Lesson 11: Sophistic Reasoning


In our last lesson we talked about dialectic, and Aristotle's Topics. Dialectic gave us the tools or weapons for a fair intellectual combat, the dialectical syllogism and induction. These tools do not give their possessors the ability to come to certain knowledge because that is reserved for the demonstrative syllogism. But they do give him a dialectical power, an ability to dispute in a reasonable way about anything.

But just as there are weapons for a fair intellectual combat, so there are weapons for an unfair intellectual combat. We could make a comparison to boxing. It is fair for a boxer to use boxing gloves, but not to use brass knuckles. Gloves are weapons of fair combat, brass knuckles are weapons of unfair combat. Just as in boxing, so also in intellectual combat there are fair and unfair weapons. Induction and the dialectical syllogism are like boxing gloves, while the tools of sophistical reasoning are the brass knuckles of intellectual combat. In this lesson we are going to talk about Aristotle's Sophistical Refutations. In that book he describes sophistical reasoning and the weapons used by the sophist. Knowing those weapons, we can defend ourselves from his unfair intellectual combat.

What Order My Lessons Have Taken

Before we cover the sophistic part of logic, I want to discuss the order of my lessons. We talked about the judging part of logic in lessons 7, 8, and 9. In lesson 10 we talked about the beginning of the discovering part of logic, dialectic. It seems that in this lesson I should complete my discussion of the discovering part of logic, instead of jumping to the third and ultimate part of logic, sophistical logic.

I discuss sophistic before rhetoric and poetics for two reasons. My first is a simple appeal to tradition. If we look at the traditional arrangement of the texts of Aristotle, we find that the Topics is followed immediately by the Sophistical Refutations. The Rhetoric and Poetics are usually placed outside the collection which is called the Organon. While it might be better to place those two treatises in the Organon, there is a reason for this tradition. It is that the term logic has many meanings in an ordered relationship. That is, logic is a word used analogously of, say, the Categories and the Poetics. Let me explain why the word is used analogously.

St. Thomas distinguishes two kinds of science, speculative and practical. The practical sciences are bodies of knowledge which aim at directing human actions. Speculative sciences, on the other hand, aim at nothing besides knowledge itself. For example, ethics is a practical science because it studies virtue, not to know what virtue is, but for the sake of doing virtuous actions. Metaphysics, on the other hand, is a speculative science. We study metaphysics simply because it is good to know the truths that it teaches.

Logic is not in itself a speculative science. We do not study logic just for the sake of knowing logical truths, but for the sake of using that knowledge to direct our minds to other knowledge. Still, the ancients placed logic in the genus of speculative science because it is the tool of speculative science. We use logic primarily as a tool to acquire knowledge for its own sake. And it is evident that the main treatises in Aristotle's Organon are ordered to speculative knowledge, knowledge for its own sake.

It is clear that all of the treatises up to the Posterior Analytics contribute to our study of that book. Moreover, that book is itself the crown of logic, since through its tools we gain certain and reasoned-out knowledge. And since dialectic is also ordered to a discovery of the truth, then dialectic also is included in logic as the tool of speculative science. In fact, even sophistic reasoning is a tool of speculative science because, by avoiding fallacies and by defending ourselves from the fallacies of others, we move ourselves closer to the goal of having speculative knowledge.

From all of these considerations we can gather the following definition of logic in the strict sense of that term: logic is the art which directs the actions of reason in its acquisition of speculative knowledge. When we look at rhetoric and poetic, we see that they are not parts of logic thus strictly defined. For both rhetoric and poetic have an end outside of speculative knowledge and appeal to means which are outside of the realm of the intellect. Thus, neither directs reason in its acquisition of speculative knowledge.

First, rhetoric aims at something besides knowledge. Rhetoric aims at persuasion, and when one is persuaded of something, he is not simply persuaded that one side or another of a controversy is true. He is persuaded that one side or another of a controversy is good, and thus that one thing ought to be pursued, and another to be avoided. And when we talk about the good, and pursuit and avoidance, we are talking about the realm of action and we are going beyond the realm of speculative science. Thus rhetoric aims at something apart from speculative knowledge.

Likewise, poetics aims at something other than knowledge. Poetics directs the action of the intellect in making poetry (imaginative literature, not just verse). But literature aims primarily at beauty and at pleasure from the perception of beauty, both of which always have the characteristic of being good. But when we bring in the good and the bad, we are concerned with desire and human action, and our end is not just knowledge. Thus, poetics and rhetoric both aim at something beside knowledge.

