Perhaps Plato’s most famous contribution is his Theory of Forms (or Ideas; Eidos); it is demonstrated in the Euthyprho and most clearly formulated in his dialogues the Republic and the Phaedrus, although the theory underpins most of his works. 

Consider the following passage from the Euthyprho:

1. Socrates asks Euthyphro “So tell me now, by Zeus, what you just now maintained you clearly knew: what kind of thing do you say that godliness and ungodliness are, both as regards murder and other things; or is the pious not the same and alike in every action, and the impious the opposite of all that is pious and like itself, and everything that is to be impious presents us with one form or appearance insofar as it is impious?”
   

Essentially, Euthyphro had asserted that he knew what was piety; so, Socrates is asking him to tell him what it is.

Euthyphro first answers: “I say that the pious is to do what I am doing now, to prosecute the wrongdoer … not to prosecute is impious.”

Socrates, however, responds, “… try to tell me more clearly … you did not teach me adequately when I asked you what the pious was, but you told me that what you are doing now … is pious.”

Socrates’ objection is that Euthyphro has told him one pious action, instead of what is piety in and of itself. 

This illuminates the theory of forms.  The form is that which is, in and of itself; it is like the genus of which there are many species, or instantiations of that thing.  Socrates wants to know the form of piety, that by which we know the many pious actions to all be pious. 

According to this theory, what we encounter in the world through sensory experience is not the truly real; instead, what is truly real is the eternal and unchanging Forms or Ideas, which can only be grasped intellectually. 

The best way to understand this is to think about circles: imagine the perfect circle; this circle does not exist in the natural world, instead there are round things in the world, but no perfect circle.  The perfect circle is the Form “Circle.”  When we measure this or that round thing, we compare its roundness (mentally) to the perfect one, the Form (which we have an idea of in our minds even though we have never encountered it in the everyday world).  Perfection, therefore, is what is ideal; all of the ideals are Forms.  Beauty is also a Form; it is something that you cannot point to in the world, but it exists as some sort of ideal measure against which we compare things.  Good is also considered a Form.  As Plato expresses it, things “participate” in the in the Forms, so a beautiful or good thing participates in the Form/Idea of Beauty or Goodness. 

This is the most basic understanding of the forms.  There are, however, many further attributes, which are very interesting. 

Forms / Ideas have four main characteristics: they are eternal, unchanging, unmoving, and indivisible.  And some of the forms are ranked higher than others, for example, the Form circularity participates in the form beautiful, but the form beautiful does not participate in circularity. 

Plato’s Phaedrus offers the elaboration of how we know the forms by a myth of the soul.  He explains, through Socrates, that our soul is like the composite figure of a charioteer pulled by two horses.  The divine soul has noble horses, but, our mortal soul has horses of mixed blood, one is noble and the other is ignoble.  Thus, we have a great deal of trouble controlling them.  When the soul is perfect, and winged, it will soar the heavens and the realm of Forms beyond the heavens.  But, with our less than perfect horses, we lose control of the horses, their wings will fail them, they lose their feathers and fall to earth to be embodied in a human form.  This will be the “hour of agony and extremest conflict of the soul.”  Why do some souls lose their feathers?  Because some are fed upon evil and foulness instead of beauty and goodness when the charioteer cannot control his horses.

So what is the realm above the heavens where souls can feed on beauty, wisdom, and goodness?  It is the realm of Forms.  It is the place of true knowledge.  The gods have access to this realm all the time, but other souls only get to see various glimpses of it.  In this realm the soul “… beholds justice, temperance, and knowledge absolute, not in the form of generation or of relation, which men call existence, but knowledge absolute in existence absolute; and beholding other existences in like manner, and feeding upon them, she [the soul] passes down into the interior of the heavens and returns home [to heaven] …”  This is the life of gods.  The forms are the absolute thing-in-itself, The Good, The Just, The Beautiful …  Everything that is good, just, or beautiful down here mimics the Forms above the heavens. 

So, the charioteers who cannot control their horses can only see a glimpse of the Forms before falling to earth.  The order in which our souls fall to earth creates a hierarchy of people based upon how much of the Forms their souls saw.  The souls who:

Saw the most: become embodied as philosopher, artist, musician, or lover.

Saw in 2nd degree: become righteous king, warrior, or lord.

