonderful lustre, also the radiance of gold and the white which is in the earth is whiter than any chalk or snow." Moreover the plants are better: "and in this far region everything that grows - trees and flowers and fruits - are in a like degree fairer than any here." Gems lie about like ordinary stones: "and there are hills, having stones ... more transparent, and fairer in colour than our highly-valued emeralds and sardonyxes ...." And for the humans, "... they have no disease, and live much longer than we do, and have sight, and hearing and smell ... in far greater perfection. They converse with the gods and see the sun, moon and stars as they truly are ...." Indeed, for Plato, "god" is identical to the Form of the Good.

At first reading the land of the pure and site of all the Forms leaves one with a sense of bewilderment! We thought only a singular man really exists and that he resides in an atemporal and aspatial domain free from change. When people die and become detached from the material world their souls ought to achieve reunion with the Form of man and disappear, or some such thing. Instead we read of entire populations of happy men enjoying the sight of numerous gems among the plants that grow. Moreover they may live long but they still seem to die. The reunion is logically troubling as well. If the Man exists independently then we are not he and there is no reason to be united with him. Moreover, if the copies do not really exist then neither do we. And finally, if Man is one Form appearing in many places no reunion is necessary.

Plato's story illustrates that he was always groping for answers rather than presenting a structured doctrine. He says himself:Phaedo paragraph 114.A man of sense ought not to say, nor will I be very confident, that the description which I have given of the soul and her mansions is exactly true. But I do say that he may venture to think ... that something of the kind is true.

The ideal state Plato 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 mimes, a corruption of the real one. This world was created by the Good according to the patterns of the Forms. Man's proper service to the Good is cooperation in the implementation of the ideal in the world of shadows; that is, in miming the Good.

To this end Plato wrote Republic detailing the proper imitation of the Good, despite his admission that Justice, Beauty, Courage, Temperance, etc., cannot be known. Apparently they can be known to some degree through the copies with great difficulty and to varying degrees by persons of varying ability.

The republic of Plato is not a modern democracy. Many of its institutions and values have been tested in world affairs and have been condemned. Plato could not have known the future impact of his thought, but even in the Athenian democracy in which he resided Socrates was considered anti-democratic. After his star pupil Alcibiades, later a general, went over in disgust at democracy to the Spartan enemy in the Peloponnesian War, as a result of which Athens lost the war, the rump state turned on Socrates and condemned him for "corrupting the youth" (namely Alcibiades).

The republic is a greater imitation of Justice:Paragraph 420.Our aim in founding the state was not the disproportional happiness of any one class,The word is ethnos, "people". For the full range of meanings consult the American Heritage Dictionary online under ethnic. but the greatest happiness of the whole; we thought that in a state which is ordered with a view to the good of the whole we should be most likely to find justice.

The key to 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, at Athens lawgivers were appointed to reform the constitution from time to time (for example, Draco (lawgiver), Solon). In speaking of reform, Socrates uses the word "purge" (diakathairountes)Paragraph 399e line 5. in the same sense that Forms exist purged of matter.

The purged society is a regulated one presided over by academics created by means of state education, who maintain three non-hereditary classes"Types" (genē) rather than the English economic classes or the favored populations of the real Greek cities. 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 sets individuals up in their occupation. Plato 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, ...."Paragraph 424. 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 ...."Paragraph 407. 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."Paragraph 410. This remarkable doctrine usually attributed to the "survival of the fittest" of Charles Darwin appears to be much more ancient; however, nothing at all in Greek medicine so far as can be known supports the airy (in the Athenian view) propositions of Socrates.

Many other principles of the ideal state are expressed: the activities of the populace are to be confined to their occupation and only one occupation is allowed (only the philosophers may be generalists). The citizens must not meddle in affairs that are not their business, such as legislation and administration (a hit at democracy). Wealth is to be allowed to the tradesmen only. The marketplace must not be regulated but left up to them. The guardians and the philosophers are not to own fine homes or cash reserves but receive a small pension from the state. None of these items are consistent with an unknowable Good. Socrates seems to know very precisely what is good.

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."Paragraph 412. 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."Paragraph 389.

Evidence of Forms Plato's main evidence for the existence of Forms is intuitive only and is as follows.

