Logic - Study Materials

Lesson 7: The Third Part of Logic and the Syllogism

In our last lesson we completed our discussion of the second part of logic, which was about the statement. We saw that there were four kinds of statements, the universal affirmation and denial, and the particular affirmation and denial. We talked about the two basic kinds of opposition between statements: that between the contrary statements, statements which differ in quality but are both universal; and that between contradictory statements, statements which differ both in quality and quantity. We are ready, then, to move on to the third part of logic, the logic of the third operation of the intellect. In the third operation, we do not simply understand what something is, nor simply make statements about the true and the false, but we reason discursively from one truth to another.

St. Thomas Compares Natural and Rational Processes

In his Prologue to Aristotle's Posterior Analytics, a prologue which really introduces the whole of the Organon, St. Thomas goes over the subdivisions of the third part of logic. To explain his divisions, he makes a comparison between the process of discursive reasoning, and the processes in the natural world. He makes this comparison because in both cases we are talking about a process, a kind of change or motion from one thing or state to another. In reasoning we go from one truth to another, in nature things go from one state to another. The kinds of processes in nature, then, can illuminate the different kinds of rational processes.

St. Thomas identifies three basic kinds of processes in the natural world. He writes:

In certain things, nature acts by necessity, that is, in such a way that she cannot fail. In other things she works more often than not, although sometimes she falls short of her proper operation. There must be two kinds of actions in the latter case, one which happens for the most part, as when a complete animal is born from the seed; the other is when nature falls short of what is fitting, as when some monstrosity is born from the seed because of the corruption of some principle.

The events of nature, St. Thomas is saying, happen either by necessity, or usually in the same way. When they usually happen in the same way, there are two possible outcomes: the thing that usually happens happens, or the rare exception happens. An example of something that happens by necessity is the sun rising: there is no natural cause that is capable of keeping the sun from rising in the morning (or to be more precise, the earth from turning on its axis). Most natural processes, however, do not happen by necessity.

The example St. Thomas uses is the generation of a complete animal. He assumes, of course, that events in nature happen for a purpose, and that they usually achieve the purpose, and that the purpose is some good state. When nature fails to achieve its purpose, it is a bad thing. In the generation of an animal, usually the process results in a complete animal, for example, a dog which has all of its limbs and internal organs. Sometimes because of a genetic defect, a defect in the principle of generation, what results in not a complete animal, but a monstrosity, perhaps a dog without its proper limbs. That happens sometimes, but rarely, and when it does happen it is a bad thing. These are the three kinds of processes in nature.

St. Thomas then compares this to the processes in reasoning. He writes:

One process of reason produces necessity, so that there is no possibility of falling short of the truth. We achieve the certainty of science in this process. There is another process of reason which concludes to the truth for the most part, but not with necessity. The third process of reason is that in which reason falls short of the truth, because of a failure to follow some principle in reasoning.

St. Thomas is saying that, like in nature, so also in reasoning there are processes which absolutely cannot fail. This is like the process of the sun rising. There is a second process in reasoning which usually achieves the truth, but is capable of failing. That is like the natural process in which a complete animal is generated. Finally, there is a third process, in which reason fails to find the truth because it does not follow the correct rules, the true principles, of reasoning. That case is like the generation of the monstrosity.

Since there are three processes in discursive reasoning, there are going to be three parts to the third part of logic. The first part governs the first process, which never fails, so that it achieves certainty. This part of logic is called the judging part, since we make a judgement when we are certain about something. The jury judges the defendant guilty when it no longer has a reasonable doubt of his guilt. The second part governs the second process, which succeeds for the most part, so that it achieves probability. This part of logic is called the discovering part of logic. This is called discovering because our discoveries are not certain, merely probably true.

Let me give an example to clarify this point. In his Summa Theologiae, St. Thomas gives five proofs for the existence of God. Those proofs yield a certain conclusion, and are formulated according to the rules of the judging part of logic. Before St. Thomas formulated these proofs, some of which he has received from previous philosophers, thinkers had been trying for centuries to discover whether God existed. The process by which someone discovers the truth about the existence of God is a different process than the one used to prove that He exists. These earlier philosophers, then, were guided by the second part of logic in their search for the existence of God. For example, if we look to Plato, he gives some very good reasons to think that God exists, but his arguments are not entirely indisputable. They yield a conclusion which is only probable. Plato is guided in his arguments by the discovering part of logic, but St. Thomas by the judging part.

