Theory of Forms
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Plato's theory of Forms or theory of Ideas asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. When used in this sense, the word form or idea is often capitalized. Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato's own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.
- Terminology 1.1
- Intelligible realm and separation of the Forms 1.2
- Ideal state 1.3
Evidence of Forms 2
- Human perception 2.1
- Perfection 2.2
Criticisms of Platonic Forms 3
- Self-criticism 3.1
- Aristotelian criticism 3.2
- Dialogues that discuss Forms 4
- See also 5
- Notes 6
- Bibliography 7
- External links 8
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, εἶδος (eidos) and ἰδέα (idea) come from the Indo-European root *weid-, "see". Eidos (though not idea) is already attested in texts of the Homeric era, the earliest Greek literature. Equally 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 philosophers, starting with Thales, noted that appearances change quite a bit and began to ask what the thing changing "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?
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 as being "in" something else, which Plato called nature (physis). The latter seemed as "wood", ὕλη (hyle) in Greek, corresponding to materia in Latin, from which the English word "matter" is derived, shaped by receiving (or exchanging) forms.
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, Parmenides 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.":p129 Matter is 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. 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). 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 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.
...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 the 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. That is, they are abstract objects. 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).
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 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 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 academics created by means of state education, 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.
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 pension from the state. None of these items are consistent with an unknowable 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." 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 perceptionWe 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 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.
PerfectionNo 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
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. 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.
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, which 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. 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.
Dialogues that discuss Forms
The theory is presented in the following dialogues:
- 71–81, 85–86: The discovery (or "recollection") of knowledge as latent in the soul, pointing forward to the theory of Forms
- 389–390: The archetype as used by craftsmen
- 439–440: The problem of knowing the Forms.
- 210–211: The archetype of Beauty.
- 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.
- 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
- 248–250: Reincarnation according to knowledge of the true
- 265–266: The unity problem in thought and nature.
- 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.
- 184–186: Universals understood by mind and not perceived by senses.
- 246–248: True essence a Form. Effective solution to participation problem.
- 251–259: The problem with being as a Form; if it is participatory then non-being must exist and be being.
- 27–52: The design of the universe, including numbers and physics. Some of its patterns. Definition of matter.
- 14-18: Unity problem: one and many, parts and whole.
- 342–345: The epistemology of Forms. The Seventh Letter is possibly spurious.
- Analogy of the Divided Line
- Form of the Good
- Jungian archetypes
- Problem of universals
- Seventh Letter
- Modern English textbooks and translations prefer "theory of Form" to "theory of Ideas", but the latter has a long and respected tradition starting with Cicero and continuing in German philosophy until present, and some English philosophers prefer this in English too. See W. D. Ross, Plato's Theory of Ideas (1951) and this reference site.
- The name of this aspect 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
- Plato uses many different words for what is traditionally called form in English translations and idea in German and Latin translations (Cicero). These include idéa, morphē, eîdos, and parádeigma, but also génos, phýsis, and ousía. He also uses expressions such as to x auto, "the x itself" or kath' auto "in itself". See Christian Schäfer: Idee/Form/Gestalt/Wesen, in Platon-Lexikon, Darmstadt 2007, p. 157.
- Forms (usually given a capital F) were properties or essences of things, treated as non-material abstract, but substantial, entities. They were eternal, changeless, supremely real, and independent of ordinary objects that had their being and properties by 'participating' in them. Plato's theory of forms (or ideas)
- "Chapter 28: Form" of The Great Ideas: A Synopticon of Great Books of the Western World (Vol. II). Encyclopaedia Britannica (1952), p. 526–542. This source 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."
- Watt, Stephen (1997). "Plato: Republic". London: Wordsworth Editions. pp. xiv–xvi.
- 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, and the famous theory has nothing at all to do with the "ideas" of English speakers. On the other hand, Plato's concept Form is as removed from the normal concept form as Idea is from idea.
- "*weid-". American Heritage Dictionary: Fourth Edition: Appendix I. 2000.
- Possibly cognate with Sanskrit bráhman. See Thieme (1952): Bráhman, ZDMG, vol. 102, p. 128."ZDMG online"..
- "*bhā-". American Heritage Dictionary: Fourth Edition: Appendix I. 2000.
