Plato, Platonic Idealism, and Neo-Platonism
Eternal truths exist in the realm of Ideas ("Idealism" = "Ideas") rather than in what we would call the natural, physical world. These eternal Truths can exist in your mind, but they can not be observed or perceived out in the physical world (think for a minute what "physical world" refers to: that world that operates on the laws of physics, or that world of objects with mass); that is to say, Truth does not exist in the world that we can see with our senses: sight, sound, etc. Plato calls this not true world the "sensible" world, meaning "the world perceived by the senses".
One way to understand this theory is to grasp that it is in most ways the opposite of scientific thinking, which is founded on the assumption that the natural, physical world is the "real" world and the only one that we can truly understand.
Here's a good way of understanding why Platonists believe this:
Every person you see and spend time with will some day die, but the concept or idea of “person” is unchanging or (relatively) eternal. Thus the physical, living people we see in the natural world are transitory but the concept -- the idea of -- "people" is eternal.
There is no single person who encapsulates the entire concept or idea person or “human being” – yet the idea “human being” describes all human beings: so the idea is more complete and thus “truer” and everlasting, compared to the people who live and die in the natural world.
This is true of everything else in the physical world: there is no one example of any thing (a tree, a piece of fruit) that perfectly represents all trees or fruit) and every physical thing is transitory: it changes. Meanwhile the concept of tree or fruit are eternally unchanging. (I'll make more sense of this, below, with circles and triangles, so hold tight and read on if you're confused.)
The Sensible and the Intelligible:
Our knowledge is divided between that which we gain through our senses, or sensible [or sensory] knowledge – what I can see and hear etc. – and that which we know intellectually, intelligible knowledge or the realm of ideas, that which I think. In Plato’s hierarchy, sensible/sensory knowledge is faulty and a mere shadow or representation of True knowledge.
"The Allegory of the Cave": what we see in the physical world, compared to true, intelligible knowledge, is like shadows compared to the "reality" outside the cave, but even this reality is a mere shadow of the sun itself.
Idealism and The Platonic Forms:
Pythagoras (c.580-490), Geometry and Idealism: This is another way of approaching Plato’s Idealism. Plato’s Idealism evolves out of Pythagorean philosophy (, which we now call “geometry” (actually, Pythagorean "philosophy" was more of a religion): a belief that mathematical formulas/proofs (which are essentially concepts, ideas) accurately describe the true or essential nature of all things.
And that these truths are eternal.
Here's a good way to understand this: consider a picture of a triangle or circle drawn in the sand or on the chalkboard, for example, in comparison to the geometric laws describing the inherent truths of triangles and circles. The concept π works well here, as would the Pythagorean principle (idea) or theorem :
If I draw a circle or triangle on the chalkboard to represent the concepts expressed in π or , you will see a sensible image: the picture, which is a "fallen" or imperfect representation of the intelligible of ideal circle or triangle: the perfect circle or triangle expressed by π or exists in your mind, in the realm of ideas (thus: it is "Idea-l"). We cannot produce in this world a picture that is as perfect, as accurate, as true, as "ideal" as that which we can represent with mathematical formulas. For Plato this is proof that the mathematical formulas -- and any kind of rational, logical thinking: philosophy -- is a better means of finding Truth than looking for it in the physical world.
The same goes for everything, including virtue, justice, love, beauty: there must be an ideal, unchanging, eternal Form that expresses all earthly, temporary representations -- there must be an eternal form of "love" that expresses and originates all love; there must be an archetypal form of "beauty" from which all beauty descends etc.
Thus, for every form found on earth – triangles, circles, humans, birds…virtue, love – there is a corresponding “true” form that exists in some higher plane. This higher plane is the realm of true ideas, and thus the term “Idealism”.
Innate Knowledge and the Soul:
At this point, Plato’s philosophy takes a definite turn toward mysticism or religion: since the truth of forms is not found in the natural world, how do we come to know them?
Well, we must be born with them, and they must precede our own existence (because they are eternal), so knowledge is innate and we in fact recollect or remember or uncover truths.
The method for doing so is through the type of philosophizing or contemplation practiced in the Socratic dialogues: attempting, largely through logical analysis (like math) to establish eternal truths. Think of the type of Socratic questioning or skepticism practiced by Socrates as an attempt to strip away false impressions and reveal the true Form of an idea.
The "Platonic Ideal" or "First Principle" or "The Good" or "The Form Of The Good":
Plato and his translators used many different terms to refer to this same/similar concept: all true ideas, or “the ideal forms” originate from The Ideal or The Good or The Form of The Good (represented by the sun in “The Allegory of The Cave”). This seems to be a single metaphysical agent from which all good and true Ideas emanate – including mathematical and factual truths and things like justice, virtue, honor etc.
Clearly at this point we have left the realm of philosophical reasoning and have entered mystical religion. It is this mystical aspect that will so greatly appeal to Hellenized Jews, and then Christians.
The Soul: Essence, Descent
The True essence of man is located in our souls, not our bodies -- remember that sensible knowledge (knowledge gained through the body's senses) is faulty. The soul descends from the "The Form of the Good" -- from eternal truth or "The First Principle" -- and is thus in a "fallen" state in this imperfect, shadow-world (represented by the cave).
The soul desires to return to the eternal Form Of The Good, and this is why we desire wisdom. Too much attention to sensible information (smell, touch, taste etc.) distracts us from the good: the pursuits of the soul, or gaining intelligible wisdom.
Examples Of Ideal Vs. Worldly Representations:
The Ideal: 1967 Shelby Cobra:
A Fallen, Worldly Form of The Ideal: 1967 Ford Shelby Mustang
A Mere Cave Puppet: 2014 Ford GT500 Mustang
A Shadow Of A Mere Cave Puppet: