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THE BIRTH OF LOGIC

At this point in our narrative it is a short step to seeing that the point of departure is Plato's theory of forms. The question that bothered Aristotle was How can anything participate in something else when the something else is a separate entity existing in its own transcendent world? Even if we consider them as models, he said, we are at a loss to explain what the motive causes are for the sensible objects to conform to them. He blamed the problems of the forms on the difficulty of arguing from the abstract rather than arguing from nature. This problem combined with his practical background in medicine brought Aristotle around to the idea that all knowledge must begin with sensible objects. At the same time he held the fundamental Greek and Platonic belief that scientific knowledge can never relate to sensible objects which come, go, and change in time. He said that Scientific knowledge deals with general concepts extracted from our experience of sensible objects. Applying this idea indiscriminately ultimately leads to a linkage between his philosophy of nature and his syllogistic logic.

A categorical syllogism is a logical argument form. Aristotle called Syllogisms rules for the direction of the mind. A syllogistic argument consists of two premises and a conclusion. The two premises are statements that are considered true, the conclusion is an undeniable implication from those premises. Each of the three statements is expressed in a rigid form. Any argument once so transformed can be determined to be either valid or invalid by a simple set of rules that have nothing to do with the substance of the argument, only of their form. The conclusion of an argument that is determined by these rules to be valid is necessarily true. This is because being valid simply means that if the premises are true then it is impossible for the conclusion to be false. In determining the validity it is the form alone that matters. Any statement, he believed, could be put into one of a limited number of forms. Once in that form one could dispense with the words that make up the statement and consider only the form. If the form was valid, then the argument was valid, if it was not then the argument was not.

Beginning with the three statements that make up the form of the argument, there are four acceptable categorical statement forms. The are simply statements that indicate that the members of one category, called the subject category or "S" either are or are not members of the second or predicate category (P). In more advanced forms of Aristotelian logic they were labeled A, E, I, and O.

A Every member of the category of things that are included in the subject of the proposition is also a member of the category of things that are included in the predicate. (All S is P)

E No member of the category of things that are included in the subject of a proposition is also a member of the category of things that are included in the predicate. (NO S is P)

I At least one member of the category of things that are included in the subject of the proposition is a member of the category of things included in the predicate. (SOME S is P)

O At least one member of the category of things that are included in the subject is not a member of the category of things included in the predicate. (SOME S is NOT P)

Every syllogism contains three such statements or propositions. Two are premises that are assumed to be true. The third is the conclusion which, if the form is valid, would also necessarily be true. Every syllogism also contained three terms, S, the subject of the conclusion, P, the predicate of the conclusion, and M, a middle term which is included in both of the premises but does not appear in the conclusion. Every argument, Aristotle said, can be expressed in such a syllogism. For example, in the following argument S would be pets since pets is the subject of the conclusion. Tails would be P, the predicate of the conclusion. Dogs does not appear in the conclusion, but does appear in both of the premises so dogs is M, the middle term.

All dogs have tails. Some pets are dogs. Therefore some pets have tails.

Thus, this argument can be expressed as the specific logical form.

All M is P Some S is M therefore Some S is P

The order of the terms and the sequence of the premises serves to identify the form. The foregoing syllogism is an AII 1 form because the major premise, that containing P, is an A statement, the minor premise, that containing the S, is an I statement, the conclusion is also an I statement, and the figure, or order of terms is number 1. Every argument of the form AII 1 is valid. The meaning of the terms is irrelevant, all that matters is the form.

On the other hand if we take the argument;

All girls curl their hair Some boys curl their hair Therefore some boys are girls

This argument is obviously invalid. It is also AII but the order of terms is different. Its complete form is AII 2 and every argument of the form AII 2 is necessarily invalid. If it is possible to make an invalid argument using a particular form then any argument that uses that form is invalid regardless of the meanings of the terms. It is impossible to make an invalid argument using a valid form, and it is impossible to make a valid argument using an invalid form. That does not mean that the conclusion of the argument is not true. It only means that the conclusion is not necessarily implied by the premises, that it is possible for the premises to be true and the conclusion to be false. What is important is this sense of necessity. Being a valid argument means more than that the conclusion is implied by the premises. It means that it is impossible for the conclusion to be false if the premises are true. It is this absolute character of the valid argument that is important.

Just as the syllogism extracts the form from specific arguments and determines their validity without regard to their particulars, scientific knowledge must extract from sensible objects the general terms by which they can be understood. And these general terms must be just as absolute as the syllogistic form. It is no wonder that he claimed that the syllogism was the fundamental tool of knowledge.

