Logic

Logic Is the Study of Arguments

Most people think that an argument is merely an ugly conversation. Yet the word argument came from a Latin word that meant a way of proving something. When you make a logical argument, you give someone reasons to accept that what you are saying is true. Logic is the discipline that teaches you how to draw reasonable conclusions from evidence. Logic helps you spot potentially dangerous or costly errors in reasoning. As Mr. Spock from Star Trek might have put it, “Logic can help you live long and prosper.”

The Grammatical Bases of Logic

Arguments are made up of sentences. Thus, you must know how to analyze the structure of sentences before you can begin to study the structure of arguments. Arguments are made up of sentences in which the main verb is in the indicative mood. Before you can begin to study logic, you must be able to identify sentences and recognize the mood of verbs. You must also be good at identifying and using conjunctions, such as and and or and if and then. You must be good at identifying and using adjectives such as all, some, and no and adverbs such as not.

How to Study Logic

Logic involves rules that must be learned and applied. I learned some of these rules in math class in junior high school. I learned others by studying logic in college. I learned still more from studying logic books that I checked out of the local library.

Whoever loves knowledge loves correction. If you want to learn logic, you must learn how and when to apply the rules of logic. You must also find some sort of training program in which your mistakes will be pointed out to you and corrected. At the very least, you must have some sort of book with solved problems. People who have poor skills in logic are generally unaware that their skills are poor. Because of their poor skills in logic, they lack the ability to spot their mistakes, or even to understand the significance of the mistakes that are pointed out to them. As a result, they are often overconfident to the point of being obnoxious. Some of the features of narcissistic personality disorder are really the result of the overconfidence that can result from lack of training in logic.

The Personal and Political Implications of Logic

The ancient Greeks valued logic for personal and political reasons. The study of logic helps one learn to be a more reasonable person: a more pleasant companion and a better citizen of a democracy. The French philosopher Voltaire understood the political implications of skill in logic. As he put it, “Those who can make you believe absurdities can make you commit atrocities.” After World War II, many social scientists started trying to figure out how fascists managed to seize power in seemingly civilized countries. One approach was to look at the personalities of the people (authoritarian followers) who provided support for antidemocratic political movements. Authoritarian followers tend to have several noteworthy personality traits, including submission to authority figures and a willingness to use aggression in the service of authority figures. Yet another important trait of authoritarian followers is poor skill in logic. As Robert Altemeyer explained in his book The Authoritarians,

Authoritarian followers drive through life under the influence of impaired thinking a lot more than most people do, exhibiting sloppy reasoning, highly compartmentalized beliefs, double standards, hypocrisy, self-blindness, a profound ethnocentrism, and—to top it all off—a ferocious dogmatism that makes it unlikely anyone could ever change their minds with evidence or logic.

Altemeyer found that authoritarian followers had trouble seeing the problem with the following argument:

  • All fish live in the sea.
  • Sharks live in the sea.
  • Therefore, sharks are fish.

As Altemeyer explained,

The conclusion does not follow, but [people who score high on measure of right-wing authoritarianism] would be more likely to say the reasoning is correct than most people would. If you ask them why it seems right, they would likely tell you, “Because sharks are fish.” In other words, they thought the reasoning was sound because they agreed with the last statement. If the conclusion is right, they figure, then the reasoning must have been right. Or to put it another way, they don’t “get it” that the reasoning matters—especially on a reasoning test.

The conclusion that sharks are fish is true, but the argument is deeply flawed. One of the premises is false (some fish do not live in the sea). Also, the argument itself is invalid. The conclusion is false because some of the things that live in the sea are not fish. Therefore, the fact that something lives in the sea does not prove that it is a fish.

Deductive and Inductive Reasoning

When you study logic, you will focus mainly on two different kinds of arguments: deductive and inductive. The purpose of a deductive argument is to prove that the conclusion cannot be false. Mathematical proofs are examples of deductive arguments. A deductive argument is said to be valid if the conclusion must be true if the premises are true. If an argument is valid and its premises are true, then it is said to be sound. If at least one of the premises is false or if the argument itself is invalid, then it is said to be unsound. If an argument is sound, its conclusion is true. If the argument is unsound, its conclusion could be true or false.

