User:JohnD'Alembert/sandbox

The Spherics of Theodosius

The Spherics is an ancient mathematical treatise on spherical geometry that especially studies problems that arise in early Greek astronomy. Since many of its theorems are elementary, it long served as a first introduction to mathematical astronomy and provided the foundations for much later theoretical astronomy, including more advanced works like the Spherics of Menelaus and the Almagest of Ptolemy. As part of a collection of short treatises known as the "Little Astronomy," the Spherics was used as a textbook through the early modern period in both Arabic and Latin translations.

The surviving medieval manuscripts attribute the Spherics to an obscure figure, Theodosius of Bithynia, who may have lived in the first century BCE. There is, however, a scholarly consensus that Theodosius was merely an editor or compiler and that many of the theorems included in the Spherics had already been proved centuries earlier.

Controversy over Theodosius of Bithynia and the Ur-Spherics

agree many theorems cited earlier attempt to reconstrcut Ur-Spherics rejeected by Neugebauer wide turn against reconstructions, unverifiable thus conclusion many theorems date to fourth century BCE but no recent attempts to reconstruct Ur-Spherics

Overview of Content

no axioms but clear deductive structure ...

presumes theorems proved in Elements Schmidt on center ascension problem

Transmission and Medieval Manuscripts

available online

OLD DRAFT OF THEORY OF FORMS ARTICLE

Hi, thanks for encouraging my proposal to revise and expand Theory of Forms. I’ve taken many good points from the existing English article and often followed the long article on German Wikipedia. Please feel free to revise and improve this! Here are some things I was aiming to achieve:

• In the introductory sections, I aimed at user-friendly simplicity and clarity, accessible to students and others studying the ToF for the first time. I added informal, step-by-step sketches of some well-known arguments and criticisms.
• In the later sections, I aimed at a clear and broader coverage of somewhat more advanced material, esp. providing pointers to well-known developments and debates in the scholarly literature.
• In the history sections, I aimed at brevity and merely outlined the major developments (with lots of links to other Wikipedia pages).
• Plato was what we would call a philosopher, mathematician, and scientist, and I suppose this article reflects my grad school courses in both the philosophy and science of ancient Greece. Please feel free to add material that brings out other aspects of his thought.
• I’ve everywhere aimed to adhere to what academics call the ‘Principle of Charity’: to always begin by presenting the arguments of both advocates and critics in the most natural and plausible way possible. Thus I’ve tried to bring out both the strengths and weaknesses of the Theory of Forms. I’ve also tried to emphasize its broader, cultural importance.

Introduction

A philosopher sees through appearances to the underlying Forms.(Camille Flammarion, Paris, 1888)

Plato’s Theory of Forms holds that there are immaterial entities, called ‘Forms’ or ‘Ideas,’ that explain the similarities, patterns, and order we see in the world around us. Forms are eternal and unchanging objects, like numbers or scientific laws, that we grasp with the mind and not with the senses.

Plato’s ‘revolutionary’ theory was the core of his thinking and ‘his most famous contribution to philosophy.’ It has been called 'one of the richest and boldest metaphysical theories ever invented in Western thought.' It has been debated for twenty-five centuries and has exerted a broad influence on developments in European philosophy, religion, science, art, art theory, and literature. It constitutes a main current in European intellectual history and remains an important theme in contemporary philosophy. In historical importance, Plato’s Theory of Forms ranks alongside Darwin’s Theory of Evolution or Einstein’s Theory of Relativity.

Plato drew one inspiration for his conception of Forms from geometry. He held that students do not study the slightly crooked triangles they happen to draw. Rather, they study the general nature of a triangle that has perfectly straight edges. As he put it, they study not this or that particular triangle but ‘what a triangle really is’ or the ‘triangle in itself.' Other examples of Platonic Forms include ‘Redness in itself,’ ‘Equality in itself,’ ‘Beauty in itself,’ and ‘Justice in itself.’

Philosophers have compared the nature of Plato’s Forms to the laws of modern science. A law of science such as Newton’s Law of Gravity is immaterial, is not restricted to any place or time, and yet operates in the same way in many places (by making things fall). Similarly, the Form of Redness is immaterial, is not restricted to any place or time, and yet brings about similarities in many places (by making things red). Some philosophers hold that the laws of modern science are just examples of Platonic Forms. 'Form of Redness' is thus shorthand for a recurrent combination of more general chemical and physical laws.

Plato’s historic contribution was to emphasize that our world has, in addition to particular, material things, a mysterious, law-like order, and that the task of philosophy and science is to investigate that order. Students of Plato in the Academy developed the first geometric models of the solar system, which became the root of modern astronomy, and historians have seen this discovery as the fruit of Plato’s call to seek the Forms.

Key Terms: Forms, Ideas, and Universals

In contemporary English, 'Form' is the preferred terminology. Philosophers often capitalize 'Form' to distinguish Plato's Forms from ordinary forms and shapes. The English 'form' derives from the Latin forma, which was already used in ancient and medieval times as a Latin translation for Plato’s word for 'Form'.

Through most of history, however, Plato’s Forms were called Ideas. This word has shifted its meaning since Plato: 'Idea has a history of two-thousand years, and there is no other word in the philosophical vocabulary that is so heavily weighted down by the conceptual labors of centuries.' In the modern era, ‘idea’ came to denote a concept in the mind. Since Plato’s Forms are mind-independent, English-speaking philosophers stopped using the word 'idea' in this context and began calling them 'Forms' to avoid any confusion.

Before Plato, the Greek words he used for the Forms, idea and eidos, both meant the visually apparent shape or form or kind of a thing: that is, the 'look' or 'aspect' of a thing. Thus ideas were originally not mental concepts. Both these words are related to the Greek verb meaning ‘to see’ (eidein). In Latin, Plato's terms also came to be translated by species, which is related to the Latin verb specare, meaning ‘to see’ (cf. English 'spectacles'). Thus the biological term 'species' derives from Plato’s word for 'Form'.

Plato also called a Form kath’ olou, which meant ‘of the whole’ and gave rise to the English word ‘catholic.’ Though rare in Plato, it was Aristotle’s preferred term. For both it meant a Form or property that was common to every member of a species and thus belonged to 'the whole' of the species. In Latin, kath’ olou was translated as 'universal' because such features are universal within a species. Today the word 'universal' is often used simply as a synonym for 'Platonic Form'. However, Plato and Aristotle disagreed about whether the Forms were transcendent (see below), and thus some writers reserve the word ‘Form’ for Plato’s transcendent Forms and use ‘universal’ for Aristotle’s immanent properties. Roman Catholics call themselves ‘catholics’ because they believe they are the ‘universal’ Christian church.

The words ‘ideal’ and ‘idealism’ also derive from Plato’s usage. He often depicted his Forms or Ideas as perfect exemplars and believed that philosophers should live in accordance with the highest ‘ideas,’ and this gave rise in modern European languages to notions of striving to live up to ‘ideals.’