The argument from 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 reflected 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 an idea of the basic form Blueness as it applies to them. Says Plato:Cratylus (dialogue) paragraph 440.Aristotle in Metaphysics A.987a.29-b.14 and M1078b9-32 says that Plato devised the Forms to answer a weakness in the doctrine of Heraclitus, who held that nothing exists, but everything is in a state of flow. If nothing exists it can't be known, and so Plato took the universals of Socrates and made them into distinct beings that can be known. Socrates did not think they were separate beings.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.

The argument from perfection No one has ever seen a Perfection 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:Cratylus (dialogue) paragraph 389.... when a man has discovered the instrument which is naturally adapted to each work, he must expess this natural form, and not others which he fancies, in the material ....

Perceived circles or lines are not exactly circular or straight, 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 his theory, as he offered his own criticisms of it in his dialogue Parmenides (dialogue). 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 dialog does present a very real difficulty with the Theory of Forms, which was overcome later by Aristotle, but not without rejecting the independently existing world of Forms. It is debated whether Plato viewed these criticisms as conclusively disproving the Theory of Forms. It is worth noting that Aristotle was a student 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.

The 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:Parmenides (dialogue) 131. 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 up to the famous Third Man Argument of Parmenides,The name is at least as old as Aristotle, who says in Metaphysics A.IX.990b.15: "(The argument) they call the third man." A summary of the argument and the quote from Aristotle can be found in the venerable (downloadable Google Books). Grote points out that more likely than not Aristotle lifted this argument from the Parmenides of Plato; certainly, his words indicate the argument was already well-known under that name. which proves that forms cannot independently exist and be participated.Analysis of the argument has been going on for quite a number of centuries now and some analyses are complex, technical and perhaps tedious for the general reader. Those who are interested in the more technical analyses can find more of a presentation in and

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 the Form and a particular are alike then there must be another, or third, man or greatness by possession of which they are alike. An infinite Infinite regress must result (consequently the mathematicians often call the argument the Third Man Regression); 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 Representative realism, 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.

Plato's 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.Plato to a large extent identifies what today is called insight with recollection: "whenever on seeing one thing you conceived another whether like or unlike, there must surely have been an act of recollection?" - Phaedo paragraph 229. Thus geometric reasoning on the part of persons who know no geometry is not insight but is recollection. He does recognize insight: "... with a sudden flash there shines forth understanding about every problem ..." (with regard to "the course of scrutiny") - The Seventh Letter 344b. Unfortunately the hidden world can in no way be verified in this lifetime and its otherworldness can only be a matter of speculation (in those times before the knowledge of revelation and faith).Plato was aware of the problem: "How real existence is to be studied or discovered is, I suspect, beyond you and me." - Cratylus paragraph 439. Science would certainly reject the unverifiable and in ancient times investigative men such as Aristotle mistrusted the whole idea. The comedian Aristophanes wrote a play, the Clouds, poking fun of Socrates with his head in the clouds.

Aristotelian criticism The topic of Aristotelian criticism of Plato's Theory of Forms is a large one and continues to expand. Aristotle did not just criticise Plato but Platonism typically without distinguishing individuals. Moreover, rather than quote Plato he chose to summarize him often in one-liners not comprehensible without considerable exegesis and sometimes not then. As a historian of prior thought Aristotle often uses the prior arguments as a foil to present his own ideas. Consequently, in presenting the Aristotelian criticisms it is necessary to distinguish what Aristotle wrote, what he meant, whether Plato meant that, whether valid and what the relationship to Aristotle's concepts: a formidable task extending over centuries of scholarship. This article presents a few sample arguments addressed by a few sample scholars. Readers may pursue the topic more fully through the citations and bibliography.

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, which the artificer places in the gold, are not substance, but gold is. Aristotle after stating that according to Plato all things studied by the sciences have Form asserts that Plato considered only substance to have Form giving rise to the contradiction of Forms existing as the objects of the sciences but not existing as non-substance.Ross, Chapter XI, initial.

Despite Ross's objection that Aristotle is wrong, that Plato considers many non-substances to be Forms, such as Sameness, Difference, Rest, Motion, the criticism remains and is major. Ross's summary dismissal: "We need not concern ourselves with Aristotle's argument" is hasty. Plato did not know where to draw the line between Form and non-Form. As Cornford points out,Pages 82-83. things about which the young Socrates (and Plato) asserted "I have often been puzzled about these things"Parmenides (dialogue) paragraph 130c. referring to Man, Fire and Water, appear as Forms in his later works, but others do not, such as Hair, Mud, Dirt, about which Socrates is made to assert: "it would be too absurd to suppose that they have a Form."

