Metaphysics Notes

Chapter I

Section 1

Philosophy in the West began, for the most part, in Ancient Greece. In the period of the Fifth Century BCE, particularly in Athens, an incredible number of remarkable thinkers, artists, politicians, etc., participated in the life of the city-state. Their accomplishments have guided and inspired the entire development of Western culture. It’s pretty obvious then, that we ought to know something of their philosopher’s ideas. The most famous are, of course, Socrates, Plato and Aristotle. Prior to these are the so-called Pre-Socratics. The Pre-Socratic philosophers include: the Ionians who attempted to formulate materialist explanations of reality, the Eleatics, who proposed various intellectual conundrums about the nature of being and thought and the Sophists, who taught rhetoric and were an important social force (as their contemporary intellectual descendants are today). Socrates, Plato and Aristotle represent almost a school of thought. Socrates taught Plato, though he did not write down his teachings. After he was executed, Plato did write down what Socrates had taught, in the forms of dialogues, as well as much more which Plato probably thought he might have taught had he lived. Aristotle studied in Plato’s school, the Academy, until after many years he left to form his own. One might characterize all of their philosophizing as the attempt to solve a number of problems left to them by their predecessors in a systematic way.

Western philosophy is traditionally held to have begun with Thales. Thales is said to have taught that water is the source of all things. What this means is unclear. Perhaps he was saying that the essential element out of which things arise is water. He may have thought this because of the water, or sap or blood present in living things and their need for water. It is thought that Thales would have believed this primordial water was unbounded and probably alive, which would account for its ceaseless movement in rivers and oceans.

What's important about Thales' theory is that it seems to assume that there is "a source of all" and it identifies this source as a perceptible element. The assumption here is actually more interesting and important than the theory. It points to a direction of investigation, namely the search for the source of all things.

Thales had a student named Anaximander. Anaximander is important because he criticizes and moves beyond his teacher's theory. Anaximander believed that the source of all was not unbounded water but simply the "Unbounded." By this he apparently meant something that was not only not bound in terms of its extent but neither was it bounded in terms of being one of the perceptible elements like water. The view was common, until fairly recently with the advent of chemistry, that the basic elements were earth, air, fire and water. Thales had simply chosen one of them as the primordial source of the others. This seems to be the reason that Anaximander disagreed. Presumably, Anaximander realized that if there were unbounded water, fire, another equally perceptible element could not be. The reason for this being that they are opposed: water puts out fire. Anaximander's solution was to make the Unbounded something beyond or before the other perceptible elements. This way it would not be opposed to any of them as they are to each other. The perceptible elements would then be precipitated out of the Unbounded much as rain is precipitated out of clouds.

This proposal is remarkable because a) it is a rational criticism of a previous philosophical theory, the first we know of in the Western tradition and b) it proposes the existence of a source of perceptible things which is not itself perceptible. This is something that is often called a "theoretical entity." An entity is a thing (from the Latin, entitas, and a theoretical entity is one that is called for by a an explanatory theory. It is of course a very important problem in philosophy and in science whether or not one should propose the existence of theoretical entities. When a proposed theoretical entity later on becomes perceptible by the invention of some new instrument like a telescope or microscope, the proposal has been successful. If it does not, or it seems that it perhaps may never be observed, it is another question. However, Anaximander seems to deserve credit for employing a new form of explanation.

Another interesting point about Anaximander's theory is that he believes that the opposed elements, once they have been precipitated out of the undifferentiated Unbounded, are at war with one another. This is due to their inherent opposition. The qualities of the elements, that they are Hot, Cold, Wet and Dry, insures that they are in a state of conflict. What is it, one might ask, that keeps this conflict from getting out of control? According to Anaximander, it is Time that imposes a cosmic harmony. When one of the elements begins to hold to much sway, as in winter or summer, drought or flood, Time steps in to restore harmony. This picturesque notion follows the pattern of Greek tragedies of Aeschylus, where Hubris or Pride leads to the undoing of the tragic hero, through a necessary retribution. It is important philosophically because what it asserts is the reality of a cosmic principle of harmony or justice. A qualitative analysis of things, not only in terms of their being hot or cold but also in terms of their being just or unjust, is objectively grounded in the order of the universe.

Anaximander had a student himself, named Anaximenes. His student rejected his theory as well. At this point, one might begin to think, "Now wait a minute, where is all this going?" Well, the answer is, this is how it will continue. The history of philosophy is the history of one long argument about many different topics and it proceeds precisely in this manner. If one is to learn to appreciate philosophy, one of the first things that they have to get used to is the ongoing character of its conversation. Philosophy, unlike many other disciplines, cannot be conceived of as collection of facts and laws. Philosophy is the ongoing argument. Even when one comes to a conclusion that they are convinced of, the way they have reached the conclusion and the reason they continue to hold to the conclusion, are the arguments. Someone comes to a conclusion through a process of argumentation, they then remain with that conclusion precisely because they believe that that conclusion can withstand any and all criticisms. Thus to know any philosophy at all is to know the arguments. In a sense, in philosophy, it is more critical to know what the problems are, than to know what the answers are.

Anaximenes theory is bit of a surprise. He seems to revert to the kind of theory that Thales had offered even though his own teacher had seemingly refuted it. Anaximenes holds that air is the source of all things. He accounts for the possibility of one of the opposed, perceptible elements being the source of the others by a remarkable and ultimately very important theoretical move. Anaximenes suggests that air becomes the other elements through rarefaction and condensation. In other words, when air becomes thicker, as it appears to on a cloudy day, it turns into water (or rain). Water then can become even thicker, like a rock, when it turns into ice. This then is the genesis of earth. Fire, is a more rarified version of air. If one goes to a mountain top the air is thin, and when one looks up the fire of the sun is apparent. Regardless of the primitive nature of this theory, it is important theoretically because it suggests that a quantifiable, mechanical process may be responsible for the perceptible elements and qualities that we are aware of in ordinary experience. Quantity, then, is more basic than quality. While this suggestion is at the heart of modern science, there remains a perennial question of which, quality or quantity, if either, is more basic.

These three philosophers are known, with others as the "Pre-Socratics" because they come before that famous thinker. Among the others, which deserve mention, are Pythagorus, Democritus, Heraclitus, and the Sophists. Pythagorus (of the Pythagorean theorem) thought that all things were numbers. Whatever this means, it certainly seems to predate the idea that mathematical relationships are at the heart of the things around us, an idea exploited by modern, mathematical physics. Another idea central to contemporary physics is that larger observable bodies are composed of smaller ones called atoms. This was the theory of Democritus. He believed that these tiny indestructible particles were eternal, remaining throughout the coming and going of the larger things that they made up. Heraclitus is generally associated with the idea that there is nothing that stays the same, "all is in flux." He supposedly said that "you cannot step in the same river twice" meaning that at each moment every thing changes just as the water of a river will have moved on between the first and second steps. The Sophists is a name for a kind of cultural movement in Ancient Greece in which the ability to use rhetoric or persuasive speech was taken to be of the utmost importance. Since Athens was at one time a popular democracy, unlike a representative republic like the United States, each citizen voted on all important matters. They needed to be able to persuade large crowds of the fellow citizens, lest a popular vote go dangerously against their interests. Although contemporary political systems like the US are not like this, we nevertheless employ lawyers and lobbyists to make persuasive speeches and arguments on our behalf. The problem of course with this practice is that it is primarily concern with self-interest not "the Truth." Some of the Sophists evidently believed that this was not a problem because there was no such thing as the truth, only the opinions of some society or individual. One of them, Protagorus, is supposed to have said, "man is the measure of all things, of the things that are, that they are, of the things that are not, that they are not." Presumably what this means is that things are as people perceive to be, or as we might say today, "The perception is the reality." In addition to attempting to deal with what the other philosophers had held, Socrates, Plato and Aristotle were very concerned to deal with this last notion. This is what we today call "relativism."
Section 2

There is one more Pre-Socratic philosopher to mention, who I take to be far more central to our concerns and the whole history of Western metaphysics. His name is Parmenides. Parmenides wrote a poem, a good portion of which survived, called The Way of Truth. In it he proposed a remarkable, even unbelievable theory. The reason that this unbelievable theory is so important is that his argument for it seems to be unimpeachable. Though he presents this in terms of a goddess offering him a revelation, the argument is short and seemingly logical. What Parmenides sets out to do is to try, as the other Pre-Socratics had, to understand something about the nature of reality. Where his predecessors had largely concerned themselves more with the constitution of the physical universe, Parmenides wanted to understand reality. Consequently, he must have asked himself, "What is reality?" The answer has to be, what is, what exists is reality. But what is that? In probably the most abstract question ever asked, and ever can be asked, Parmenides is asking, what is "is" what is it "to be"? Here is his answer:

What is, is.
What is not, is not.
What is cannot be what is not
Therefore, what is cannot not be
Therefore, what is must be
Therefore, what is, is eternal
Therefore what is, is unchanging
Therefore, what is, is one.

The consequence of all this is that what exists, are not the things around us because they are many, different and changing. All that really exists for Parmenides is what he calls “the One.” How does this follow from this rather brief and highly abstract argument?

First let’s take the denial of the reality of the things around us which it is commonsensical to believe in. These things, whether they be living things or inanimate objects or artificial objects, all come into being at some point and then pass away. Living things are born, mature and then die. Inanimate things eventually are worn down and decay, even if it takes centuries to do so. Why should this mean they are not real? Well for Parmenides the problem is that coming into being and perishing both imply an impossible passage from either non-being to being or being to non-being. Just as anyone might say that it is impossible to get something from nothing, Parmenides is convinced that it is not possible for what is to come from what is not. What is not is nothing. However, the response to this seems obvious. The living thing that is conceived is not from nothing but from some previously existing things, perhaps sperm and egg. The problem from Parmenides’ perspective, though, is that we must say that the sperm and the egg are or exist. When they change in conception, then they are not. Change is a passage from being X to be Y. This means that at one time Y is not, then later Y is. Y has gone from non-being to being. Or, we can think of change as implying that X becomes non-X. If X is not then it is nothing and, then later X is. Similarly, if we are talking about X passing away, then we are saying that X is, then it is not. But what Parmenides asked, could make that which is become that which is not. That which is, just is. And that which is not is nothing. The whole notion of change, according to Parmenides, is unintelligible. Parmenides follower, Zeno, articulated similar paradoxes about motion.

Parmenides is also questioning the intelligibility of plurality, the idea of there being many things. Nothing could seem to be more obvious. Yet, when we think about being abstractly, it does not seem that being can be divided. What could divide being? Think about being as a pie. If we assert that there are many things then we are saying that the pie of being is cut into many slices. How, though, did we cut the pie? We needed a knife. The knife was able to cut the pie because it is hard and the pie is soft. The knife has a characteristic which is opposed to the characteristic of the pie. What, then, is opposed characteristic of the knife which can cut the pie of being? Obviously, non-being is opposed to being. The cuts in the pie have to be made by a non-existing knife which then leaves non-existing spaces between the slices. Not only does a nonexistent knofe not seem to be up to the job but if the divisions between the slices are nonexistent, then the pie is one. There is a similar problem with the idea of empty space or an absolute vacuum. Is it something or is it nothing?

It is hard for us to understand Parmenides point if we try to remain within commonsense. But this is precisely what Parmenides is questioning, the intelligibility of the commonsense understanding of reality. It is hard to know what to do with this insight/puzzle, however. One way of looking at it would be to think of Parmenides as having achieved a rational insight into a kind of mystical, religious view. Having grasped the argument, one is then enlightened about the unreal character of passing things and learns to accept that only the One (God?) is ultimately real. But what does one then do? Pray to the One, contemplate the One? I’m not sure. The other way to look at this is to see it as presenting a fundamental problem for understanding. What Parmenides has shown us is that when we say that something is, that something must have identity and stability. Whatever I say is, cannot already have changed into something else. If it has then what I said existed no longer exists. It is already different from what it was. And if it does change it is different form itself. But nothing can be different from itself. Thus to think of reality must mean to think of something that is one. However, Heraclitus had said, “All is in flux.” So how are we to make sense of the idea, which all of us accept as common sense, that the many, different and changing things around us are real? This is a question that Plato and Aristotle attempt to answer.
Section 3

Plato, whose theories we’ll deal with first, was a student of Socrates. Socrates was a remarkable and eccentric figure who went about Athens entering philosophical discussions with his fellow citizens. He often questioned well-known people about their opinions, or what they thought was more than opinion, their knowledge about the good, the just and the beautiful. Often the outcome of these discussions was that it was revealed that Socrates’ interlocutors did not know what they thought they knew. This did not please them, and as they were often powerful, and Athens had endured a civil war, Socrates was accused of impiety, tried, convicted and executed. His student Plato sought to revenge him in a sense by writing down what Socrates had not. He wrote dialogues which show Socrates engaged in these conversations. Some of these, particularly about his trial, are probably fairly accurate as they would have been written and published shortly thereafter. The later ones, however, employ Socrates merely as a character and probably never took place at all.