Basic Features of the Theory

The Discovery of Abstract Objects

Philosophers distinguish ordinary material things from real but immaterial things such as numbers and scientific laws. The first are called 'concrete' and the latter 'abstract'. The existence of abstract objects has always been controversial because they cannot be directly touched or seen. Many modern and ancient philosophers and some scientists and mathematicians have, however, maintained that abstract objects exist. They hold, for example, that when Newton discovered the Law of Gravity he discovered something, namely a law that is as real in its own way as matter and energy. They hold, for another example, that in addition to three eggs or three apples the number 3 exists in its own right, and that mathematics is the study of such abstract objects. Philosophers have argued for the existence of many kinds of abstract objects: scientific laws, numbers, mathematical truths, sets, propositions, words, fictional characters, musical and literary works, etc. For example, Kurt Gödel, an eminent Twentieth-Century mathematician, said:

… the assumption of such objects is quite as legitimate as the assumption of physical bodies and there is quite as much reason to believe in their existence. They are in the same sense necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions.

Plato is generally credited with the discovery of abstract objects, which he called 'Forms.' The core claim of Plato's Theory of Forms is that abstract objects exist and explain many features of reality, human knowledge, and even values and morality. The philosopher James Robert Brown provocatively suggested that this was the 'greatest discovery in the history of thought.' It is at least agreed that the Greek study of patterns abstracted from nature, society, and mathematics, which was encouraged by Plato's philosophy and his school, laid the foundations for much of modern science and thought.

Allegory of the Cave and the Appearance-Reality Distinction

Plato's Allegory of the Cave: the shadows on the wall receive their shape from the placards, just as the things that appear in our world receive their features from Plato's Forms.

Plato illustrated the Theory of Forms and some of its key terminology with his famous Allegory of the Cave. According to this story, humans are like prisoners forever chained in a dark cave (perhaps reminiscent of a modern cinema). They can only look forward at a large wall in front of them. Far behind and above them there is a bright fire. Between the fire and the prisoners, placards shaped like animals and other things are carried back and forth so that their shadows are projected on the far wall, just as puppeteers might project shadowy images for children. Throughout their lives, the prisoners see only the shadows and thus come to believe they are real. Philosophers are prisoners who manage to throw off their shackles, turn around, and catch sight of the real moving shapes. Some of them escape altogether and manage to climb up out of the cave into the sunlight.

As Plato explains, this illustrates several aspects of his Theory of Forms. The prisoners see only the shadows, and these are analogous to the appearances that we see in the world around us. The figures carried back and forth are the Forms, which in contrast to the shadows are real. The shadows receive their shape and features from the Forms and thus, Plato says, they imitate or participate in the Forms. The prisoners who turn away from their customary view are like philosophers who turn away from the ordinary senses and use reason or the mind’s eye to grasp the Forms. Those who escape and see the sun are philosophers who catch sight of the ultimate Form, which Plato calls the Form of the Good.

A similar appearance-reality distinction is part of modern science. The apparently solid and colored things we see around us are actually, scientists say, some 99.9 percent empty space and composed of colorless atoms. Things feel solid only because our hands are also 99.9 percent empty space. The colors we see are the product of a complicated interaction between the atoms, light, and our eyes. Real, material things are not as they appear.

The Power and Economy of the Theory

Philosophy is often considered to have three parts: a theory of reality or 'metaphysics,' a theory of value or 'ethics,' and a theory of knowledge or 'epistemology.' In a well-known article, ‘On the Economy of Plato’s Theory of Forms,’ Harold Cherniss showed that the Theory of Forms is powerful enough to provide the foundation for all three parts of Plato’s philosophy: 'the doctrine of ideas is the cornerstone of his thought… the center of gravity of all the Platonic writings.'

In short, Plato’s metaphysics asserts that reality is the Forms, that we can know only the Forms (other beliefs are mere opinion), and that ethical value lies in objective Forms that should guide our moral choices. Accordingly, Plato’s theory does not rest on or presume any theories of logic, of negation, of causation, of space, of time, of properties, or of particular things but rather seeks to be the foundation for such theories.

Harold Cherniss, a prominent American Plato scholar, defended the unity of Plato's thought and attacked theories about his so-called unwritten doctrines (c. 1941-2).

Cherniss argued that its sweeping explanatory power was Plato’s main justification for the Theory of Forms. In modern language, it was as general and basic as discovering ‘there are laws of science.’ Plato could with a single theory answer questions like:

• Why is there order and not utter chaos in the world?
• Why is there regularity? Why do the same patterns recur over and over?
• Why are there kinds of animals? Why do cats give birth to kittens and not puppies?
• Why do the stars and planets trace out geometric patterns in the sky?
• How is it possible to know some permanent truths (2+2=4) in a changing world?
• What is mathematics about and why it true?
• What should education aim at? How can we investigate nature?
• Why is it just to do some things and wrong to do others?
• What is beauty and why are we attracted to it?

In each case, the real and unchanging Forms and the order they impose provided an answer.

Connecting Forms to Things: Participation and Space

William Blake shows God reaching down into creation with a geometer's compass to give things their form (1794, Europe a Prophecy, British Museum).

Plato called the relation between a Form and the corresponding appearance 'participation' (methexis) or 'imitation' (mimesis). Things that appear red are therefore said to participate in the Form of Redness, and things that fall participate in the Form of the Law of Gravity. Plato’s dialogues are literary, however, and do not strictly adhere to any technical vocabulary. His Phaedo suggests the name used for participation is not important.

Though Plato strongly asserted the existence of both the Forms and their influence on things, he acknowledged that questions about their connection remained open and his dialogues discuss several puzzles about participation. His student Aristotle, however, mocked Plato for not having any precise theory of participation. There is no consensus among modern scholars about how Plato understood participation.

Although Plato's dialogues speak freely of things and individuals, many scholars deny that Plato's metaphysics included individual things made of matter and persisting through time. A famous passage in Plato's Timaeus conceives of participation as a projection of 'images' of the Forms onto space itself (chora), or at least onto a pervasive medium (called the ‘receptacle’) that resembles our modern concept of space. This passage suggests that, for Plato, things are merely transitory images on the 'mirror of space,' and there are no particular, individual, material things that move through space. Kahn holds, for example, that Plato's metaphysics does not include 'natural individuals.' As Cherniss put it,

What Aristotle calls the separateness of particulars is to Plato just this being in space which is not separateness at all but rather the fleeting inherence in a medium of the scattered reflections of indivisible reality.

Philosophers have compared debates over the way Plato’s Forms participate in things to similar debates in contemporary philosophy of science about the way the laws of science affect material things. Modern science accepts the existence of laws but the question of how a single scientific law operates on many things at once is still an open problem.

Family Tree of Forms: Species and Genuses

Carl Linnaeus organized species of animals and plants into a hierarchy that led to the system still used in biology today. His plan and terminology descended from Plato’s Theory of Forms. Here, the title page of his System of Nature advertises its organization of living things into three kingdoms (regna) and then into ‘classes, orders, genuses, and species' (here 1760; first edition, 1735).

Plato held that the Forms are organized into a vast hierarchy. As in modern biology, a group of things or animals at the lowest level whose members share similar traits corresponds, for Plato, to a 'species.' A group of species that share similar traits is a 'genus'. A yet higher group of groups is a higher genus. Plato held that each species and each genus was characterized by a single Form. The hierarchy of species and genuses is the basis for Plato’s ‘Method of Division’ (see Diairesis).

There is some evidence that Plato and the Academy began the biological classification of living things into species and genuses. That is, the Theory of Forms guided early scientific investigations. A short passage survives from a lost play by Epicrates that pictures Plato and his students puzzling over a pumpkin: they were ‘separating into categories the ways of life of animals, the nature of trees, and the classes of vegetables.’ Plato’s student Aristotle is sometimes known as the first biologist because he continued this project in his treatises The History of Animals and The Generation of Animals.

The nature of the connections between the Forms within Plato's hierarchy is debated. Some argue for the existence of a real connection; others argue that each Form is independent and there are only ‘logical’ connections between them.

Form of the Good

Plato calls the Form at the apex of the hierarchy that includes and unites all the others the 'Form of the Good.' Many contemporary philosophers accept the 'fact-value distinction,' which asserts that real, material things do not have intrinsic ethical value. In contrast, Plato held that ethical values were just as real as other qualities: goodness came by participating in the Form of the Good. Plato does not treat it as a person or accord it free will, but some later philosophers argued that the Form of the Good played a role in his system like that of a monotheistic God: the Form of the Good is somehow one, all-embracing, and all-uniting.

The Location of the Forms: Immanence versus Transcendence

There is a long-standing debate over the location of Plato’s Forms. There are passages in the dialogues that say the Forms are outside of space and time (in what philosophers colloquially call 'Plato’s Heaven') yet somehow manage to influence things within space and time. Such forms are called 'separate' or ‘transcendent.’ Other passages in Plato’s dialogues suggest the Forms are somehow 'present in' the things that participate in them, and therefore are inside space and time. Forms inside ordinary things are called ‘immanent.’ Ross lists the relevant passages and finds that the so-called early dialogues treat the Forms as immanent, while later dialogues increasingly make them transcendent.

Both options raise difficulties and interpreters of Plato disagree about his own view on this issue. Plato’s Parmenides portrays a young Socrates struggling with these issues, and suggests he will resolve them as he makes progress in philosophy. Of course, the same dilemma arises with questions about the location of numbers or scientific laws. Recent debate on these questions is reviewed below.

Instead of 'immanent' and 'transcendent', modern philosophers often use the terms 'concrete' and 'abstract.' A concrete object is an ordinary material thing. The word 'abstract' today has a general, negative meaning: an abstract object is not a concrete object in space and time. Transcendental Forms are thus sometimes called 'abstract objects.'

Political, Erotic, and Spiritual Dimensions

For Plato and ancient Platonists, the Theory of Forms had political, erotic, and spiritual dimensions. Robert Hankins summarized how Plato’s alienation from the politics of his day connected the Theory of Forms to his political program for reform. In his youth, Plato lived through times of terrible chaos and destruction. After the plague wiped out perhaps a third of its citizenry, Athens was defeated and occupied by its arch-enemy Sparta, and then saw thousands more die in a bloody civil war that pitted friends and family members against each other. Plato's father died at the time of the plague, his older cousin died leading a faction in the civil war, and Plato's teacher Socrates was executed during the score-settling that followed. Though Plato’s dialogues keep this tragic history off-stage, his Theory of Forms was meant in part as a remedy:

Plato, after all, had been a nearly classic case of the internal exile … Intellectual revenge took the form of a merciless anatomizing of contemporary Athens. Its heroes were shown to be self-seeking demagogues; its political life was but the interplay of irrational passions; its art, poetry and eloquence were vitiated by false imitation, deception, and impiety. Plato’s solution to the problem of Athenian culture lay in a kind of rational mysticism, which sought to escape the vice and confusion of the vulgar, occasioned by their immersion in the senses, and to ascend through dialectic and philosophical eros to the 'unhypothesized first principles,' the Ideas … it was only through the presence of such 'friends of the Forms' that social and political life could hope for a true reformation. The philosopher alone could rule without discord … since he alone knew what justice was.

Friedlander’s classic survey of Plato's thought, Plato: an Introduction, emphasized the erotic, spiritual, and even mystical aspects of the Theory of Forms. Plato’s Symposium, for example, treats the discovery of the Forms as a spiritual journey driven by erotic love that culminates in an ecstatic vision of some higher reality. Friedlander also regards Plato, however, as a ‘rational mystic’ because his spiritual ascent involves argument and knowledge:

Plato’s 'dialectical journey,' his rise from the darkness of the cave to the light of the sun … [has] equivalents in any form of Mysticism… Plato’s highest idea … is reached not through [the ordinary mystic’s] lonely introspection, violent leaps, and submergence in darkness but through a path by which knowledge grasps the nature of being. Without arithmetic, geometry, astronomy, musical theory, without the discipline of philosophical dialectics, the goal cannot be approached …

Debating the Forms: Realists versus Nominalists

Philosophers who defend the truth of some version of the Theory of Forms are traditionally called 'realists,' because they hold that either immanent or transcendental Forms are real. These include historical figures such as Plato, Aristotle, Plotinus, Proclus, Augustine, Aquinas, Russell, and Moore. Recent defenders of Forms and universals include Armstrong, Dretske, and Tooley. Other recent philosophers argue for the existence of abstract objects like numbers, sets, or propositions that resemble Plato’s Forms in some ways. These include Frege, Quine, and Putman.

Critics of the Forms are often called 'nominalists' (from the Latin nomen meaning 'name') because they hold that general terms like 'red' and 'redness' do not refer to Forms but are just names. Some nominalists believe such names correspond to concepts in the mind. These include Abelard, Ockam, and Locke.

Mathematicians who reflect on their discipline have often argued for the existence of some kind of abstract Forms or abstract mathematical structures. They are usually called ‘Platonists,’ but the relation of their views to the historical Plato is debated. These include Cantor, Frege, Gödel, and others.

Physicists who can be counted 'Platonists' include: Galileo, Pauli, Ne'eman, and Frank Wilczek. Wilczek, a recent Nobel Prize winner in physics, said

A great vision of science [from Pythagoras and Plato to Kepler and Wheeler] … has been that physical reality embodies ideally simple mathematical laws…[In today's physics that] great vision lives and thrives. Pythagoras and Plato intuited that the world should embody beautiful ideas; [the modern scientists] Newton and Maxwell demonstrated how the world could embody beautiful ideas, in specific impressive cases. Finally in the 20th century in modern physics, and especially in quantum physics, we find a definitive answer: Yes! – the world does embody beautiful ideas.

David Ross, a leading twentieth-century historian of ancient philosophy, said in the conclusion to his important study Plato’s Theory of Ideas (1951) that science and mathematics showed our reason can grasp the underlying structure of the world, i.e., that Plato’s Forms exist:

The senses present to us a world of particular events in which qualities are present almost inextricably conjoined and confused; if we were left to the senses alone we should never be able to disentangle them and reach a clear understanding of the structure of the world. But in reason we have a faculty by which we can grasp the universals in the pure form and to some extent see the relations that necessarily exist between them. The best example we have of this power is to be found in mathematics, and Plato was the first thinker who clearly saw this.

Writers like Wilczek and Ross accept that modern science has demonstrated that nature has an invisible, mathematical order accessible to reason. At this general level, the difference between modern science and Plato's Theory of Forms is for them merely a matter of terminology.

Motivations and Arguments for the Forms

The Need for Interpretation

Plato's arguments for the Forms are some of the most famous in the history of European philosophy, and have served to train philosophers since the time of the Academy. However, since Plato's dialogues are literary and read like short dramas, his theories and arguments must be inferred and reassembled from passages scattered through his works. Much of the scholarly literature aims at first constructing plausible interpretations before proceeding to assess Plato's views.

Several well-known issues complicate this process of interpretation. Many of Plato's dialogues hardly mention the Forms:

Having studied the writings of modern thinkers on 'Plato's doctrine of Ideas' … one might be surprised at how little the latter contain of this principal element of Plato's philosophy… nowhere do we find a 'doctrine' as such, or a system comprising the order of these Forms, communicating their knowledge, or clarifying their relationship to the world of appearance.

Although a dozen or more long passages discuss the Forms, they are usually mentioned in passing while addressing some other topic. Moreover, Plato's characters often compound this problem by treating the Theory of Forms not as a radical innovation but as an old and widely known doctrine, and therefore introduce the theory briefly and elliptically. Historians do regard the theory as Plato's innovation and thus this mode of presentation is part of Plato's puzzling literary strategies.

From Schleiermacher to Gadamer, some modern philosophers have in fact altogether rejected the project of extracting Plato's arguments from their dramatic context. They argue that the dialogue form was essential to Plato's dialectical methodology or to inspiring inquiry, and that 'reconstructing' his arguments and theories necessarily distorts and damages his philosophy. Most scholars aim for some middle ground: they construct interpretations based on both the dramatic context of Plato's arguments and their logic.

The Greek Enlightenment: from mathematics to Forms

A series of breakthroughs during the Greek Enlightenment (5th – 4th c. BCE) laid the foundations for the later growth of European science and, many argue, for Plato’s Theory of Forms. Greek thinkers discovered that both musical scales and astronomy had mathematical structures. The fifth century revolution in Greek mathematics led to new efforts to organize all of mathematics into logical systems based on clearly defined axioms. In the first half of the fourth century BCE, Plato’s Academy became the leading center of research in this ongoing scientific revolution and drew in students and experts from across the Greek world. Plato himself was regarded in ancient times as a leading mathematician. Plato's dialogues, including the Republic, Timaeus, Meno, and Epinomis, show an easy familiarity with these innovations, which all involve repeated patterns and the creation of abstract concepts. Many writers have therefore seen the growth of early science as an important source for Plato’s Theory of Forms. For example, John Burnet, the editor of the Oxford edition of Plato’s dialogues, said:

It seems evident that the doctrine arose in connection with the study of mathematics, which had already reached the stage of making confident assertions about things [such as perfect triangles] which are never perceived by the senses, and that it was extended so as to cover certain objects of moral and aesthetic importance [such as ‘justice’ and ‘beauty’] which seemed to have a similar character to the mathematical 'forms,' in so far as we know what they mean, though we have never met with a perfect example of any of them.

Just as Kant's philosophy has been seen as a response to Newton’s breakthroughs during the Scientific Revolution of the 1600’s, Plato’s Theory of Forms can be read as a philosophical system based on the Greek Enlightenment’s discovery of general patterns in nature.

In the past, some scholars interpreted Plato as an opponent of science or empiricism but this has been widely debunked.

Socrates: from definitions to Forms

Reginault, 'Socrates Tears Alcibiades from the Embrace of Sensual Pleasure' (c. 1785)

Aristotle was perhaps just drawing on the dialogues when he described the origin of the Forms in this way:

[Plato’s teacher] Socrates investigated ethics … and sought its universal principles. He was the first to seek to know its rational definitions. After Socrates showed the way, Plato assumed definitions came about through the Forms and not through sensible things …

Following this, some scholars believe that Plato’s Theory of Forms developed out of his teacher’s search for definitions. When Socrates asked, for example, what bravery is, his conversation partner responded by listing examples: this is brave, that is brave, etc. Socrates replied that he was instead seeking a definition of what the examples have in common and makes them all instances of bravery. Thus Socrates presumed that a definition reveals one essential feature that the many brave things share. Some ancient and modern interpreters believe Plato turned this into a metaphysical theory by positing a Form for each definition. Plato’s Form of Bravery is the one thing that makes many things brave.

Among ‘most modern interpreters’ this view of the origin of the Theory of Forms is often combined with theories about Plato’s development that divide the dialogues into three periods, early, middle, and late. The earlier dialogues that portray Socrates seeking definitions do not expound the Theory of Forms at length. Middle and late dialogues such as the Symposium and Republic say much more about the Forms. Thus the sequence of dialogues seems to reveal a shift from seeking definitions to a metaphysical Theory of Forms. Some scholars, however, reject the division into early, middle, and late periods and the idea that Plato’s philosophy developed in any significant way.

Recollection: from reason and logic to the Forms

Humans seem to have two sorts of knowledge and Plato invoked the Theory of Forms to explain their difference. One comes from external sources such as experience or learning. The other seems to arise internally from reasoning or logic. Plato vividly showed that an uneducated slave boy, prodded into reasoning by Socrates' questions, had knowledge of geometry. Plato concluded this was 'innate' or 'inborn' knowledge of the Forms.

After Plato distinguished these two sorts of knowledge, explaining the source of internal knowledge became a central theme of European philosophy. Seventeenth century philosophy is often thought of as a rivalry between the 'Rationalists' and 'Empiricists' because the two schools disagreed about whether the mind and reason or only experience could produce knowledge. Descartes, often regarded as the founder of modern philosophy, famously defended innate ideas and told the story of Plato's slave boy to justify them. After Locke attacked innate ideas, Kant aimed to reconcile both views by building his system upon a demonstration that certain concepts were innate to our souls.

The theory of evolution later encouraged various biological or genetic versions of the theory of innate ideas. Darwin himself wrote 'Plato says . . . that our ‘‘necessary ideas’’ arise from the preexistence of the soul, [and] are not derivable from experience—read monkeys for preexistence.' New versions of the doctrine of innate ideas have thus been revived among contemporary linguists, cognitive scientists, and evolutionary biologists, such as Noam Chomsky and Steven Pinker, who argue that speech and language depend on an inborn knowledge of grammar.