Rhetoric and poetics also use tools that go beyond the intellect. For example, in rhetoric, I appeal to the emotions of those to whom I am speaking and in poetics, I make representations to which people have a desire or an aversion. Emotion and desire, however, are outside the intellect and clearly outside the realm of logic, as that term is usually understood. The means used by logic in the strictest sense of that term always relate to knowledge. Once again, rhetoric and poetics fall outside of the subject of logic strictly defined.

But they do not fall outside of logic in every way in which the term could properly be used. We can give a second definition of logic which is different but related to the first. We could say that logic is the art which directs the actions of reason. This definition differs from the first by cutting off the last part of the first, in its acquisition of the speculative knowledge. And when we cut off that last part, we use the term logic in a broader sense and include rhetoric and poetic. They can be included in this analogous sense because they still are arts which direct reason in its actions. That is, it is reason that undertakes the task of persuading, and it is reason that directs the action of making poetry. Thus this broader sense of the term logic includes everything that is included in the narrow sense, plus rhetoric and poetics.

The Third Meaning of the Term Logic : Symbolic Logic

Logic also has a third meaning. If you look in your local library for a book on logic, most likely you will encounter a book filled with horseshoes and squiggles and parentheses and upside down letters, that is, a book filled with symbols. The symbols will be arranged in things that look like equations. We call that symbolic or mathematical logic. When we talk about that as logic, we are using logic in a third meaning. In that case we say that logic is a study of the relations that occur between symbols. This study is called logic because there is a likeness between logic as Aristotle talks about it and the relations between symbols. The relations between symbols produce certain necessary consequences, just like the premisses of a syllogism produce certain necessary consequences. Because of this likeness, the term logic has acquired a third meaning.

This is not, however, a third analogous use of the term logic, but a use of the term that is purely equivocal. This may seem strange, since we said before that terms that are used analogously have different but related meanings, and this seems to fit the bill. When I talk about symbolic logic as being logic, logic has a different but related meaning to when I talk about the Categories as being part of logic. But we need to remember that analogy had a purpose. The purpose of analogy was to make what one thing is better known by showing that it has a likeness to another very well known thing. And what is necessary for analogy is that the likeness between the two is very central to what they are. But if the likeness between the two things is superficial, then calling them by the same name does not help us understand the less known one; rather, it makes the less known one even more obscure to us. It points to a superficial and accidental likeness as if it were essential to the thing. This happens when we use the term logic to apply both to the symbolic logic and to Aristotle's logic.

The primary purpose of Aristotle's logic is to direct the actions of reason. Some of those actions have necessary consequences, but others do not. For example, the syllogism has a necessary consequence attached to it, but induction does not. Thus that there are necessary relations in symbolic logic makes it like Aristotle's logic only in a superficial way.

More importantly, symbolic logic does not really direct the actions of reason. Symbolic logic is about directing the manipulation of symbols, but the manipulation of symbols in not a strictly rational action. This is clear because even an obviously non-rational thing, such as an adding machine, can manipulate symbols. The manipulation of symbols does not require the understanding of the nature of a thing, while reasoning is rooted in such an understanding. Thus when we apply the term logic to symbolic logic, we are using that term purely equivocally, in a way that obscures the nature of both symbolic logic and Aristotle's logic. It is probably better not to use the term logic at all, and call symbolic logic the art of calculation.

Sophistic and Deceptive Likeness

Symbolic logic having a deceptive likeness to Aristotle's logic calls to mind sophistic logic, because sophistic and the art of the sophist are rooted in deceptive likeness. But before we plunge into the subject of sophistic logic, we should indicate the order in which we are going to take it up. First, we are going to talk about what a sophist is. Second, we are going to talk about the kind of power that the sophist has, the sophistic power. Third, we are going to talk about the tools that the sophist uses.

In his commentary on Aristotle's Metaphysics St. Thomas describes the difference between the philosopher and the sophist. He writes:

But the philosopher differs from the sophist in choice, that is, in selecting or willing or in desiring a way of life. For the philosopher and the sophist direct their life and actions to different things. The philosopher directs his to knowing the truth, whereas the sophist directs his so as to appear to know what he does not.

Here we see that notion of deceptive appearance. The philosopher wants to know the truth and be wise. The sophist wants to appear to know a truth he does not in fact know. He wants to appear wise, when he is in fact not wise.

Aristotle in the beginning of Sophistical Refutations makes a similar point:

The art of the sophist is the semblance of wisdom, without the reality. And the sophist is one who makes money from an apparent, but unreal wisdom.

Aristotle is thinking of something very specific. There were men in his time who went to the Greek city-states and offered to teach for a fee the arts of disputing well, living well, and being powerful. These men often made great sums of money from their teaching. These men, however, did not care about actually being wise or about actually being able to teach the art which they claimed to possess to their pupils. It was enough for them that they could appear to be wise, and appear to teach this art, so that their pupils would pay them. Thus anyone who values more the appearance of wisdom than its reality is a sophist in his heart, that is, by his choice.