Saw in 3rd degree: become politician, economist, trader.

Saw in 4th degree: become lover of gymnastics, physician.

Saw in 5th degree: become prophet, hierophant (interpreter of sacred mysteries).

Saw in 6th degree: become poets, imitators.

Saw in 7th degree: become artisan, husbandman.

Saw in 8th degree: become sophist (rhetoricians with questionable argumentative reasoning) or a demagogue (leader who obtains power by passionate appeals to prejudices of the people).

Saw in 9th degree: become tyrant.

Plato proposes that 10,000 years must elapse before soul can return to where she came from and that only the soul of the philosopher can return in 3,000 years.  After first life, souls receive judgment: some go to hell (“houses of correction under the earth”), some to heaven.  1,000 years later, the souls may choose what to be embodied as (except, those who have not seen the truth, without intelligence, cannot be human).

Another depiction of the Theory of Forms is the Allegory of the Cave, in his masterwork The Republic.  Here, we find all of reality divided into two realms: the sensible and the ideal.  The sensible realm is envisioned as a cave where people are chained.  Behind these people a fire throws shadows of things on a wall like a movie theatre projects images.  The prisoners can only see the shadows, so, to them, the shadows are their world, they are the truth.  Yet, we can understand, as readers, that these shadows are flawed representations of objects.  The shadows are a source of error, illusion, and ignorance.  So, in analogy, we experience in our world imperfect things like the prisoners in the cave experience the shadows.  In the dialogue, one prisoner is cut free and forced to go out of the cave.  He does not willingly go, because his experience tells him that the real is the wall of shadows.  But, he is forced out into the light; initially, it is blinding and painful (much like the process of learning anything new).  Eventually, however, his eyes adjust and he has the epiphany that his senses deceived him and he sees the truth, of which the shadows were mere representations.  After experiencing the truth, he returns to the cave to teach his fellow prisoners the truth (which, as you can imagine, was not popularly received). 

According to Plato, knowledge is true because it is knowledge of what is.  It is not enough to know the truth, you must strive to become the truth.  Here epistemology becomes ontology: to know is to be.  Ignorance is almost universal, but what allows us to come out of the cave and see the light of knowledge is the Forms.  Everyone, in his/her soul has the Forms which can be remembered.  Something like innate knowledge.  Remembering these Forms is what constitutes true knowledge.  To remember the Forms is to know the absolute truth and to become just and wise. 

In the Symposium Plato tells us that the way a person can go from imperfection (a prisoner in the cave) to perfection and true knowledge is by love.  Love is a longing for, a striving for the object of perfection.  Love seeks to possess the beautiful and to recreate in beauty.  He believes that humans only come truly alive when they love, or, more accurately, when they seek a beloved (which can be a person, an idea, or a thing).  Love is the force that brings all things together and makes them beautiful.  It is that by which we can become perfect.

Love begins as an experience of lacking something (keep in mind how the definition of wisdom was knowing what one does not know, i.e., what knowledge one lacks).  Love provokes thought and effort in the pursuit of that which is lacking.  The deeper the thought and effort, the greater the love.  Physical love, having sexual relations, and physical beauty all play a role in this force, but they are lower forms of love.  This is related as akin to a “ladder” of love, which one climbs up to truth.  A higher instantiation of love, for example, consists in sharing beautiful thoughts with a beautiful person.  The next rung is when the singular focus becomes a broader one, as a love of humanity.  Then one realizes that to love a person is not as great as having love for the higher systems that humanity is a part of: the moral, social laws.  Love now transcends people to love what is like the functioning of and participating in a city-state.  Then the person sees that there is something higher than the city-state, and develops a love for the whole realm of beauty, or the integrated beauty of everything that is.  From this level, the person is ready to make a leap to the love-beauty-truth that is beyond all mortal things.  These levels continue in an ascent to the Absolute Beauty or Goodness.  To progress to this Absolute Love is to enter “the mysteries,” which essentially is a will to immortality.  It is the desire to create immortal “children,” ideas, and these “children” grant the author immortality.  Love is that by which we know and realize the truth.  Love, like wisdom, is a process of seeking higher stages of being. 

Thus, we see how the theory of forms underlies Plato’s greater philosophy, from epistemological questions as to how we know something to social and ethical questions about how we strive for wisdom.