"All western philosophy consists of footnotes to Plato", Alfred North Whitehead once said famously. And with much justification, if indeed philosophers can be judged as much by the influence they have wielded as by anything they wrote or taught.
Platonism inspired and informed the earliest teachings of the Christian Church; crept into the thinking of various medieval scholastics; figured strongly in the doctrines of certain Renaissance thinkers; invigorated a sect of influential philosophers in Britain in the late seventeeth century (known as the "Cambridge Platonists"); elicited the contempt of Nietzsche and his followers in Europe; and affected innumerable artists, mystics, poets, and prophets over the ages.
The linchpin of Platonism is the theory of forms.
"What is this Theory of Forms?
Definitions. Every discussion of a general issue turns ultimately upon one or more general notions or ideas. Even to debate whether, say, fearlessness is a good quality is to work with the two general notions of fear and goodness. Two disputants may disagree whether fearlessness is a good or a bad quality, but they are not even disagreeing unless they know what fear and goodness are. Their debate is likely, at some stage, to require the explicit definition of one or more of the general terms on which the discussion hinges. They may accept a proferred definition, but even if a proferred definition is justly riddled by criticism, this criticism teaches what the misdefined notion is not. If "fearlessness" were misdefined as "unawareness of danger," the exposure of the wrongness of this definition would by recoil bring out something definite in the notion of fearlessness. The Socratic demolition of a proferred definition may be disheartening, but it is also instructive.
Standards of measurement and appraisal. Some general notions, including many moral notions and geometrical notions, are ideal limits or standards. A penciled line is, perhaps, as straight as the draftsman can make it; it deviates relatively slightly, sometimes imperceptibly, from the Euclidean straight line. The notion of absolute straightness is the standard against which we assess penciled lines as crooked or even as nearly quite straight. Rather similarly, to describe a person as improving in honesty or loyalty is to describe him getting nearer to perfect honesty or loyalty.
Immutable things. Ordinary things and creatures in the everyday world are mutable. A leaf which was green yesterday may be brown today, and a boy may be five feet tall now who was two inches shorter some months ago. But the color brown itself cannot become the color green, and the height of four feet, ten inches, cannot become the height of five feet. It is always five feet minus two inches. A change is always a change from something A to something else B, and A and B cannot themselves be things that change.
Timeless truths. What we know about particular things, creatures, persons and happenings in the everyday world are tensed truths, and what we believe or conjecture about them are tensed truths or tensed falsehoods. The shower is still continuing; it began some minutes ago; it will stop soon. Socrates was born in such-and-such a year; the pyramids still exist today; and so forth. But truths or falsehoods about general notions such as those embodied in correct or incorrect definitions are timelessly true or timelessly false. Just as we cannot say that 49 used to be a square number or that equilateral triangles will shortly be equiangular, so we cannot say, truly or falsely, that fearlessness is now on the point of becoming, or used to be, indifference to recognized dangers. If this statement is true, it is eternally or, better, timelessly true. We can ask questions about fearlessness or the number 49 but not questions beginning "When?" or "How long?"
One over many. It is often the case that we can find or think of many so-and-so's or the so-and-so's, for example, of the numerous chimney pots over there or of the prime numbers between 10 and 100. Things, happenings, qualities, numbers, figures, can be ranged in sorts or characterized as sharing properties. Hence, where we speak of the so-and-so's - say, the storms that raged last week - we are talking of storms in the plural, and we are thereby showing that there is something, some one thing, that each of them was -- namely, a storm. Or if there are twenty idle pupils, there is one thing that all twenty of them are -- namely, idle. Sometimes we do not and even cannot know how many leaves, say, there are in a forest, and we may ask in vain, How many leaves are there? But however many or few there are, there must still be one thing - namely, leaf - which each of them is. It is one or singular; they are many or plural. We have not seen and may never see all or most of them. But it, that which each of them is, is in some way known to us before we could even begin to wonder how many leaves there are.
Intellectual knowledge. For our knowledge of, and our beliefs and opinions about the things, creatures and happenings of the everyday world, we depend upon our eyes, ears, noses and so on, and what our senses tell us is sometimes wrong and is never perfectly precise. There is nobody whose vision or hearing might not be even slightly better than it is. On the other hand, our apprehension of general notions is intellectual and not sensitive.
Conceptual certainties. Last, but not least in importance, dialectical debates are concerned only with general ideas, like those of fearlessness, goodness, danger and awareness. The answerer's thesis is a general proposition, such as "Virtue is (or is not) teachable" or "Justice is (or is not) what is to the advantage of the powerful." When such a thesis has been conclusively demolished, something, if only something negative, has been conclusively established about virtue or justice. In the domain of general ideas or concepts certainties, if seemingly negative certainties, are attainable by argument. About things or happenings in the everyday world no such purely ratiocinative knowledge is possible.
Ontology of Forms. Most of the above ways of characterizing general ideas or concepts has been brought out severally or together in Plato's elenctic dialogues. Yet his Socrates did not in these dialogues put forward the Theory of Forms. The Theory of Forms, as first fully developed in the Phaedo, is a unified formulation of these several points, but it is also more than this. For Plato now proffers an ontology of concepts. A general idea or concept, according to this new doctrine, is immutable, timeless, one over many, intellectually apprehensible and capable of precise definition at the end of a piece of pure ratiocination because it is an independently existing real thing or entity. As our everyday world contains people, trees, stones, planets, storms and harvests, so a second and superior, or transcendent world contains concepts-objects. As "Socrates" and "Peloponnesus" name perceptible objects here, so "justice," "equality," "unity," and "similarity" name intellectually apprehensible objects there. Furthermore, as the human mind or soul gets into contact, though only perfunctory and imperfect contact, with ordinary things and happenings in this world by sight, hearing, touch and so on, so the human or soul can get into non-sensible contact with the ideal and eternal objects of the transcendent world. We are ephemerally at home here, but we are also lastingly at home there. The immortality of the soul is proved by our ability to apprehend the everlasting concept-objects that Plato often calls the Forms. . ."
-Gilbert Ryle
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
We call both the sky and blue jeans by the same color, blue. However, clearly a pair of jeans and the sky are not the same color; moreover, the wavelengths of light reflected by the sky at every location and all the millions of blue jeans in every state of fading constantly change, and yet we somehow have 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."
No one has ever seen a perfect circle, nor a perfectly straight line, yet everyone knows what a circle and a straight line are. Plato utilises 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..."
"The Platonic idealist is the man by nature so wedded to perfection that he sees in everything not the reality but the faultless ideal which the reality misses and suggests..."
-George Santayana