A man appears wise without actually being so if he takes on the superficial characteristics of wisdom. In other words, the sophist takes on a certain deceptive likeness of wisdom. Aristotle makes a comparison between precious metals and non-precious metals. Tin, for example, has the outward appearance of silver, and brass has the outward appearance of gold. The inexperienced, seeing that kind of likeness, might mistake tin and brass for silver and gold. In the same way, a wise man has certain outward appearances. The sophist imitates those outward appearances, and his power to imitate them constitutes his sophistic power.

What are those superficial characteristics? In another passage near the beginning of the Sophistical Refutations, Aristotle describes the likeness between the wise man and the sophist.

It is the business of one who knows a thing himself to avoid mistakes on the subject which he knows, and to be able to show up the man who makes them. And of these accomplishments, the one depends on the power to render an answer, and the other upon the securing of one.

One task of the wise man is to avoid making mistakes in a dispute. First, he avoids contradicting himself in a dispute about a subject which he understands. Second, when others contradict him, he refutes their arguments. These are the superficial characteristics of the wise man.

If the sophist wants to appear to be the wise man, the sophist must take on the appearance, first of avoiding being refuted himself, and second of refuting those who disagree with him. That is why Aristotle's book on the sophistic part of logic is called Sophistical Refutations. The sophist avoids being refuted, and tries to refute others. Or rather I should say, he wants to appear to avoid being refuted and appear to refute others.

It might be helpful here also to contrast the sophist with the dialectician. We saw that dialectic was a power of fair intellectual combat. Its purpose was to refute the dialectician's opponent and avoid allowing the dialectician to be refuted. The dialectician used probable arguments against his opponent and avoided the probable arguments brought up by his opponent. Like the wise man, the dialectician refutes and avoids being refuted.

The sophist wants to appear to refute. How does he do that? Aristotle outlines two ways:

Sophistic arguments are those that appear to reason to a conclusion from probable premisses but reason badly, or those which truly reason to a conclusion but from premisses that only appear to be probable.

Aristotle says that there are two ways the sophist can achieve his end of apparent refutation. One is to seem to reason well even when reasoning badly. That is, the sophist seems to make a good syllogism, but his syllogism is actually a bad one. The second is to make a good syllogism but to start from premisses that are not really probable, but only seem to be so. That is, he starts from premisses that look like, but are not, the premisses granted by his opponent. The tools that the sophist uses to accomplish these two tricks are called fallacies. Our next task, then, is to identify the main kinds of fallacies and give a couple of examples of them.

Fallacies: Weapons of Unfair Intellectual Combat

When we are trying to understand the nature of the fallacies, we will examine examples that are very obvious because we are not so much concerned with actually seeing a sophist in action, as in understanding the tools or weapons which the sophist uses. Only a bad sophist would use the particular examples that we will look at because these arguments are too obviously fallacious, but we take obvious examples so that we might understand what the fallacies are. Later we will be able to detect the weapons when they are less obvious.

Aristotle says there are two basic kinds of fallacies, those which depend upon the use of language, and those which do not depend. Language can be a sophistic weapon because words have many meanings. Aristotle explains it as follows:

For names are finite, and so is the sum total of definitions, while things are infinite in number. Inevitably, then, the same definitions and a single name have a number of meanings. Accordingly, just as in counting, those who are not clever in manipulating their counters are taken in by the experts, in the same way in arguments too, those who are not well acquainted with the force of names misreason, both in their own discussions, and when they listen to others.

Aristotle compares reasoning here to the science of accounting. Accounting is a very complicated business, and those who are expert accountants can deceive those who are not expert accountants; that is, they can cook the books. They can make it appear that something has been paid for when it is not been paid for. And then they can steal the money. The same thing is possible with language. Words have many meanings. Those who are not adept at using words and do not realize that words have many meanings can be taken in by those who are adept. Just like the dishonest accountant can make something that has not been paid for look like it is been paid for, so the dishonest user of words can treat a word that has two meanings as if it had only one.

That words have two meanings is not necessarily a bad thing. The proper analogous use of a word is a good thing. But when one uses those two meanings of a word as if they were just one meaning for the sake of appearing to refute but not, he has used the fallacy of equivocation. The fallacy of equivocation is the first sophistical weapon.

Let us give an example. An activist for animal rights might protest a baseball game. And she reasons as follows: Baseball mistreats animals. This is because using an animal to hit a hard baseball is mistreating it. But using a bat is using an animal to hit a hard baseball. Therefore using a bat is to mistreat animals, and baseball always does that.