There is a temptation to think that, since the judging part of logic gives a certain conclusion, while the discovering part gives us only probability, we should only use the judging part and leave aside the discovering part. There are two ways to answer this objection. First, discovery always comes before judgement. If Plato had not tried to discover the existence of God, and given a good but not foolproof argument for it, then St. Thomas would probably never have given his proofs for it. Second, an absolute proof is much harder to understand than a good argument, and a good argument prepares our minds for understanding the absolute proof. Few men are really able to understand St. Thomas' proofs who have not carefully analyzed good arguments for the existence of God first. If we neglect the discovering part of logic, we often will not be able to understand the proofs which are guided by the judging part.

There is a third part of the logic of the third operation that deals with the failure in the process of reasoning which results from not following the rules of good reasoning. St. Thomas calls this part of logic Sophistic. Of course, the point of this part of logic is not to make us reason badly, but to enable us to avoid reasoning badly and to identify bad reasoning in others. Aristotle discusses this in the book Sophistical Refutations. We will cover this part of logic much later in the course.

To sum up. There are three grades of reasoning, and three parts of logic which guide them. The first process achieves certainty, and is guided by the judging part of logic. The second achieves probability, and it is guided by the discovering part. The third is the failure to achieve the truth, and we avoid this through our study of the Sophistic part of logic.

In this lesson we are going to begin our consideration of the judging part of Aristotle's logic. Before we talk about the details of this part, I would like to follow St. Thomas and make some further distinctions about the kinds of reasoning processes. St. Thomas writes:

The certainty of judgement we possess through resolving comes from either the form of the syllogism alone, and the book Prior Analytics which is about the syllogism considered simply is ordered to this, or also from the matter, when essential and necessary propositions are taken, and the book Posterior Analytics, which is about the demonstrative syllogism, is ordered to this.

What is clear from what St. Thomas says is that the process of reasoning that achieves the truth by necessity is called the syllogism. What exactly a syllogism is we will discuss later in this lesson. Still, we can see that he makes a distinction between necessity which comes from the form of the syllogism, and necessity coming from the matter of the syllogism.

To explain this necessity in reasoning processes I will compare it to a kind of physical necessity. Suppose that I have a triangular piece of ice. Two things follow necessarily from this. First, the triangle made of ice has three angles which add up to 180 degrees. No matter what kind of triangle it is, this must be true. Second, the triangle made of ice, if it is left at room temperature, will necessarily melt. The two necessities, however, have different sources. The angles adding up to 180 degrees follows from the shape, or form, which the ice has taken on. Everything triangular necessarily has such angles. The fact that the ice triangle will melt has a different source, not the form or triangular shape, but the matter, the fact that it is made of ice. Thus, some necessities come from the form of a thing, some from the matter.

Something parallel happens in the process of reasoning. Some reasonings derive their necessity from their form only, while others derive a further necessity from their matter. First, let us consider an example of reasoning which has necessity according to its form alone. All running things are also moving, and since Socrates is running, Socrates must also be moving. The conclusion, Socrates is moving, follows necessarily from the two premisses. But the necessity in this case comes only from the form of the syllogism: given that the two premisses are true, the conclusion is necessarily true because it necessarily follows from the two premisses. But the conclusion, Socrates is moving, is not necessary in itself. In fact, later it might not be true because one of the premisses, Socrates is running, might later be false. He might be running now, but later he might be sitting. It is necessary only if the premisses are true. It is clear, then, that sometimes the necessity comes from the form of the syllogism by itself.

There are syllogisms, however, in which the conclusion derives a further necessity from its matter, the premisses which make it up. For example, we know that all triangles have three sides, and it is also true that all three-sided figures must have angles that add up to 180 degrees. It necessarily follows that all triangles have angles that add up to 180 degrees. That is, the conclusion is necessarily true not only if the premisses are true. The conclusion is necessarily true simply speaking. That is, unlike the previous case, the conclusion must always be true, can never be false. Why? Because the premisses from which it follows can never be false: the are necessarily true. A triangle must have three sides and three-sided figures must have 180 degrees. Thus, in this process of reasoning, we have an absolute necessity which has its source, not just in the form of the syllogism, but also in its matter, the premisses which make up the syllogism.

There are two books of Aristotle's Organon which deal with the necessary processes of reasoning. The first, the Prior Analytics, deals with the necessity which comes from the form of the syllogism alone, leaving aside the matter involved. The second, the Posterior Analytics, deals with the necessity which comes from the matter of the syllogism and which results in absolutely necessary conclusions.