In contrast, the purpose of an inductive argument is to show that the conclusion is unlikely to be false. Most of the arguments that are made in court cases and most scientific arguments are inductive arguments. The conclusion of an inductive argument can be false, even if the premises are true and even if there is nothing particularly wrong with the argument. As a result, inductive arguments cannot be described as valid or invalid. Instead, it may be described as strong or weak.

Explanation of inductive versus deductive reasoning

Logical Fallacies

A logical fallacy is an error in reasoning that makes a deductive argument invalid or that weakens an inductive argument. There are two basic kinds of logical fallacy. A formal fallacy is related to some flaw in the structure (form) of the argument. Informal fallacies are errors that are not related to the structure of the argument.

Formal Fallacies

To understand a fallacious argument, let me first give you a valid argument called modus ponens. In each of the following, I have used a capital letter to stand for a proposition (a sentence that can be true or false):

If P then Q.

P

Therefore, Q.

If the statement If P then Q is true, and P is true, then Q must be true. (This modus ponens argument is valid because of the meaning of If P then Q). But there is something wrong with the following argument, which commits a logical fallacy called affirming the consequent:

If P then Q.

Q

Therefore, P.

Here’s an example. Suppose that that the following statement is true: If it is my birthday today, then we shall have cake. If you know that today is my birthday, then you know that we shall have cake. But the fact that we are having cake does not prove that today is my birthday. Likewise, if you conclude that because it is not my birthday, we are not having cake, you make an error called denying the antecedent or the inverse error.

Informal Fallacies

Informal fallacies are errors that do not spring from some problem with the structure of the argument. One classic example is the post hoc ergo propter hoc (after it, therefore because of it) argument. A cause must happen before its effects. Yet not everything that happens after some event is a result of that event. For example, not every bad thing that happened to a patient who has received a drug is a side effect (result) of taking that drug. To figure out whether some problem is a side effect of a drug, you generally have to compare patients who received the drug to patients who got a placebo treatment. If the problem really is a side effect of a drug, the side effect should be more common among the patients who received the drug than among patients who received the placebo.

Another common informal fallacy is the argument from authority. The argument from authority is an inductive argument. It’s based on the idea that experts generally make true statements about their area of expertise. So if an expert says something related to his or her area of expertise, that statement is unlikely to be false. Note, however, that it is entirely possible for even a world-renowned expert to make a mistake or even to lie. (Ideally, people who get caught lying or making too many mistakes lose their standing as experts.) Since authority figures can make false statements, the argument from authority can never be valid. Instead, it can be described as strong or weak, depending on the reliability of the authority figure in question.

I have encountered many people who do not understand how to use an argument from authority. For example, I have seen people claim that the work of some prominent scientist has been “debunked” by a blogger who does not have even a bachelor’s degree in science. (Of course, a betting man would bet on the scientist, not on the uneducated blogger.) I have also seen people claim that we should always ignore the opinions of experts, out of the fear of committing the argument from authority fallacy. Yet an argument from authority does not prove that its conclusion is true. The expert’s reputation merely lends weight to the idea that his or her statements are unlikely to be false.

From Logic to Rhetoric

As I explained above, the main verb in a proposition must have a verb in the indicative mood. As a result, sentences in which the main verb uses a modal auxiliary, such as should or must, cannot really be used as premises or conclusions in classical logic. So logic can take you only so far when you are trying to figure out what you should or must do. If you want to decide what you want to do, you need to rely on your feelings as well as your reason. When you want to persuade someone else to do what you want, you must use more than logic. You must use rhetoric. Rhetoric is the art of persuasion, particularly the art of persuasive speech and writing. Logic is an important element in rhetoric. Thus, the classical liberal arts curriculum gave students some basic skills in logic before teaching them skills in rhetoric.