"Spoken words are the symbols of mental experience and written words are the symbols of spoken words," are the words that open On Interpretation. These words lay the groundwork for the whole of the Organon, the set of books which outline his basic logical approach to knowledge. It's purpose is to discuss how we can interpret experience through words. His aim was to present an analysis of the actual process of thought, expressed in language in a way that will help us to reason more correctly. For it was the actual process whereby people reason that interested Aristotle, and not some abstract concept of knowledge. The greatest accomplishment of the Organon is that it created an underlying foundation for the study of logic through the separation of the contents of an argument from its form. By applying this approach to things found in nature, Aristotle was able to derive a level of knowledge of the sensual world that was denied by the Platonic idealistic approach. Aristotle pioneered the use of symbols in analyzing thought. It is by using symbols that we can analyze the form of arguments at the same time ignoring what the argument is about, he said. A symbol is an abstraction from the argument in the same way that generalizations about natural things are abstractions from our experience of them. Aristotle would even go farther and claim that his pure syllogisms (a pure syllogism is any syllogism of the first figure that has a valid form), when they were applied to first principles, that is principles no one would question, were the essence of deductive thought and would lead from known and accepted facts to true knowledge of new and hitherto unknown facts.

Logic, then is the second of those tools that Aristotle used to understand the universe. Before we can apply logic to things we find in nature we must begin with something about what we experience we know to be true. While this is a problem that has engrossed philosophers for millennia, what he was referring to was the simplest things. First principles, those things or principles that no one would disagree with. Simply that which is obvious. Second, beginning from this solid stance he would have us apply valid reasoning, that is, reasoning using valid logical arguments that cannot possibly lead to false conclusions.

The Categories then takes us to the next stage in our development of knowledge of the world around us. It dealt with categories of being. That which we can determine about something that is simply because it is. This is another of those concepts that separate Aristotle from is teacher. What is, according to Plato, is the world of the forms. The sensual world is not because it is never the same, it is constantly changing, it is always in the process of coming into being. But Aristotle taught that the world before us is, meaning everything we experience, has being. But, since it is always changing we cannot have direct knowledge of it. When we name something we are symbolizing its existence just as when we use a symbol in a logical argument we are symbolizing the form of the argument. So the Categories teaches how we can apply words to our experience to increase our store of knowledge about things that are. First, he said, things are named. By things he meant anything that we find through experience. Naming something makes it accessible to reasoning. Since Aristotle is interested in reasoning about things rather than ideas, he said that words used as names, though they are symbols of mental experience, refer to things that actually exist. Things can be named specifically, with a name that designates them as specific identifiable objects. They can also be named equivocally when the name refers to the class of which the thing is a member. Whichever applies, The Organon begins with the assumption that things we name are the beginning of our treatment of experience. Its subject is simply what we can say about things that we experience and how we can say them. The Categories deals with mechanisms by which, through the use of logic, we can increase our understanding of what it is we experience.

Knowing that something exists, that it is, forms a beginning of our treatment of experience. What is it that we can say about things simply because we know they exist? First, when Aristotle would say that a thing is present in a subject what he meant was that it must be incapable of existence apart from the subject. For example if he was to say that reason is present in man what he would mean would be that reason cannot exist apart from men. Anything which can be said about a subject is predicable of that subject. For example if he said that Joan is blond he would be saying that blondness is predicable of Joan. Thus, some things are predicable of subject but not present in it, for example 'man' is predicable of an individual man but never present in one.

To think about something is to think about what exists in reference to it. Therefore Aristotle's ten categories of thought are ten categories by which we can determine the essence of something which is, what it is to be something that is. These categories are; "substance, quantity, quality, relation, place, time, position, state, action, and affection." It is through combinations of these terms that assertions are made concerning either sensible or non-sensible things. When we make any assertion using these categories, then that assertion is necessarily either true or false. It is this necessity that makes Aristotle's approach to logic so powerful. What is necessary cannot not be, and it cannot be different than it is. This is because it deals with categories of being, of what is. And it is also why his logic is called categorical logic. If we use these categories to assert things about something that is we can develop valid syllogism's from these assertions and thus learn new things about what we formerly knew very little. When we reason in this way we must only reason from true premises developed from true categorical assertions using valid logical forms, for only then will we come up with valid and incontrovertible conclusions.

From this starting point it is easy to see that the ultimate general term, that is the most general term possible, must stand for absolutely anything that we can talk about, that is, that we can apply the categories to. This is obvious when we realize that for Aristotle what we can know is only derived from what we can talk about. Such a general term, if one existed, would be of particular importance. The term he used was substance. As the specific subject of thought It had to be something that existed, that had being. Thus, it could be anything which is neither predicable of a another specific thing nor present in it, because such things derived their existence from the other thing. We can translate that as meaning anything that can never be said of something else, nor is a necessary part of something else. Examples of substances would be a particular man or horse, or even particular structures determined through reasoning. A substance is not simply something which exists, it is some particular something which exists on its own and not as a part of something else. What is predicable of a substance is the genus or species to which it belongs. What are present in a substance are its attributes, those traits that make it what it is and not something else. For example, when we say that John is a man we say that the genus man is predicable of the substance John. When we say that Jane is a red head we are saying that red hair is present in the substance Jane, that red hair is an attribute of Jane and without it she would not be Jane.