Plato made his 'epochal discovery: of knowledge which needs no confirmation from sense-experience and admits of no refutation from it …' and found therein another motivation for his Theory of Forms. His surprising theory, the doctrine of recollection, is 'one of his most notorious legacies.' It has two aspects. The dialogues portray logical reasoning or 'dialectics' as a recovery of the knowledge already within us:

… for Plato the mind has no independent structure: it is simply the capacity of the human soul to cognize, and thus to identify with, the structure of objective Being [i.e., of the Forms]…

Plato solves the problem of the origin of this innate knowledge by positing that -- prior to birth -- each soul has a vision of the Forms that is retained but somehow obscured. This fits with the doctrine of the soul's transmigration that Plato apparently inherited from the Pythagoreans. Rediscovering the knowledge within us, either through introspection or submitting to questioning, was 'recollection' of that primordial knowledge. This may be one of Plato's 'myths,' but this doctrine of recollection shows how the problem of innate knowledge is solved by the Theory of Forms.

Ethics: from objective values to the Forms

Ethics in Plato's dialogues rests on two seemingly contradictory doctrines, Socratic Ignorance and Moral Absolutism. The first asserts we cannot know what is just and good, the second asserts justice and goodness are absolute and objective values. The Theory of Forms ties these together into a coherent system.

Socratic Ignorance is not the same as skepticism or relativism. A skeptic abandons the search for knowledge because it is unattainable. A relativist holds that whatever we believe is true 'for us' or relative to us, and that all knowledge is merely subjective. Socratic Ignorance is instead a kind of fallibilism. In the dialogues, Socrates steadfastly seeks knowledge and holds that it is is objective: its truth does not depend on our beliefs. He also holds, however, that our best knowledge is fallible and might be overturned by new evidence or arguments (like modern scientists who accept that even their best theories may be overturned in the next revolution). Socrates is ignorant in the strict sense: because he knows nothing with certainty. Thus for Plato moral beliefs may be wrong and are revised if better reasons or arguments come along.

Plato was a champion of Moral Absolutism. Popular morality in ancient Greece was a mixture of traditional conventions and religious beliefs. In the fifth century BCE, itinerant teachers known as Sophists attacked tradition and spread a wave of moral skepticism and relativism. One of Plato's great themes, and the subject of his best known work, the Republic, was the establishment of a secular moral absolutism based on reason and argument. Plato rejected both the 'might makes right' of traditional morality and the fashionable skepticism of the Sophists. In their place, Plato argued there is such a thing as justice, that right and wrong are not a mere matter of opinion, and that the best life is the moral life. The invention of a morality based, not on religion, but on rational argument was one of Plato's most lasting and influential, if always controversial, contributions.

The Theory of Forms made it possible to combine Socratic Ignorance with Moral Absolutism. For Plato, our actions are really and objectively just when they participate in the Form of Justice. Moral qualities, like all other properties, depend on the Forms. Knowledge of the Forms, however, depends on reason and argument and is therefore fallible. Plato does not portray our moral judgements as coming from any special revelation, mystical vision, or inner intuition of the Forms. Many dialogues show that claims to know what is right and wrong can be overturned by argument. Thus Plato has another motivation for his Theory of Forms: it grounds ethical values and makes them real and absolute, but insists that knowledge of those values is fallible and not absolute.

The Argument from Knowledge

Argument from Knowledge

1. There is knowledge. (Assumption)
2. Knowledge implies the existence of objects that exist
permanently. (Assumption)
3. Therefore, there are objects that exist
permanently. (from 1,2)
4. But sensible objects are in flux and do not exist
permanently. (Assumption)
5. Therefore, there are some objects that are not sensible
and exist permanently, and we call these the Forms. (from 3,4)

Plato’s dialogues argue from the existence of knowledge to the existence of the Forms. The Greek word for knowledge, episteme, is often translated as 'science' because in Latin 'science' just means 'knowledge.' Thus, this is also known as the 'argument from the sciences.'

There is a strong conception of 'knowledge' in Plato’s dialogues. They say, for example, that it is wrong to speak of 'true knowledge' or 'correct knowledge' because what we know cannot be wrong. That is, the concept of knowledge already includes the idea that it is true and correct. If we know 2+2=4 then it cannot be that 2+2=5. The dialogues also assume that knowledge has an object: it is always 'knowledge of something.' Since knowledge is always true, its objects must be permanent. If we know 2+2=4 then it will never be that 2+2=5.

Before Plato, the philosopher Heraclitus held that the sensible things in the world are always changing and, since they are changing, they are not the same. If our hair grows, we are not exactly the same person as before. Heraclitus believed that if we are not the same in any way we are not one and the same person as before. Therefore, he concluded, since everything we see around us is changing in some way, no matter how minute, nothing is really the same and lasts from instant to instant. Our world, he said, is in a constant 'flux' and nothing is permanent. He famously said 'It is impossible to step in the same river twice.'

The strong concept of knowledge together with the concept of a ceaselessly changing flux leads to a valid argument for Plato’s Forms.

The One over Many Argument

The One over Many Argument

1. Many different things are the same color of red. (Assumption)
2. If many different things are the same color of red, then the
color of red is not identical to any of them. (Assumption)
3. Therefore the color of red is not identical to any of the
red things. (from 1,2)
4. If things are not identical, then they are distinct. (Assumption)
5. Therefore the color of red is distinct from red things. (from 3,4)
6. If many things are red yet the color of red is distinct from
those things, then the color of red is a Platonic Form. (Assumption)
7. Therefore, the color of red is a Platonic Form. (from 1,5,6)

This famous but controversial argument says simply: if many things share a common property, then there is a common property that they share. That is, it moves from the fact the same property occurs in many things to the claim that it has one and the same, intrinsic nature that is repeated in many things at once. Such a repeated property is called a 'One over Many' or just a 'Form.'

This argument was already a theme of discussions in Plato’s Academy and, in various ways, is still vigorously debated by philosophers today. Plato’s dialogues, however, do not use this as an argument for the Forms. There is a much-discussed passage in the Parmenides that comes close to advancing the argument:

I suppose this is what leads you [Socrates] to suppose that there is in every case a single Form: when several things seem large to you, it seems perhaps that there is a single Form which is the same in your view of all of them. Hence you believe that the [Form of] Largeness is a single thing.

Many later philosophers, however, have debated whether the mere existence of repeated properties implies the existence of Forms. Intuitively, the proposed argument usually turns on the assertion that if a ball and fire engine are both red, then redness is not identical to that ball or that fire engine. If different things are the same color, the color must have its own independent nature that is ‘in’ or ‘belongs’ to the different things yet remains the same, and is thus a Form.

This argument leaves open the question of the whether a 'One over Many' Form is immanent or transcendent. Criticisms of this argument are reviewed LINKbelow.

The Argument from Relatives

The Argument from Relatives

1. A house appears intrinsically large and intrinsically
small. (Assumption)
2. The house is not really intrinsically large and intrinsically
small. (Assumption: law of non-contradiction)
3. Therefore the house appears intrinsically large and intrinsically
small, but is not really so: these are 'mere appearances.' (from 1,2)

4. The house is either intrinsically large or relatively
large. (Assumption)
5. The house is not intrinsically large. (from 3)
6. Therefore the house is relatively large. (from 4,5)
7. If the house appears intrinsically large but is really
relatively large, then an invisible relative exists. (Assumption)
8. Therefore, an invisible relative exists, which we call
the Form of Largeness. (from 1, 6, 7)

This argument appears in several different versions and ‘… little consensus has emerged about its basic structure.’ It turns on a distinction between two kinds of properties. 'Intrinsic properties' such as redness involve only one thing. 'Relational properties' (Gk: ta pros heteron ) such as being taller involve two or more things. Things related by relational properties are called 'relatives.' Plato focuses on 'provocative' cases where a single thing appears to have two contradictory properties at once. For example, when three fingers are compared, one may be at once smaller and larger. Plato exploits this apparent contradiction to construct an argument for the Forms.

There is a simple version of the Argument from Relatives in the Republic. It is reminiscent of cases where 'beauty lies in the eye of the beholder.' When a painting appears beautiful to one person and ugly to another, it cannot be both intrinsically beautiful and intrinsically ugly at once because that would be a contradiction. Thus neither beauty nor ugliness is intrinsic to the painting; they are instead relations between it and the viewers. That is, beauty does not reside wholly in the painting and is instead a relational property involving relatives outside the painting. The argument in the Republic is similar and more general. It holds that the same problem affects many other properties considered objective or physical. A house appears large to one person and small to another (comparing it to a mouse or a mountain). Therefore, the house by itself is really neither large nor small. Like beauty, largeness is a relational property involving a relative outside of the house.

As the outline shows, the argument first establishes that a house which appears intrinsically large is not really so. This is an example of Plato's appearance-reality distinction: the mere appearance without a corresponding reality is not nothing but is 'between being and not being.' The argument concludes that a house which appears intrinsically large but is really relatively large must be related to some invisible relative, i.e., to a Form.

Debates over the metaphysics of relational properties have also been a central theme of modern philosophy. Contemporary philosophers accept the existence of relational properties and represent them with symbols, such as 'Larger (house, mouse).' This seems to be a relation between two visible relatives, but largeness 'is not something that can be simply seen.' Metaphysical theories of such relations rely on further, usually mathematical connections between sizes or shapes (e.g., that the house is 10m high, the mouse is 3cm high, and 10m > 3cm). That is, modern theories also explain largeness by something outside the house that is formal, and thus in some ways resemble Plato's argument.

Criticisms of the Theory of Forms

The mathematician and philosopher Alfred North Whitehead famously said 'The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.' It is frequently remarked that criticisms of the Theory of Forms are a special case of this dictum: most of the well-known criticisms that have dominated the debate since Plato were already discussed in Plato’s dialogues. Plato's Parmenides portrays a young Socrates struggling with some particularly strong criticisms of the Forms. A minority of critics find them so compelling they believe Plato himself must have abandoned the theory, but most agree that dialogues written after the Parmenides rely on the Theory of Forms and that Plato therefore believed he had answers to the objections.

The Battle of the Giants: Materialists vs. Friends of the Forms

Plato knew that the Theory of Forms was controversial. In a famous passage, Plato forsaw a perennial war between those who believe that only material things exist and those who argue for abstract objects like the Forms and numbers:

It seems there is a veritable battle of the giants (a 'gigantomachy') on account of the dispute over the nature of existence … Some drag everything invisible and in heaven down to earth. They really grasp with their hands rocks and trees and touching this sort of thing insist only that which can be approached and handled exists. They define 'existence' as the same as 'being a material body.' If anyone else says there are other abstract things that have no material body, they despise him utterly and will listen to nothing more… Those who argue against the materialists must gird themselves with defenses drawn from the invisible things above, forcefully contending that the true existents are incorporeal and grasped by the mind … There is, between these two sides, a tremendous and eternal battle …

Plato called those who defend abstract objects the 'Friends of the Forms.' Plato did concede, however, that it was both 'difficult to accept and difficult to reject' the Theory of Forms.

The Third Man and Self-Predication

The Third Man Argument

1. There is a group of things with a similar property. (Assumption)
2. If there is a group of things with a similar property, then there is a
separate Form that explains the similarity (Assumption: separate Forms).
3. Therefore, there is a separate Form. (From 1,2)
4. This Form, however, also exemplifies the property. (Assumption: self-predication)
5. Thus there is a new group of things with a similar property,
namely the original group together with the separate Form. (From 1,3,4)
6. But this new group now implies the existence of yet another, separate Form
to explain the similarity they share (From 2,5).
7. This reasoning can be repeated and thus
implies an infinite regress of Forms. (From 1-6)
8. Infinite regresses are generally seen as a pathology in any theory. (Assumption)
9. Therefore, the Theory of Forms is pathological. (From 7,8)

The Third-Man Argument against the Theory of Forms is mentioned in the dialogues and discussed by Aristotle, who gave it the name ‘Third Man.’ The central issue is whether or not Forms are examples of their properties: is the Form of Redness actually red or the Form of Largeness actually large? This is called 'self-predication,' and Forms that are examples of their properties are said to ‘exemplify’ those properties.

The assumption of self-predication interacts with another thesis to generate a paradox. Many passages in the dialogues assert that whenever many things are similar, there is a Form that explains that similarity. Assuming that this Form is separate from the things that participate in it leads to the argument at right. Defenders of the Forms generally disagree that Forms exemplify properties in the same way as ordinary things, and thus deny step 4 of this argument. There is also a debate over how or whether the Forms are separate from the things that participate in them.

The Greatest Difficulty: No Knowledge of the Forms

The Greatest Difficulty

1. Relations hold between two relatives. (Assumption)
2. A relative is either a Form or a thing. (Assumption: Theory of Forms)
3. Therefore, relations hold between two Forms, two things, or a Form
and a thing. (From 1,2)
4. There are no relations between a Form and a thing.
(Assumption: no cross-realm relations).
5. Therefore, relations hold between two Forms or two things. (From 3,4)
6. Knowing is a relation between a piece of knowledge and its object.
(Assumption)
7. Therefore, knowing holds between Forms or between things. (From 5,6)
8. Human knowledge is a thing and not a Form. (Assumption)
9. Therefore, there is no human knowledge of the Forms. (From 7,8)

In Plato's Parmenides, one objection to the Theory of Forms is called the 'Greatest Difficulty.' The problem centers on the nature of relations. It is agreed that a master owns a slave, and this relation holds between two relatives. However, the Form of Master is related not to an ordinary slave but to the Form of a Slave. That is, relations hold within the realm of Forms or within the realm of becoming, but not between or across the two realms.

This creates an obstacle for our hopes of knowing the Forms because knowing is a relation between a piece of knowledge and its object. The knowledge that we humans have cannot be related to any object in the realm of the Forms. Therefore, we cannot have any knowledge of the Forms. The Parmenides concludes that someone with wide experience who was willing to follow long arguments can escape this difficulty, and proceeds in the second half of the dialogue to give a long and detailed argument whose interpretation is disputed. Plato's Republic suggests that knowledge of the Forms is possible.