One of Plato’s most famous dialogues, probably from the middle period of his writing, is the justly renowned, Republic. In it, Plato lays out a theory of what a just society would look like. Along the way, he sets out a theory of knowledge and reality upon which his ethics and political theory can be based. Since we are mostly concerned with Parmenides’ problem, I will concentrate on Plato’s answer to that in this and other dialogues.

Remember that for Parmenides, the only thing that can be conceived to exist is something that just is. The thing that is said to exist must not be conceived to be capable of change, difference or plurality. There is, according to this view, nothing between the absolute unchanging reality of the One and absolute nothingness. On this view, if taken literally, neither we nor Parmenides exist! One wonders then, who is he talking too?

Plato takes Parmenides problem seriously, so he must devise a way in which he can incorporate his insight into a less paradoxical view. Like Parmenides, Plato must admit that:

Is = Is

And also that:

Is Not = Is Not

One would think that he would also be forced to admit that:

Is  Is Not
Or, What is in no way is not

This, last however is not what Plato does. Instead, he claims that there is a way in which what is can be what is not. This is the world of change and plurality, the material world around us. It can have this paradoxical character because it is not fully real. The things in this world are not really real. They exist in a kind of twilight zone. Consequently, instead of Parmenides monism (the belief that there is only one thing), Plato offers a more elaborate theory. There are seemingly three levels:

Is
Is & Is Not
Is Not

Corresponding to the levels are levels of knowledge:

Knowledge  Is
Opinion  Is & Is Not
Ignorance  Is Not

We can only know what is. We certainly cannot know what is not for it is nothing. However, we can have opinion regarding the many different changing things around us. This is less than knowledge but more than ignorance. Plato further calls these "powers" like the power of sight or hearing. Sight and hearing are distinguished form one another by their objects; sights sees colors and shapes, hearing hears sounds. Analogously, knowledge knows what is knowable or intelligible and opinion opines about that which we can have opinions but not knowledge about.

This is a clever solution to the problem but one which immediately raises a number of questions. First, why can we not know what is material and changing and second what are the true objects of knowledge? First, we cannot know the things in the material world precisely because they are in a constant state of change. Even if the change is imperceptible, all that means is that we do not know about it. So we think they are not changing but they are. We do not know them. The true objects of knowledge must then be something that does not change. But what is there that does not change?
Section 4

Plato’s answer to this question is complicated. However, a particular episode described in another dialogue, Meno, gives us a good introduction. At one point in the dialogue, Socrates calls an uneducated servant boy into the discussion. He begins asking him questions about performing a geometrical demonstration. Since the boy is uneducated, he does not know the answers to the questions offhand. However, by drawing in the sand and asking the boy questions, Socrates is able to elicit from him a geometrical demonstration/construction. Socrates draws the surprising conclusion from this that the boy always knew the answer and merely had to remember it! Why does Socrates say this? The issue here is not whether or not Socrates’ leading questions were really a form of teaching. It has to do with the nature of mathematical and geometrical knowledge, In the case of a geometrical figure, in this case a square, what Socrates does not point out is that neither he nor the boy have ever seen an actual square! An actual square would have to have perfectly straight lines, are absolutely equal, with absolutely equal angles. This is certainly not the case with the drawings Socrates is employing nor with any others, not matter how good, made since. Nor can lines and points, in the geometrical sense be the same as any drawings of them. Lines have no width and points have no extension but our drawings of them have to. Yet despite the fact that the boy and all of us have not ever seen a square we are able to understand its properties. Moreover, those properties are not subject to change. Nor are they different in one place from what they are somewhere else. Thus it looks like in the case of geometry we possess unchanging, universal and immaterial truths! The same sorts of arguments apply to mathematics. Although we can seemingly learn to count by practicing with apples and oranges, our capacity to understand numbers soon outstrips this. We understand numbers which we have never counted. Moreover, we have never seen a number. We have seen so many objects but never the number. We have seen the numeral like "5" or "V" which stands for the number but not the number itself. How is it that we can understand them?

What is the real meaning of Socrates' so-called doctrine of recollection that we remember rather than learn the truth. We cannot learn the truth because that would mean that our understanding of it would somehow depend upon our experience. Rather, the truth must exist in a timeless form and we are capable of recognizing it. Recognize is a good word for it because the recognition of the truth is a kind of re-cognizing. When we have the experience of saying, "aha! That's the answer" that's an example of our capacity to recognize a truth which transcends us and our experiences.