Logicians make a relevant distinction here. The necessity which comes from the form of the syllogism alone and is conditional on the truth of the premisses is called the necessity of consequence. That which comes from both the form and the matter, and is not conditional on the truth of the premisses (since the premisses themselves must be true), is called the necessity of the consequent. In our examples, "Socrates is moving" has the necessity of consequence, but not of the consequent, while "triangles have 180 degrees" has a necessary consequent.

Let us sum up how we have divided the third part of logic so far. The third part of logic as a whole, which directs the process of reasoning, has three separate parts, a judging part, a discovering part, and a sophistic part. The judging part is called that because it achieves some kind of certainty or necessity. That necessity comes from either the form alone, as discussed in the Prior Analytics, or from the matter, as is discussed in the Posterior Analytics. These are the two parts of the judging part of logic. We are now ready to look at St. Thomas's discussion of the discovering part.

St. Thomas is also going to divide the discovering part of logic, this time into three parts which correspond to three books in Aristotle's Organon, the Topics, the Rhetoric, and the Poetics. St. Thomas again makes a comparison between the processes of reasoning and processes in nature. He writes:

Just as we notice a kind of gradation in natural things which act for the most part, since the stronger the natural power the less often it fails to produce its effect, so also we find some gradation in the process of reason which is not entirely certain. The process of reason has that gradation insofar as it approaches more and less to perfect certainty.

St. Thomas does not gives examples here, so we will supply our own. There are some processes in nature which achieve their end almost always. For example, the process of generating a new animal almost always produces a complete animal, an animal with all its limbs and internal organs. On rare occasions an animal is born which is missing a limb or organ. Other processes of nature achieve their end very often, but failures are not that uncommon. For example, nature intends to produce human beings whose eyes can see every color, but a significant minority of people are color blind. It is much more common for people to be color blind than for them to be born missing a limb. Finally, there are processes in nature which, while working more often than not, very commonly fail. For example, the body naturally aims at health and avoids sickness, and most people are healthy more often than not. Yet clearly minor sicknesses are fairly common. Nature fails to preserve health much more often than she fails to produce a complete animal. Thus not all natural processes which admit of exceptions admit them to the same degree.

There is a similar gradation in reasoning. Sometimes reasoning which achieves the truth for the most part results in a very solid opinion. For example, after a long period of deliberation a statesman may decide that a war is probably necessary. His careful thought has yielded a solid opinion. Now a solid, well-reasoned opinion may be wrong, but most of the time it is right. Aristotle discusses this kind of reasoning in the Topics and calls it dialectic.

There is another kind of process of reasoning, called rhetoric, that does not produce a solid opinion, but a strong suspicion that one side of an issue is right. For example, after the statesman has decided that war is necessary, he will try to persuade the public to support the war. Of course, he cannot go through his entire thought process in a speech to the public, so his speech gives reasons which are less certain than his own process of thought. Thus, the public will have less solid reasons than he does for thinking that war is necessary. Yet, if he gives a good speech, the public will rightly have a strong suspicion that he is right and will support him in the war. Aristotle discusses the kind of reasoning in the Rhetoric.

Finally, we can have a tendency to fall on one side of a controversy, not because we have been given arguments, but because one man has used his reason to construct a convincing representation which attracts or repels us. For example, in Macbeth Shakespeare portrays ambition so vividly and horribly that the play tends to make us think that ambition is bad. Of course, this tendency which comes from a story is not as certain even as rhetorical persuasion. Still, perhaps when it is done properly, it is a not unfitting guide for the mind. Aristotle discusses the process of reason used by the writer to make this representation in his book the Poetics.

Thus, the discovering part of logic has three parts. The first, which produces solid opinion, Aristotle calls dialectic and this is covered in his Topics. The second, which is less certain and produces only strong suspicion, is called rhetoric and is covered in Aristotle's book the Rhetoric. The third, which is least certain and which produces a mere tendency to think in a certain way, is covered in his Poetics. These are the three parts to the discovering part of logic.

Aristotle discusses the last part of logic, the sophistic part, in his book Sophistical Refutations. Just as nature fails because of a defect in some principle of generation (what we now call a genetic defect), so reason fails when it does not follow some principle of rational discourse. The sophistic part of logic, by pointing out such defects, helps us guard against them in ourselves and others, so that we reason easily, in an orderly way, and without error.