It is easy to see the fallacy in that case. The word bat has two meanings but the animal rights activist is using the word bat as if it had only one meaning. Bat can mean both the flying nocturnal animal, and it can mean a wooden stick. She is assuming that the two meanings are the same when she says that to use a bat to hit the baseball is to use a nocturnal animal to hit the baseball. She has apparently refuted the baseball fan, but she has not actually done so.

The fallacy of equivocation can be used more subtly when the words have different but related meanings. We saw before that the word logic had two different meanings; one in which it was the science which directs the actions of reason toward its goal, knowledge of the truth; and another in which it was the study of the relations between symbols.

One might then make an argument which uses the fallacy of equivocation in a much more subtle way. He might say, Because logic is about the relations between symbols, and modern logic studies those relations more rigorously than Aristotle's logic does, it must be the case that modern logic is superior to Aristotle's logic. The fallacy in that argument is once again the fallacy of equivocation. The word logic when predicated of Aristotle's logic and when predicated of modern symbolic logic has two different meanings. Aristotle's logic is not a study of the relation of symbols, it is the art which directs the acts of reason toward their goal of the truth. Thus the argument does not validly conclude that symbolic logic is superior to Aristotle's.

The Fallacy of the Accident

The second tool used by the sophist is called the fallacy of the accident. It is a fallacy that does not depend upon the use of language, but rather on the deceptiveness of the relationship between accidents and the subjects to which those accidents belong. As we noted before in our discussion of the predicables, some predicates belong essentially to a thing. When a predicate belongs essentially, it belongs universally: all of the subjects must have that predicate. For example, having three sides belongs essentially to the triangle and every triangle must have three sides. Other predicates belong accidentally to their subjects. When a predicate belongs accidentally, it does not belong universally. Tanness belongs accidentally to man, and thus some men are tan, but others are not. The sophist treats an accidental predicate as if it were essential, and uses that to secure illegitimately a universal proposition as a basis for reasoning. This is the weapon that is the fallacy of the accident.

The following example might help us to see how this fallacy works. Prior to the age of exploration, northern Europeans would have had very few, if any, occasions to see human beings of other races. Thus they might tend to mistake the accident of white skin color for something that is essential to human nature. In other words, all the men that they have seen are white, therefore they think that whiteness is essential to being a man. When they first see men who are not white, let us say Indians, they might be tempted to deny their humanity. Their syllogism then would take the following form:

All men are white.
No Indian is white.
Therefore no Indian is truly a man.

This syllogism does not make a deceptive use of language. The important terms, Indian, man, and white, are all being used with only one meaning. The mistake is the statement All men are white. That statement assumes that whiteness is essential to humanity although it is merely accidental.

In general, the sophist looks for an accidental characteristic, has his opponent grant that characteristic as accidental, but then appears to refute his opponent because he takes that characteristic as if it were essential. In our example the sophistic racist who is arguing against a good man would get the good man to grant the statement Men are white. The good man recognizes that statement in its accidental form, that is, whiteness is an accident of some men. But the racist, being sophistic, would take that statement as if it were meant essentially and act as if his opponent had granted that all men were white. Then he could secure his desired conclusion. Of course, the more that something accidental seems essential, the more deceptive a tool the fallacy of the accident is, and the more powerful a tool it is for the sophist.

The fallacies of equivocation and the accident are the two main fallacies. Other fallacies work because they have a likeness to these two. That is, other fallacies dependent upon language work because they have a likeness to the fallacy of equivocation, while other fallacies that are not dependent of language work because they have a kind of likeness to the fallacy of the accident. If we understand the fallacy of equivocation and the fallacy of the accident, then we are fairly well prepared to defend ourselves against any of the weapons of the sophist.


That concludes our study of the sophistic part of logic. We now have a general idea of how to approach reading the book Sophistical Refutations. In our final lesson we will talk very briefly about the main tools of the final two parts of logic, rhetoric and poetics. Even though those parts of logic in themselves aim at something beyond knowledge of the truth, nevertheless three particular tools, two used by the rhetorician and one by the poet, are also useful for the philosopher and the theologian. Our consideration will focus on those three tools.


1. Short essay: explain why there are two meanings of logic.

2. State whether the reasoning is syllogistic, inductive, or sophistical. If sophistical, identify the kind of fallacy.

Hitler and Stalin killed millions of innocent people, and both were raised as Christians. Therefore, all Christians are bloodthirsty.

People who are interested in triangles should study geometry. The readers of the National Enquirer are interested in love triangles. Thus, they should study geometry.

Trees, shrubs, grass, and generally all plants rely on sunlight for life.

Those who study logic are well-prepared to become good philosophers. Mathematicians often study symbolic logic. Therefore, they are well-prepared to become good philosophers.

Every immaterial substance is immortal. Since the soul is an immaterial substance, it is also immortal.


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