When we seen that the drawings and numerals that we employ in doing math or geometry are not the realities with which we are concerned, we are then forced to consider what those realities are and what the relation is between the realities and the drawings. For Plato, the drawings are images and he develops a fascinating theory about the relationship of image to reality in his famous Allegory of the Cave from the Republic. In the allegory of the Cave…

In an allegory, things stand for something, so what do these things stand for? The shadows on the wall stand for sense perception. We are not literally chained in a cave but we are chained from birth to our bodies. Our bodies constantly bombard us with sensation and that is our first acquaintance with reality. And just like the prisoners in the cave, we learn to give names to the things that we see from those around us. But where do they learn these words? Well, the obvious answer is from their parents, etc. but is there no other source? The other source would be books, from the dictionary to novels to newspapers to Sacred texts like the Bible, the Koran or some other foundational book for a culture. The puppets behind the parapet stand for these books. Like the puppets, books are artificial objects that are representations of how things are. These books are not perceived by all, only by those who have gone so far as to turn around and examine them. That is, by the educated. Nevertheless, the cast long shadows over everyone, governing silently the perceptions of reality which the average person has. The philosopher, however, not only reads these books but also seeks to evaluate them in terms of the truth of their representation of reality. In order to this, the philosopher must further up the cave passage and then out in order to perceive the real things that the images are based on. The last thing of all that can be seen is the sun or the Good, that is, the principle of intelligibility or the power through which everything else becomes understandable. Why it is the Good that makes all else intelligible will be come clear in a moment.

But now we must explain what the things are outside the cave. In the story they are just real things, people and animals, which can been depicted and shadowed in the cave. In terms of the allegory, they represent something very different from the ordinary physical objects that we believe in. In fact, they represent what Plato calls the Forms. The Forms are like the square we think of when we look at an imperfect drawing, or the number, which we think of when we see a numeral. These ideas (in Greek, Eidos) do not exist in the physical world but they do exist. In fact, for Plato they are more real than the things in the physical world. The things in the physical world are all imperfect and changing. Plato agrees with Parmenides that being must just be. Things in the physical world never just are. So Plato asserts the existence of non-physical objects which just are. Not only are they numbers and geometrical ideas but also the perfect Form of the Human and the Dog and everything else. What we see with our eyes and perceive with our other senses is a changing and imperfect reflection of the ideal Form.

This theory probably strikes most people as outlandish. However, it would explain the universal and unchanging character of mathematical and geometrical truths. If we were some how able to access a domain of unchanging mathematical ideas, then it would make sense of the fact that we all understand mathematics in the same way. The idea seems particularly peculiar, however, when we are talking about dogs and cats. It would seem strange that there should be an unchanging Cat somewhere. It would explain, however, why we can call many different and changing cats by one name and understand that they are all cats. The point must be kept in mind that the real purpose of this theory, for Socrates particularly, was to refute the position of the Sophists. Remember that the Sophists were the teachers of rhetoric who held that there was no objective truth, only the opinions of various people. Since all there is, is opinion, it is very important to be able to mold opinion through persuasive speech. Socrates is horrified at the idea that the only guide for the life of the polis or the city is the self-interested opinions of the most persuasive speakers. He believes that there is a higher standard. That standard is the Form of the Good (and the Just and the Beautiful). When we call something “good,” or “just” or “beautiful” it cannot only be because it appears that way to us, or that is how people happen to think of it, or that is how some Sacred text has it. It must be because there is something that simply is good, just or beautiful. These are the Forms of the Good, the Just and the Beautiful.

We need these Forms not only as a guide to political life and as a refutation of the relativism of the Sophists but also because without them we have no complete explanation of things. This last argument, that a complete explanation requires a reference to the Form of the Good is found in the dialogue Phaedo.
Section 5

In the Phaedo, a dialogue that takes place in Socrates' prison cell on the last day of his life, is primarily about the immortality of the soul. Socrates' argument that he has nothing to fear from death, given that the soul is immortal, rests on a complete investigation of the causes of coming into being and passing away. He recounts his early interest in the speculations of the Pre-Socratics and how they came to be unacceptable to him.

As is Plato’s custom occasionally, Socrates is here depicted as making funny and paradoxical remarks to make his point. In the dialogue, he says that he studied the writings of his predecessors but found that they only made him more confused and that he unlearnt what he knew before. Before, he thought he knew that a man grew in size by adding substance to himself through eating and that seven might become nine or bigger by the addition of two or that a man might be taller than another by a head. Now he says he understands none of this. Why? Because each of these would be a case of something large becoming larger by the addition of what was smaller. And this means that the cause of largeness is smallness!