Aristotle's thought distinguishes between accidental and essential form.This distinction is made in Posterior Analytics paragraph 73a-b. In a nutshell, the Form of the essence of course is essential but in defining it any attribute that is necessarily said of it and is true in every instance is essential; otherwise, it is accidental; e.g., a line is essential to a triangle but its length is accidental. The triangle of course is an essence. Neither man suspected in any way that after the study of essential form reached a crescendo with Thomas Aquinas the major advances in civilization would come from the detailing of accidental form: the "little things" of Plato, to which we might add cells, molecules and the various entities revealed by the microscope.

Another argument of Aristotle attacked by Ross is that Socrates posits a Form, Otherness, to account for the differences between Forms. Apparently Otherness is existing non-existence: the Not-tall, the Not-beautiful, etc., so that every particular object participates in a Form causing it not to be one essence; that is, a Form to exclude the essence but allow all others. According to Ross, however, Plato never made the leap from "A is not B" to "A is Not-B." Otherness only applies to its own particulars and not to the other Forms; for example, there is no Form, Non-Greek, only particulars of Otherness that suppress Greek.

This objection does not evade the question. Whether or not Socrates meant that the particulars of Otherness are Not-Greek, Not-tall, Not-beautiful, etc., such a particular still operates only on specific essences. If it were a general exclusiveness every Form would be excluded and nothing be anything in particular. If the exclusion excludes one essence then either Otherness is not unitary or multiple Othernesses exist, each one excluding one essence. It is something and it is not something; it allows and does not allow, which are contradictory properties of the one Form.

Though familiar with insight, Plato had postulated that we know Forms through remembrance. Aristotle successfully makes Epistemology arguments against this view. In Plato the particulars do not really exist. Countering "... for that which is non-existent cannot be known"Posterior Analytics 71b.25. Aristotle points out that proof rests on prior knowledge of universals and that if we did not know what universals are we would have no idea of what we were trying to prove and could not be trying to prove it. Knowledge of the universal is given from even one particular; in fact, the Inductive reasoning method of proof depends on it.Posterior Analytics 71a-b.

This epistemology sets up for the main attack on Platonism (though not named) in Metaphysics (Aristotle).Book III Chapters 3-4, Paragraphs 999a-b, otherwise known as Β 3-4. In brief, universal and particulars imply each other; one is logically prior or posterior to the other. If they are to be regarded as distinct, then they cannot be universal and particulars; that is, there is no reason to understand that universal from the objects supposed to be particulars. It is not the case that if a universal A might be supposed to have particulars a1, a2, etc., A is missing or a1, a2, etc. are missing. A does not exist at all and a1, a2, etc. are unrelated objects.

Dialogues that discuss forms The theory is presented in the following dialogues:

Cratylus (dialogue)
389-390: The archetype as used by craftsmen
439-440: The problem of knowing Form
Laws (dialogue)
721: The Form of man immortal
Meno
71-80: Partial discovery of Forms and impossibility of knowing them wholly
Parmenides (dialogue)
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.
Phaedo
73-80: The soul before birth in the land of Forms
109-111: The pure land
Phaedrus (dialogue)
248-250: Reincarnation according to knowledge of the true
265-266: The unity problem in thought and nature
Philebus
14-18: Unity problem: one and many, parts and whole
The Republic (Plato)

Book III
402-403: Education the pursuit of Forms
Book V
472-483: Philosophy the love of Form. The philosopher-king must rule.
Books VI-VII
500-517: Philosopher-legislators guardians of the Beautiful and Just implement archetypical Order. Metaphor of the sun: sun is to sight as good is to understanding. Allegory of the cave: struggle to understand Forms like men in cave guessing at shadows in firelight.
Books IX-X
389-599: 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.

Seventh Letter (Plato)
342-345: The epistemology of Form
Sophist (dialogue)
246-248: True essence a Form. Effective solution to participation problem. Being is effective power.
251-259: The problem with being as a Form; if it is participatory then non-being must exist and be being.
Symposium (Plato)
210-211: The archetype of Beauty
Theaetetus (dialogue)
184-186: Universals understood by mind and not perceived by senses
Timaeus (dialogue)
27-52: The design of the universe, including numbers and physics. Some of its patterns. Definition of matter.

Notes

Bibliography

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External links

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