What he called secondary substances are things in which primary substances are included, such as the species man or the genus animal. Primary substances are what underlie every specific thing which we can talk about. Everything except a primary substance is either predicable of a primary substance or present in one. In other words what is not a primary substance is either something that can be said about a primary substance or something that determines what a primary substance is.

However, Aristotle said that for anything to become knowable, the philosopher must examine the set of particulars that are involved in determining what it is to extract their common form. Remember that because particular things are constantly changing, knowledge of them by themselves is not possible. Aristotle lived in the same world as Plato and began with the same assumptions. This means that though it is individuals that are the only realities there can be no knowledge of them directly because knowledge is only of essences and essences are of the general terms which are predicated of particular things. Thus, Aristotle's theory of knowledge starts with what it is we can talk about, the ideas that we can communicate to others through the use of words. But from there it merges with Plato's idea that particulars are not knowable because they belong in the world of the changeable and not in the world of the unchanging. But there is a great difference even here because for Plato the forms are real and the individual entities are not. For Aristotle it is the individual entities that are real and the essences are simply what we as reasoning men have extracted from our experience of them.

As a result the concept of primary and secondary substances outlined in the Organon is stated quite simply. However, it raises the same problems that earlier philosophers struggled with. When Aristotle speaks of substance he is speaking either about concrete physical objects, or specific conceptions about specific objects developed through reasoning. At the same time it was an established and accepted fact that such objects are constantly changing. As a result, knowledge can only consist of facts concerning what Aristotle called secondary substances. In other words we can know practically nothing about a particular horse because it is constantly changing. At the same time we can know a great deal about horses. What we can know about a particular horse we know only because it is a member of the species horse. As you can see this appears to be a return to Plato's forms. In a sense it seems to be exchanging general terms for abstract forms. In fact this is a trap some philosophers fell into in the middle ages which led them to postulate the real existence of the things that we relate to when we use general terms. However, the reliance on abstract forms was something that Aristotle was trying to get beyond. The difference is this. For Plato reality resided in the forms. For Aristotle reality resided in the concrete physical objects, or specific conceptions about physical objects. Returning to what I said earlier, how then can either concrete physical objects or specific concepts about them be the subjects of scientific enquiry? Unlike Plato, Aristotle taught that the separation of the form from the particulars was a mental act, an act of reasoning, not something that takes place in nature. Not unlike the separation of form from the subject matter of an argument in logic. Thus the Aristotelian step from the particular to the general was a special kind of logic that we call "inductive logic."

The Prior Analytics set down more details of Aristotle's syllogistic logic. As you may recall, a syllogistic premise must be either an affirmation or a denial of something concerning something else. If it is true and obtained from the first principles of a science, and by that we mean that it was obtained through inductive logic, then it is demonstrative. By first principles he meant those principles which were developed through inductive logic and also are generally accepted without question. If, on the other hand, a syllogism is chosen from a pair of contradictories for the sake of argument then it is dialectical. Demonstrative arguments lead to scientific truth, dialectical arguments lead to persuasion.

Aristotle becomes his most mystical, and hence his most misunderstood, in his Metaphysics. The word incidentally was not Aristotle's, but that of a Greek commentator who lived not long after Aristotle. It simply meant after physics. Its most important connotation is that Aristotle did not approach these problems until after he had perfected his physics. This illustrates another distortion of Aristotle's thought that plagued the middle ages and the centuries following. What later philosophers would call "metaphysics" Aristotle would call "first Philosophy". But remember though logically first, it is considered second because we can only learn of it after we have extracted the forms from the physical objects around us. Thus, in trying to understand the Metaphysics it is important to keep in mind that Aristotle maintained that what was real was particular things.

An important concept for Aristotle that would not occur to someone like Plato, was the origin of cause, change, and movement. Only particular things are caused. Plato's forms were eternal immovable and unchanging, his sensual world was a world where each existing thing is a shadow of its form. In Aristotle's sensual world form is what makes particular things what they are. The Greek concept of cause which Aristotle shared was broader in scope than the word we use. It included everything that was responsible for any things that are coming to be. In the Physics he said there are four causes for the existence of anything. The first is the material cause, that out of which the thing comes to be and which persists in it. For example the wood in a chair. The second or formal cause is the form or pattern, the formula of its essence and its genera, what it means to be the thing it becomes. The third or efficient cause is the primary source of change. The advisor is the efficient cause of an action, the father is the efficient cause of the child. The fourth is the end, what the thing is for. In the Metaphysics he used a simpler explanation, he called the four causes the underlying matter, the substance or essence, the source of motion, and the good or result aimed at.