Now before you even try to understand this, it is best that I proceed with the rest of the discussion and come back to this. Socrates proceeds to tell another story. In it he hears that a philosophers named Anaxagorous has been quoted as saying, “Mind rules.” Socrates says he was very excited by this news because it meant to him that the philosopher was going to explain how things were governed by some kind of cosmic mind and this kind of explanation appealed to him. So Socrates rushed out and bought Anaxagorus’ books only to be deeply disappointed. Instead of talking about the Mind that rules, he talks like the other Pre-Socratics about earth, air, fire and water. What is wrong with that? Well, Socrates says, suppose someone were to ask him now, sitting in prison with his friends who have offered to help him escape, “Why are you sitting here?” The Pre-Socratic answer would be that he has bones and sinews and they make it possible for him to sit. Further, he has a mouth and he can make sounds with the air and that causes the conversation, etc. But this is all wrong! The very same bones and sinews could get up and walk away. The reason the bones and sinews are where they are is because Socrates believes that it is right that he accepts the penalty of death that the Athenian court has imposed upon him. If his concept of what was right and good and just told him that he should escape, then the bones and sinews would do as they were told. As Socrates says, “to call these things causes is to confuse the true cause and that without the cause could not be a cause.” This is the distinction between necessary and sufficient causes. A necessary cause is something without which the effect cannot take place, like oxygen is necessary in order for combustion to take place. However, oxygen is not a sufficient cause, the sufficient cause is something which of itself is sufficient or enough to make the effect take place. Bones and sinews are necessary to do anything but they are not a sufficient explanation of why someone does what they do. Given that the necessary causes, like bones and sinews and a body in good health are in place, what is necessary to explain what people do? Their conception of the Good is what explains what they do! That conception may be mistaken, it may be simply inherited from their parents or their culture, or even some bizarre cult but it will determine what they do. People will seek what they believe to be good. That is why Socrates believes it is so important that there be a way to be right about what is good.

On hearing this argument, one might be tempted to say that the only thing that Socrates has proven is that human beings act in accordance with some idea of the Good, so no explanation of their behavior, which ignores this factor, will be adequate. However, that does not go for the rest of the universe. While human beings may believe in some idea of the good maybe the Sophists are still right. That’s only their opinion as to what is good. The Good is not “out there” part of the nature of reality or the structure of the universe.

It is Socrates’ answer to this that is crucial. Again, Socrates says some funny and paradoxical things to make his point. He asks us to imagine three men, Phaedo, Simmias, Socrates arranged in a line from the tallest to the shortest. What would we say about these men? What we would say is important because earlier Socrates says that his confusion has lead him to try to investigate things not by looking right at them but by looking at images or representations of them. This is a kind of reversal, it seems, of the cave allegory where we are encouraged to look past the images toward the realities. But again Socrates is being ironical. He wants us to see that he thinks looking right at physical things is not looking at the reality. In fact, the words and statements we use to represent things are closer to the reality. So what would we say about the three men? Would we say that Simmias, who is in the middle, is both short and tall? Is Simmias short because he is Simmias or is he short because of Phaedo’s tallness? Is Phaedo taller than Simmias because he is Phaedo or because of Simmias’ shortness? Are shortness and tallness the same or are they opposites? Does Simmias become tall when Socrates approaches but then shorter when Phaedo approaches?

The point of these clever questions is the following. Tallness and shortness are Forms and as such they are absolutely opposed. If you are thinking of tallness and shortness you cannot think of them being the same or even in the same place. However, when you see the three men, you can see how relative to one another they can be both short and tall. Finally, their relative shortness or tallness has almost nothing to do with what makes them who they are. If Socrates were to move to a country where he was the tallest man, he would not cease to be Socrates.

The point of all this is that characteristics or properties exist at three levels:

Absolute Properties = the Forms Is
Essential Properties = the properties which make something what it is Is
Relative Properties = the perceived properties of the material world Is & Is Not Is Not As can be seen from the right side of the above, this division of reality is a somewhat more complex depiction of the levels of reality within the material realm. Socrates seems to be allowing that a kind of knowledge of the physical world might be possible through the knowledge of the essential properties of things. The examples of essential properties that he gives are:

Threeness – Oddness
Fire – Heat
Snow - Cold
In all of these cases, if one were to change the thing or property on one side, they would necessarily change the thing or property on the other. If we make three into four by adding, we make it even. If we try to cool fire or warm snow, they cease to exist. Consequently, these properties are essential to these things. This, by the way, is the argument for the immortality of the soul, which is the topic of the dialogue. The soul is considered to be the principle of life, so while the body may die, the soul that is its principle of life may not. Whether or not we think that argument works, the larger point is this: To really understand things we must understand their Form. Moreover, the Forms are related to each other, in that some are essentially connected to or opposed to others. Finally, all the Forms are attached to the Form of the Good. The Form of the Good is essential to all other Forms. This the case because to knowing what some type of thing is, is inseparable from knowing what a good example of that type would be or what that type of thing is good for. It is not possible to think of a house without thinking of the properties that are essential to it, like providing shelter and comfort. If it does not provide those things, then it is not really a house!

