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Plato
The Theory of Forms
In many of his dialogues, Plato mentions supra-sensible entities he calls "Forms" (or "Ideas"). Plato sometimes characterizes this participation in the Form as a kind of imaging, or approximation of the Form. The same may be said of the many things that are greater or smaller and the Forms of Great and Small, or the many tall things and the Form of Tall, or the many beautiful things and the Form of Beauty. When Plato writes about instances of Forms "approximating" Forms, it is easy to infer that, for Plato, Forms are exemplars. If so, Plato believes that The Form of Beauty is perfect beauty, the Form of Justice is perfect justice, and so forth.
Scholars disagree about the scope of what is often called "the theory of Forms," and question whether Plato began holding that there are only Forms for a small range of properties, such as tallness, equality, justice, beauty, and so on, and then widened the scope to include Forms corresponding to every term that can be applied to a multiplicity of instances. He may have come to believe that for any set of things that shares some property, there is a Form that gives unity to the set of things (and univocity to the term by which we refer to members of that set of things).
Immortality and Reincarnation
In the early transitional dialogue, the Meno, Plato has Socrates introduce the Orphic and Pythagorean idea that souls are immortal and existed before our births. All knowledge, he explains, is actually recollected from this prior existence. Several arguments for the immortality of the soul, and the idea that souls are reincarnated into different life forms, are also featured in Plato's Phaedo.
Platonic Love
In the Symposium, which is normally dated at the beginning of the middle period, and in the Phaedrus, which is dated at the end of the middle period or later yet, Plato introduces his theory of erôs (usually translated as "love"). Also in that dialogue, we are told of the "ladder of love," by which the lover can ascend to direct cognitive contact with (usually compared to a kind of vision of) Beauty Itself. In the Phaedrus, love is revealed to be the great "divine madness" through which the wings of the lover's soul may sprout, allowing the lover to take flight to all of the highest aspirations and achievements possible for humankind. In both of these dialogues, Plato clearly regards actual physical or sexual contact between lovers as degraded and wasteful forms of erotic expression. Because the true goal of erôs is real beauty and real beauty is the Form of Beauty, what Plato calls Beauty Itself, erôs finds its fulfillment only in Platonic philosophy. Unless it channels its power of love into "higher pursuits," which culminate in the knowledge of the Form of Beauty, erôs is doomed to frustration. For this reason, Plato thinks that most people sadly squander the real power of love by limiting themselves to the mere pleasures of physical beauty.
Plato's greatest and most enduring work was his lengthy dialogue, The Republic. This dialogue has often been regarded as Plato's blueprint for a future society of perfection. I do not accept this opinion. Instead, I would like to suggest that The Republic is not a blueprint for a future society, but rather, is a dialogue which discusses the education necessary to produce such a society.
The Republic discusses a number of topics including the nature of justice, statesmanship, ethics and the nature of politics. It is in The Republic that Plato suggests that democracy was little more than a "charming form of government." And this he is writing less than one hundred years after the brilliant age of Periclean democracy. After all, it was Athenian democracy that convicted Socrates. For Plato, the citizens are the least desirable participants in government. Instead, a philosopher-king or guardian should hold the reigns of power. An aristocracy if you will – an aristocracy of the very best.
Plato's Republic also embodies one of the clearest expressions of his theory of knowledge. In The Republic, Plato asks what is knowledge? what is illusion? what is reality? how do we know? what makes a thing, a thing? what can we know? These are epistemological questions – that is, they are questions about knowledge itself. He distinguishes between the reality presented to us by our senses – sight, touch, taste, sound and smell – and the essence or Form of that reality. In other words, reality is always changing – knowledge of reality is individual, it is particular, it is knowledge only to the individual knower, it is not universal.
The unphilosophical man – that is, all of us – is at the mercy of sense impressions and unfortunately, our sense impressions oftentimes fail us. Our senses deceive us. But because we trust our senses, we are like prisoners in a cave – we mistake shadows on a wall for reality. This is the central argument of Plato's ALLEGORY OF THE CAVE which appears in Book VII of The Republic.
Plato realized that the Athenian state, and along with it, Athenian direct democracy, had failed to realize its lofty ideals. Instead, the citizens sent Socrates to his death and direct democracy had failed. Plato wanted to rescue Athens from degeneration by reviving that sense of community that had at one time made the polis great. The only way to do this, Plato argued, was to give control over to the Philosopher-Kings, men who had philosophical knowledge, and to give little more than "noble lies" to everyone else. The problem as Plato saw it was that power and wisdom had traveled divergent paths -- his solution was to unite them in the guise of the Philosopher-King.
Aristotle
Plato's most famous student was ARISTOTLE(384-322 B.C.). His father was the personal physician to Philip of Macedon and Aristotle was, for a time at least, the personal tutor of Alexander the Great.
At the age of eighteen, Aristotle became the student at the Academy of Plato (who was then sixty years of age). Aristotle also started his own school, the Lyceum in 335 B.C. It Aristotle was a "polymath" – he knew a great deal about nearly everything. Very little of Aristotle's writings remain extant. But his students recorded nearly everything he discussed at the Lyceum. Regardless, Aristotle lectured on astronomy, physics, logic, aesthetics, music, drama, tragedy, poetry, zoology, ethics and politics. The one field in which he did not excel was mathematics.
As a scientist, Aristotle's epistemology is perhaps closer to our own. For Aristotle did not agree with Plato that there is an essence or Form or Absolute behind every object in the phenomenal world. Or, as one historian has put it: "The point is, that an elephant, when present, is noticed." In other words, whereas Plato suggested that man was born with knowledge, Aristotle argued that knowledge comes from experience. And there, in the space of just a few decades, we have the essence of those two philosophical traditions which have occupied the western intellectual tradition for the past 2500 years. Rationalism – knowledge is a priori (comes before experience) and Empiricism – knowledge is a posteriori (comes after experience).

Causality, The Four Causes

• The material cause is that from which a thing comes into existence as from its part, constituents, substratum or materials. This reduces the explanation of causes to the parts (factors, elements, constituents, ingredients) forming the whole (system, structure, compound, complex, composite, or combination), a relationship known as the part-whole causation. Simply put it is the influence of the material substances on the event. So imagine two dominos, the first of which is lighter. The first is knocked over into the second but does not have enough power to knock it over, this is Material cause.
• The formal cause tells us what a thing is, that any thing is determined by the definition, form, pattern, essence, whole, synthesis or archetype. It embraces the account of causes in terms of fundamental principles or general laws, as the whole (i.e., macrostructure) is the cause of its parts, a relationship known as the whole-part causation. Plainly put it is the influence of the form (essence) of the things on the event. So take the two dominos again except this time the second is shaped to prevent it from falling *eg. triangular.* this is formal cause.
• The efficient cause is that from which the change or the ending of the change first starts. It identifies 'what makes of what is made and what causes change of what is changed' and so suggests all sorts of agents, nonliving or living, acting as the sources of change or movement or rest. Representing the current understanding of causality as the relation of cause and effect, this covers the modern definitions of "cause" as either the agent or agency or particular events or states of affairs. More simply again that which immediately sets the thing in motion. So take the two dominos this time of equal weighting, the first is knocked over causing the second also to fall over. This is effectively efficient cause.
• The final cause is that for the sake of which a thing exists or is done, including both purposeful and instrumental actions and activities. The final cause or telos is the purpose or end that something is supposed to serve, or it is that from which and that to which the change is. This also covers modern ideas of mental causation involving such psychological causes as volition, need, motivation, or motives, rational, irrational, ethical, all that gives purpose to behavior.

Metaphysics

Aristotle defines metaphysics as "the knowledge of immaterial being," or of "being in the highest degree of abstraction." He refers to metaphysics as "first philosophy", as well as "the theologic science."

Substance, potentiality and actuality

Aristotle examines the concept of substance in his Metaphysics, Book VII and he concludes that a particular substance is a combination of both matter and form. As he proceeds to the book VIII, he concludes that the matter of the substance is the substratum or the stuff of which it is composed, e.g. the matter of the house are the bricks, stones, timbers etc., or whatever constitutes the potential house. While the form of the substance, is the actual house, namely 'covering for bodies and chattels' or any other differentia. The formula that gives the components is the account of the matter, and the formula that gives the differentia is the account of the form.
The coming to be is a change where nothing persists of which the resultant is a property. In that particular change he introduces the concept of potentiality (dynamis) and actuality (entelecheia) in association with the matter and the form.
Referring to potentiality, this is what a thing is capable of doing, or being acted upon, if it is not prevented by something else. For example, the seed of a plant in the soil is potentially (dynamei) plant, and if is not prevented by something, it will become a plant. Potentially beings can either 'act' (poiein) or 'be acted upon' (paschein), which can be either innate or learned. For example, the eyes possess the potentiality of sight (innate - being acted upon), while the capability of playing the flute can be possessed by learning (exercise - acting).
Actuality is the fulfillment of the end of the potentiality. Because the end (telos) is the principle of every change, and for the sake of the end exists potentiality, therefore actuality is the end. Referring then to our previous example, we could say that actuality is when the seed of the plant becomes a plant.
In conclusion, the matter of the house is its potentiality and the form is its actuality. The formal cause(aitia) then of that change from potential to actual house, is the reason (logos) of the house builder and the final causeis the end, namely the house itself. Then Aristotle proceeds and concludes that the actuality is prior to potentiality in formula, in time and in substantiality.
With this definitionof the particular substance (i.e., matter and form), Aristotle tries to solve the problem of the unity of the beings, e.g., what is that makes the man one? Since, according to Plato there are two Ideas: animal and biped, how then is man a unity? However, according to Aristotle, the potential being (matter) and the actual one (form) are one and the same thing.

Hellenistic Philosophy
Both Epicureanism and Stoicism sought to give ataraxia , or peace of mind. For Epicurus the aim of life was pleasure; the highest pleasure was absence of pain; pleasure of the mind was preferable to that of the body. The soul dies with the body, so we must not fear death or afterlife; the gods exist but do not concern themselves with humanity or natural phenomena (all of which can be explained scientifically); we should avoid public life and emotional commitments in order to escape the pains likely to be caused by them. The physical world was explained by the atomic theory adapted from Democritus.
Stoicism. Stoic ideas appear in the greatest work of Roman literature, Vergil's Aeneid , and later the philosophy was adopted by Seneca (c. 1-65 A.D.), Lucan (39-65; poet and associate of the Emperor Nero), Epictetus (c. 55-135; see passages from the Enchiridion ), and the Emperor Marcus Aurelius (born 121, Emperor 161-180; author of the Meditations ). Stoicism is perhaps the most significant philosophical school in the Roman Empire, and much of our contemporary views and popular mythologies about Romans are derived from Stoic principles.
  Sceptisism. This is actually not a philosophical school, but one could generally group a number of Hellenistic schools under this rubric, including the Second Academy (Hellenistic Platonists), the Second Sophistic, the Cynics, the Skeptics, and so on, and, for the most part, the Stoics as well. What is important for our purposes is that all these schools to some degree or another espoused the idea that human beings cannot arrive at certain truth about anything (not all denied certainty was impossible, only that human beings could never be certain). Basically, life became this great guessing game: the lot of humanity is to be cast into a twilight world in which all that we know and think is either false or occupies some middle position between the false and the true (which was called the "probable," "readily believable," or the "verisimilar"). This comes to dominate thought in late antiquity; the first philosophical attacks Christianity levels against the thought of antiquity are refutations of sceptical principles. Of all the philosophies of antiquity, this is perhaps the most familiar to you: the skeptic principle of doubting everything became, in the modern era, the fundamental basis of the scientific method.