The Whole-Part Dilemma: One Form in Many Things

Plato generally does not advance a theory of participation, but his Parmenides raises a fundamental puzzle about one possible theory. Suppose that Forms affect appearances by being present in or immanent in them. That is, when a large thing participates in the Form of Largeness, the Form of Largeness is somehow in that large thing. This theory leads to the whole-part dilemma:

• If a Form is wholly present in each of many things, then one Form is in many separate things. This implies that one thing can be in many different places at once. This seems incredible.

• If a Form is only partially present in each of many things, then each thing is affected only by a part of the whole Form. This implies that a Form is one thing but also many (because it has parts), or that a small part of the Form of Largeness can make something Large. These also seem incredible.

Neither horn of the dilemma seems acceptable, and so interpreting participation as immanent presence seems problematic. This puzzle also affects debates over the relation between scientific laws and the phenomena they govern.

The Range of Forms: Mud and Artifacts

Plato's Parmenides raises questions about whether certain kinds of Forms exist. The dialogues suggest there is a Form for every way of appearing, or every property of things, or every general word we employ. The Parmenides asks if there are Forms for lowly things such as mud and dirt or for non-natural things like beds created by carpenters. The dialogues do not resolve these issues and they were widely discussed in the early Academy. One leading Plato scholar, Harold Cherniss, concluded ' … Plato’s only direct answer could have been … "there are ideas of all things that have objective existence – and of such things only." By such a statement ideas of artifacts would by no means have been excluded or denied …’

Aristotle’s Harsh Criticism

Aristotle rejected aspects of Plato's Theory of Forms and advanced his own, modified version of the theory (see below). His negative criticisms were sometimes stated in quite harsh language. Harold Cherniss famously argued that many of Aristotle's criticisms of his predecessors were polemical and distorted their theories. In particular, Aristotle criticized the transcendent interpretation of Plato's Forms that makes Forms separate from things, and argued instead for immanent Forms that he called 'universals.' According to Terry Penner,

Plato's Forms are often thought of as perfectly extraordinary entities, entities of a sort no sensible person would believe in. One of the earliest of such 'sensible' critics was Aristotle. Plato is certainly right to suppose that universals exist, Aristotle thought; but then why did he have to go and pin so much metaphysical baggage onto those universals. Why did he 'separate' universals from sensible particulars?

Aristotle argued: 'It would seem impossible for the Form of a thing (ousia) to exist apart from that thing, for how can a Form be the substance of something when it exists apart?'

Aristotle mocked Plato for aiming to explain the realm of things by 'duplicating' them with a separate realm of corresponding Forms: 'as if someone who wanted to count a few things thought it was impossible until their number was increased ...'

Aristotle claimed that Plato took the concept of participation from the Pythagoreans: 'Plato only changed the name of participation. The Pythagoreans says that things exist by imitating numbers, but Plato changes the name and says by participating. And what this imitation or participation might be they left to others to seek in common discussion.' Aristotle, however, went on to mock Plato for not explaining the nature of participation: 'To say that the Forms are patterns or paradigms for things and things 'participate' in them is to use empty words and poetical metaphors.'

Generally Aristotle thought that the arguments for transcendent Forms were unpersuasive:

None of the ways we [students of Plato] show the Forms exist actually show they do. From some of them no necessary conclusion follows; from some of them Forms emerge for things we think should not have Forms. According to the Argument from Knowledge there will be Forms for everything we know about, and according to the One over Many Argument there will be Forms even for non-existent things, for arguing that there is a Form for every mental concept, even for those things that have perished, implies there will be a Form whenever we have a mental image of them. Even among the better or more accurate arguments for the Forms, some imply Forms for relations, which we deny are a real kind of thing, and others are liable to the puzzle about the Third-Man… Above all, someone might be perplexed about what the Forms contribute … since they are not the causes of motion or change in things… And things are not from the Forms in any ordinary sense…

Conceptualism and God: Forms as Mental Concepts

Through history many have argued that Plato's Forms are not real entities but instead are merely mental concepts: 'redness,' they say, is merely a general concept we apply to the many red things and there is no immaterial Form of Redness that exists independently of our minds and red things. This kind of theory is known as 'conceptualism' and was first discussed and criticized in Plato's Parmenides. Two historically important replies to conceptualism were made there.

The first reply is about the connection of thoughts and reality. Since thoughts are thoughts about something, and our concept of redness is about something that exists, that concept of redness must be about something outside the mind. Since 'redness' is general and not the same as any particular patch of redness, the concept of redness must be about something general, and this is not merely a thought but a Form. Therefore, the admission that our general concepts have general objects implies that the Forms themselves exist. This line of argument is related to the famous ontological proof for the existence of God.

The second reply assumes conceptualists still accept the doctrine of participation. That is, they agree that real things still participate in or share in the supposedly merely mental Forms. This leads to absurdity: either things are made of thoughts and 'all things think' or, if things do not think, there are thoughts in things which are never thought. This peculiar line of argument is related to a later tradition of philosophies called 'Idealism' (most influentially advocated by Hegel), which holds that Being and thought are somehow the same.

Historically, the most important variation of conceptualism was the view that Plato's Forms existed in God and were the 'thoughts of God.' This interpretation was widespread among some Middle Platonists and Christian theologians: '… by the middle of second century A.D. there was very much of a consensus as to the nature of the Forms as thoughts in the mind of God.'

Outline History of the Theory of Forms

The Forms in Plato's Academy

Many scholars believe that Plato was influenced by a school of philosophy called Pythagoreanism, which emphasized the role of mathematics in nature. The current consensus is that the Theory of Forms was Plato's innovation and was not inherited from the Pythagoreans.

Aristotle gave a history of how Plato developed the Theory of Forms. It is plausible but historians debate whether Aristotle had good evidence for his account or merely inferred it from his readings of the dialogues. Aristotle claimed that when Plato was young he accepted the views of Heraclitus, and believed that all phenomena were in a flux and transitory. Later, he learned from Socrates that there must be some things that are stable and permanent. Plato's Theory of Forms combines these two views: appearances are transitory but reality consists of the permanent Forms:

In his youth, Plato became familiar with the view of Heraclitus and [his follower] Cratylus that all sensible things are in an ever-changing flux and that there can be no lasting knowledge of them, and Plato afterwards still supposed this. Socrates … was the first to turn his thought to the search for definitions; Plato accepted this but asserted that definitions were not about sensible things but about other [supra-sensible] things, for it is impossible for there to be a general definition of sensible things since these are always changing. He called these the 'Forms' …

Aristotle later repeated this history and specifically said that it was Plato who made the Forms transcendental: 'But Socrates did not make universals or definitions separate; however, his successors [namely Plato and his students] did separate them, and things of this sort they called 'Forms.'

Debates over the Forms in Plato's Academy are recorded in Aristotle's book On Ideas, which has been reconstructed from later sources, and in his Metaphysics.

According to both Aristotle and other later sources, Plato discussed certain metaphysical theories with his students that he did not include in the dialogues. These are known as Plato's unwritten doctrines. Modern reconstructions of these theories suggest that Plato extended the Theory of Forms with two higher 'principles,' but these theories are controversial (see below).