So, aside from proving the immortality of the soul, Socrates’ main point here is that we must incorporate a conception of the Good into any complete understanding of not just human action but also everything else. The true causes of things are the intelligible Forms not the material out of which they are made. Knowing that eating adds bulk does not tell you what bulk is; that is a concept or Form grasped by the mind. Knowing what two is, is not just knowing that 4 – 2 = 2. So Socrates’ “confusion” which we began with is really his criticism of any theory or explanation which seeks to fully explain the nature of reality only in terms of the material out of which something is made and/or the processes by which it comes about. (or what we call “physical science”).

There is certainly a great deal more that could be said about Plato's theory. However, these are some of the most important points to remember: Plato agreed with Parmenides that identity and stability were essential characteristics of being - to be is to be one and the same. However, he wanted to admit that the material world had some kind of reality so he said things in it were imperfect reflections of other, purely intellectuals Forms. Certain Forms were essentially related to each other, so the more we knew about these connections between Forms, the more we would know. All the Forms were essentially connected to the Good. To really understand something, according to Plato, you don't think about what it is made of or the processes by which it comes about (chairs, for instance, will still be chairs even if they are made of different materials and through different manufacturing processes), you think about what it is in a purely abstract way. This abstract thinking will lead you to the Form of the particular thing, and the Forms essentially related to that Form, the most important of which is the Good.
Section 6

Plato's student Aristotle, as happens with philosophers, disagreed with his teacher. Aristotle theory is truly systematic; he articulates an ethics, a political philosophy, the theory of logic, biological treatises, etc., etc.. We are concerned here with his metaphysics. The best way to introduce Aristotle's thought is to simply say that he brings Plato's Forms down to earth. Aristotle agrees with Plato that the object of knowledge is an unchanging form. However, the unchanging form for Aristotle is the organizing principle of the physical thing. The form for Aristotle (notice that it is not capitalized when we are speaking of Aristotle's concept of form) is a pattern of change. The development of a living thing, like the growth of an oak tree from an acorn, is a stable, identifiable pattern within the physical world. Aristotle believes there are forms but they are in this world, the only one that exists. Consequently, unlike Plato he believes that we learn through experience. After repeated experience with particular things of a certain type, we achieve an understanding of what the form, essence or nature of that kind of thing is. Aristotle also agrees with Plato that understanding something is connected to our concept of the Good. However, Aristotle does not believe there are separate Forms outside of the physical world and so there is no separate Form of the Good. Aristotle believes that the nature of each thing is aimed at some particular goal. Artificial things are made by us for particular purposes; chairs to sit in, plates to eat off. Living things and their parts are also aimed at some goal; the acorn is aimed intrinsically at becoming an oak tree, the puppy a full grown dog. The goal or end of a thing (its telos in Greek) is essential to it and part of how we understand what it is. This is what is now called a "teleological" theory and it is easy to see how central it is to biology.

For Aristotle, the Forms and the Good become the "formal cause" and the "final cause"(because of the end). He also admits the importance of a thing's material make-up and the processes by which something comes about which he calls the "material cause" and the "efficient cause." So for Aristotle, the common sense view that individual things in the material world are real is correct. He acknowledges that to understand them we need something stable and identifiable; this is their formal cause or aspect, a pattern of development or change for natural things and their final cause or their purpose for man-made things. The individual things Aristotle calls "substances" and these are what is primarily real. What is more changeable and not essential to the individual things he calls "accidents." A house or a cow is a substance. Whether either is white or black is "accidental" in that they could be either and still be what they are. So Aristotle explains how the physical world around us can be intelligible, despite all the change and difference in it, because he perceives patterns within the change. Identifying these patterns is how we achieve knowledge. For Aristotle, to be is to be a substance. Substance are one and the same throughout accidental changes. The problem of Parmenides is solved!