- Liddell, H.G.; Scott, R.; Whiton, J.M. (1891). A Lexicon Abridged From Liddell & Scott's Greek-English Lexicon. Harper. p. 725.
- "matter". American Heritage Dictionary: Fourth Edition. 2000.
- Cratylus 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 ...."
- For example, Theaetetus 185d–e: "...the mind in itself is its own instrument for contemplating the common terms that apply to everything." "Common terms" here refers to existence, non-existence, likeness, unlikeness, sameness, difference, unity and number.
- 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, 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.
- 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, 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.
- These terms produced with the English prefix a- are not ancient. For the usage refer to "a- (2)". Online Etymology Dictionary. They are however customary terms of modern metaphysics; for example, see Beck, Martha C. (1999). Plato's Self-Corrective Development of the Concepts of Soul, Form and Immortality in Three Arguments of the Phaedo. Edwin Mellon Press. p. 148.
- For example, Timaeus 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 ...."
- "No sensible man would insist that these things are as I have described them..." (Phd. 114d).
- "there is no Platonic 'elsewhere', similar to the Christian 'elsewhere'." (Iris Murdoch, "Metaphysics as a Guide to Morals" (London, Chatto & Windus 1992) 399).
- Plato's Middle Period Metaphysics and Epistemology
- Paragraph 420.
- The word is ethnos, "people". For the full range of meanings consult the American Heritage Dictionary online under ethnic.
- Paragraph 399e line 5.
- "Types" (genē) rather than the English economic classes or the favored populations of the real Greek cities.
- Paragraph 424.
- Paragraph 407.
- Paragraph 410.
- Paragraph 412.
- Paragraph 389.
- Cratylus, paragraph 440.
- Aristotle in Metaphysics Α987a.29–b.14 and Μ1078b9–32 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 then nothing can be known. It is possible that Plato took the Socratic search for definitions and extrapolated it into a distinct metaphysical theory. Little is known of the historical Socrates' own views, but the theory of Forms is likely a Platonic innovation.
- Cratylus, paragraph 389.
- Parmenides 131.
- The name is from (downloadable Google Books). Grote points out that Aristotle lifted this argument from the Parmenides of Plato; certainly, his words indicate the argument was already well-known under that name.
- 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 Hales, Steven D. (1991). "The Recurring Problem of the Third Man". Auslegung 17 (1): 67–80. and Durham, Michael (1997). "Two Men and the Third Man". The Dualist: Undergraduate Journal of Philosophy (Stanford University) 4.
- 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 world and its otherworldness can only be a matter of speculation. 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.
- Paragraph 50 a–c, Jowett translation.
- Ross, Chapter XI, initial.
- Pages 82–83.
- Parmenides, paragraph 130c.
- Posterior Analytics 71b.25.
- Book III Chapters 3–4, paragraphs 999a ff.
- See "Chapter 28: Form" of The Great Ideas: A Synopticon of Great Books of the Western World (Vol. II). Encyclopaedia Britannica (1952), pp. 536–541.
- Fine, Gail (1992). On Ideas: Aristotle's Criticism of Plato's Theory of Forms. Oxford University Press.
- Ross, Sir David (1951). Plato's Theory of Ideas. Oxford: Oxford University Press.
- Rodziewicz, Artur (2012). IDEA AND FORM. ΙΔΕΑ ΚΑΙ ΕΙΔΟΣ. On the Foundations of the Philosophy of Plato and the Presocratics (IDEA I FORMA. ΙΔΕΑ ΚΑΙ ΕΙΔΟΣ. O fundamentach filozofii Platona i presokratyków). Wroclaw: WUWR.
- Cohen, Marc (2006). "Theory of Forms". Philosophy 320: History of Ancient Philosophy. University of Washington Philosophy Department.
- "Lesson Three: Plato's Theory of Forms". International Catholic University.
- Ruggiero, Tim (July 2002). "Plato And The Theory of Forms". philosophical society.com. Philosophical Society.com.
- Silverman, Allan (June 2003). "Plato's Middle Period Metaphysics and Epistemology". Stanford Encyclopedia of Philosophy. Metaphysical Research Lab, CSLI, Stanford University.