Plato's nephew and student Speusippus, who became head of the Academy after Plato's death, rejected the Theory of Forms. This is taken to show that, despite Plato's lifelong advocacy of the theory, he encouraged independent views among his students and did not impose any orthodoxy upon them.

Aristotle’s Modified Theory: Universals and Substances

Plato's student Aristotle rejected some parts and accepted other parts of Plato's Theory of Forms. In particular, he accepted the existence of Plato's Forms but rejected their transcendence. Aristotle argued for the existence of immanent Forms in things, which he called 'Universals.' This 'rival doctrine' spread widely in the Middle Ages and in many ways established the terms of subsequent debate.

Aristotle conceived of the world as a collection of individual things that he called 'substances' (he is sometimes said to have invented the concept of the 'thing'). Socrates, horses, and trees are all substances. These substances persist through time and have the characteristic ability to change while retaining their identity. Each substance has properties. For Aristotle, a universal is a property that recurs in more than one substance: the many red things share one and the same Universal of Redness. Thus Aristotle's universals avoid the problems associated with transcendence but are still liable to puzzles about how a single universal can be in many things at once (see the whole-part dilemma above).

Each of Aristotle’s substances is composed of matter and universals. Thus, Aristotle said, a bronze sphere has bronze for its matter while the Universal of Sphericality gives it shape. Aristotle's theory is called 'Hylomorphism' because, in ancient Greek, 'matter' is hyle and 'shape' is morphos.

Aristotle's theory is therefore very different from Plato's. His Universals are immanent, while the question of whether Plato's Forms are immanent or transcendent is disputed. Aristotle's concepts of matter and substance do not figure in Plato's theory. Many would even deny that the atomic individuals that are the basis of Aristotle's metaphysics play any role in Plato's system. Some ancient philosophers, however, thought the differences between Plato and Aristotle were minor, and that their theories of reality could be reconciled and somehow reflected a deeper, common 'harmony.' Modern historians of philosophy tend to emphasize the differences, and thus to see their two theories as rivals.

Renaissance

Botticelli's Primavera (detail, c. 1482). Florentine painters led the Renaissance shift from religious to pagan, allegorical themes. Lorenzo de' Medici was the patron of both Botticelli and Ficino, and extant letters suggest Ficino may have been consulted about the subjects of Botticelli's paintings.

Though almost all of Plato's dialogues were unavailable in Western Europe during the Middle Ages, Neo-Platonism became well-known through various channels:

All mediaeval thought up to the twelfth century was Neoplatonic rather than Aristotelian; and such popular authors of the Middle Ages as Augustine, Boethius, and the Pseudo-Dionysius carried Christian Neoplatonism to England as they did to all other parts of Western Europe.

From the Twelfth Century, the works of Aristotle became increasingly available and his philosophy came to dominate late medieval Scholasticism.

Plato's dialogues were preserved in the Byzantine Empire and Latin translations of individual dialogues began to appear in Italy early in the Renaissance. Marsilio Ficino (1433 – 1499) published the first complete translation in 1484 and this rapidly spread direct knowledge of Plato throughout Western Europe. Ficino ensured that the Neo-Platonist approach to Plato became the norm.

Bust of Marsilio Ficino in the cathedral in Florence (by A. Ferrucci, 1521). He seems to play his translation of Plato like a lyre.

Kant, Tennemann, and Hegel

In the eighteenth century, as scholarly discourse began to shift from Latin to national languages like English, French, and German, the German philosopher Christian Wolff translated the Latin word idea into the German Begriff (concept) or Vorstellung (image). Kant, however, used begriff and idea alongside each other. For him, Begriff was the more objective result of thought while idea emphasized the more subjective process of thought or vision. More precisely, Kant's Begriff is a general representation that relates to objects through 'marks' or 'characteristics' that can be shared by many things; Kant's Ideas are concepts that go 'beyond the possibility of experience' in space and time.' In a well-known section 'On the Ideas in General,' Kant summarized the meaning Plato gave to 'idea' but claimed to understand it better than Plato himself:

Plato uses the expression 'idea,' as is easy to see, to mean something that can never be derived solely from the senses … For him, the Ideas are models (Urbilder) of things themselves … they stream out of the highest Reason … I will not here indulge in any literary investigation to try to discover what meaning the sublime philosopher attached to this expression. I remark only that it is not at all unusual even in ordinary conversation as well as in writing, by compraing the thoughts which an author has expressed about an object, to understand him better than he understood himself … A313-4/B370

For Kant, ideas are subjective 'concepts in the human mind, not extra-mental entities as they were for Plato… Both Plato and Kant [nevertheless in ethics] regard ideas as as normative standards against which the sensible world is to be measured …

Tennemann, System of Platonic Philosophy (1792) Said to be the first, modern monograph on Plato, Tennemann's study interpreted Plato as a rationalist, and believed a logical, philosophical system lay concealed in the dialogues.

The philosopher Wilhelm Gottlieb Tennemann (1761 – 1819) influentially portrayed Plato as a precursor to Enlightenment rationalism and Kant's philosophy. Drawing on the criticism of writing in Plato's Phaedrus and the Seventh Letter attributed to Plato, Tennemann asserted Plato had both practical and philosophical reasons for withholding his 'unwritten doctrines.' Tennemann finally laid out his grand project of close reading and comparisons between the dialogues that, he claimed, had enabled him to reconstruct much of Plato's lost esoteric philosophy.

The interpretation of Plato’s Forms was central to the Neo-Kantians at Marburg, and their debates influenced Heidegger, Gadamer, and other philosophers. Paul Natorp's Plato's Theory of Ideas (1903, 1921) argued that Plato postulated the Forms as quasi-scientific 'hypotheses' about experience, and thus that Plato was a precursor to Kant.

Recent Scholarship

The Cherniss-Owen Debate: Did Plato Abandon the Forms?

In a famous paper, the Oxford philosopher G. E. L. Owen argued that Plato’s Parmenides marked a radical change in the Theory of Forms. He claimed that Plato did not entirely reject his own theory but instead rejected a symmetrical resemblance relation between particulars and Forms (paradeigmata) as well as the sharp dichotomy between being and becoming. These two doctrines are propounded in the Timaeus, which was then widely considered one of Plato’s latest dialogues. Owen, therefore, ‘sought to make his view plausible by proposing to remove the Timaeus from the late group and place it among the middle dialogues, after the Republic but before the Parmenides. Owen launched a many-pronged attack on the traditional late dating of the Timaeus… [and] attempted to undermine the credibility of the stylometric evidence for the late date of the Timaeus …’ Another prominent scholar, Harold Cherniss, denied that Plato had abandoned the Forms in a 1957 reply and provoked a large and controversial literature on the question. According to William J. Prior in 1985,

The exchange between Cherniss and Owen initiated a debate which has continued to this day. Both positions have won some support, but neither has emerged victorious from the fray. The work of Ryle and Owen has effectively destroyed the consensus of scholars on the development of Plato's metaphysics and the date of the Timaeus, but it has not produced a new consensus. Nor has Cherniss' contrary position won the support of a majority of scholars.

In 2012, Ausland said that Owen's thesis had not won the support of the majority of scholars.