Part of the way Aristotle explains his view is by referring to how we talk about things. When we speak we usually say that something has some kind of characteristic or property; for instance, "That cow is black" or "The house is white." What is interesting philosophically about this point is that we don't say simply "white" or "black" unless we were identifying some colored objects. This is because whiteness and blackness are qualities or properties that something can have but they do not exist on their own. This is the difference between substances and properties; substances have a degree of independence whereas the properties depend for their existence on the substances. The properties change while the substance remains one and the same.

What is responsible for the existence of substances? Is it the material out of which they are made? Unlike Plato, this is important for Aristotle. However, like Plato, Aristotle thinks that the formal aspect of the thing is more important because it is closer to what the thing is, it's definition. So like Plato, Aristotle thinks that the explanations of the Pre-Socratic materialists are inadequate. Ultimately, if you say that what is, is earth, air, fire or water (or atoms and molecules for us), then you are saying that that element is substance and being a chair or an animal is merely an accidental arrangement of this substance. For Aristotle, this kind of explanation does not really capture the way things are. While things like animals and chairs may be composed of flesh and blood or wood, they are not just that. If I point at something and say, "What is it?" your answer most likely is not going to be in terms of the material out of which it is made. Pointing at an animal you will say "That's a dog" not "That's flesh and blood."
Section 7

What about Plato's point that there are no perfectly straight lines in the physical world? How do we know squares and lines even though we never have seen them? According to Aristotle, we are capable of thinking of things in different ways. For instance, although we can only see imperfect geometrical shapes made out of various materials, we can think about the triangle qua or as a triangle. We can think of triangularity without there being a separately existing Form of the Triangle. Similarly, we can think of a house as colored white or green, or we can think of it as a house, that is as a particular kind of thing. Aristotle does not explain how we are able to do this, however. Of course, no one to this day has explained how we do this and it is one of the raging controversies in contemporary philosophy, cognitive science and psychology. Aristotle's point is that Plato's hypothesis that there are separately existing Forms doesn't explain our cognitive abilities either. Moreover, Plato's theory creates a problem of how the Forms are related causally to the material world. Altogether, it just seems wiser to recognize that we have the capacity to create generalizations from experience. These generalizations are normally called "universals" by philosophers. For all the particular, individual things that we know, there are universals which those things are instances of. The dispute between Plato and Aristotle is where those universals are; are they in a separate realm of existence or somehow in our heads. Plato wants to preserve the independent objectivity of the universals, particularly the Good, by asserting their existence in a separate realm of reality. Aristotle finds this unacceptable. He thinks that when we make a true universal judgement, like "That is a tree," we assert something that is true. There really are things which are trees, various different and changing individuals which nevertheless share certain essential properties that all trees have. We use experience to discover what those properties are the make a tree be a tree.
Section 8

This is probably a good place to make one last comment about Aristotle. One of the things which Aristotle is famous for is his articulation of the rules of reasoning, or logic. One of the points that Aristotle makes in his Metaphysics is that all reasoning is based on a fundamental principle. Unlike Plato, whose dialogues never seem to reach an absolutely conclusive end and the Sophists who say there is no truth to be found, only opinion, Aristotle is quite clear about his answer. The ultimate principle of reasoning is: "It is impossible for the same attribute both to belong and not to belong to the same thing and in the same relation." This goes back to his discussion of how we talk. We tend to make statements with a subject-predicate structure. We name something with the subject term and assert that it has a certain property with the predicate term, like "The house is green." What we cannot do, according to Aristotle, is say that the house is green and that it is not green. It might be green in one place and not green in another but it cannot be both green and not green in the same way and in the same place at exactly the same time. The reason this is true is that to speak in this way would be self-contradictory and the self-contradictory makes no sense and cannot happen. The Sophists would like opinions to be both true and false but they cannot be. When we make a statement we describe the world and the world is the way it is, so our statement is either true or false. Perhaps you say "That cabbage is delicious" and I say "That cabbage is disgusting," can't both of these statements be true. Yes but only because they don't really contradict one another. What we mean to say is "According to my taste…" or "…to me." Since we are different people it is obvious that our tastes in food can be different. This does not mean that everything is relative to some person's opinion. It's still cabbage that we are tasting! This fundamental principle is normally called the law of non-contradiction. What is interesting is that Aristotle is able to spell it out completely (unlike Plato's Good), it refutes the Sophists and it again solves the problem of Parmenides because it makes sense of the idea that what is cannot be what is not. What is x cannot be non-x, not in the same way and at the same time.