Now that I have sketched the structure of the rest of logic, I can explain how the rest of this course is going to proceed. In the rest of this lesson, we are going to begin our consideration of the syllogism, and it is the main topic of his book Prior Analytics. In our next lesson we will complete our discussion of the syllogism. In the following lesson, the ninth, we will look at the Posterior Analytics in which Aristotle discusses demonstration, a syllogism that is necessary according to its matter. In the tenth lesson we will look at his Topics, in which he discusses dialectical reasoning. In the eleventh lesson we will examine the principles in his Sophistical Refutations, and in the twelfth we will look at short excerpts from his Rhetoric and Poetics.

The Parts and the Definition of the Syllogism

Now that we have discussed the structure of the third part of logic, we are ready to enter into some details. First, we are going to look at the syllogism. At the beginning of the Prior Analytics, Aristotle defines the syllogism and its parts, the proposition and the term. We will finish this lesson with a discussion of those definitions.

Aristotle first defines the proposition:

A proposition is a sentence affirming or denying one thing or another. This is either universal, or particular, or indefinite.

We can see that Aristotle clearly defines the proposition as a kind of statement and divides the statements into the kinds which we studied before, the universal affirmation and denial, and the particular affirmation and denial. For example, "all triangles are three-sided" is a statement and, as we shall see, also a proposition. He does not explain here exactly how the proposition differs from an ordinary statement.

Instead, he goes on to define the term. He writes:

I call that a term into which the propositions are resolved, that is, the predicate and that of which it is predicated, "being" being added, and "not being" removed.

The terms, then, are parts of the proposition, or more specifically, the predicate and subject of the proposition. What is not a term, nor part of a term, is the "being" verb: "is" and "is not" are left out of the terms. The terms in our example are "triangles" and "three-sided." The "are" in our proposition is not a term, nor is the "all." The "are" serves to connect the subject and predicate, the "all" tells us to take the subject universally.

The term is a simple expression, like those in the Categories. It is a part of a complex expression, like the noun and verb. But it differs both from what falls into the Categories and the noun and the verb. It differs from the first because it is defined as part of another expression, while the expressions covered in the Categories are not parts. It differs from the noun because the term is essentially part of a syllogism, while it differs even more from the verb because it leaves out the "being" notion, that is, the notion of time, which is part of the essence of a verb. This will be important to remember when we speak of the conversion of propositions.

When we put terms together using the "being" word, we get propositions, and when we put propositions together we get syllogisms, so our next task is to look at the definition of the syllogism. Aristotle writes:

A syllogism is speech in which, certain things being stated, something other than what is stated follows of necessity from their being so.

We are going to take this definition part by part. First, the syllogism is speech, like the statement. It is a tool made of words which we use to do discursive reasoning. And just as the statement was more complex than the simple expressions covered in the Categories, so the syllogism will be more complex than the statement, because it is made of more than one statement.

The "certain things stated" are the propositions or premisses of the syllogism. The "something other than what is stated" which "follows" is called the conclusion of the syllogism. Both are statements rather than simple expressions, since each is something that can be stated. Let us label some of the parts in the following example to make this definition clear:

Every three-sided figure has angles equal to two right angles.

Every triangle is a three-sided figure.

Therefore, every triangle has angles equal to two right angles.

In this syllogism, the first two statements are the propositions or premisses of the syllogism: every three-sided figure has 180 degrees, and every triangle has three sides. The third statement is the conclusion: every triangle has 180 degrees.

Aristotle writes that the conclusion of the syllogism "follows of necessity from their being so." In our example, it is clear that if three-sided figures have 180 degrees, and triangles have three-sides, by necessity triangles must also have 180 degrees: they cannot possibly have more or less. And the conclusion follows because of these propositions, and not because of some other propositions with different terms. I need only these premisses with these three terms, "180 degrees," "three-sided," and "triangle," in order to produce the conclusion of the syllogism. That is what Aristotle means when he says that the conclusion follows by necessity "because of their being so."

I want to end this lesson by comparing a syllogism to a simple tool, the loom. The loom is a framework which weaves together two things, the threads of the warp and the woof, in order to make a third thing, the cloth. The syllogism is a loom in words: it weaves together two statements in order to produce a third statement. Or we can say that it weaves together the terms of two prior statements to produce a third statement. Remember that Aristotle refers to complex expressions as "woven together." The syllogism is the main logical tool used to "weave together" simple expressions.

Conclusion

In this lesson we had an overview of the third part of logic, and we defined the syllogism and its parts. In our next lesson we are going to discuss the principles of the syllogism, and the most useful forms of the syllogism.

Exercises

Short essays (250 words).

1. Why is it appropriate for St. Thomas to compare the parts of the third part of logic with the processes of nature?

2. Why does the third part of logic center on the syllogism when the syllogism is not the only mode of discursive reasoning?

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