Graziano and Raulin (8th ed)Graziano & Raulin
Research Methods (8th edition)

Primer on Logic

Logic and Reasoning in Science

This text emphasizes the idea that science is a process of inquiry. Scientists ask questions and then proceed to answer them in the best possible way. The essence of science is its particular way of thinking--specifically, its logical processes of reasoning.

The key terms here are thinking, reasoning, and logic. Thinking is an active process in which ideas are envisioned, manipulated, and transformed through mental processes that are only now beginning to be understood. People are thinking all the time, and they do so in various forms. Close your eyes and create some pictures. The images you conjure may be in no particular order, and they might not march to any predictable conclusion. Likewise, you might think about sounds you have heard, events you have experienced, feelings and ideas you have had, and so on. 

All of that constitutes thinking, but it is not necessarily logical thinking, nor does it aim to clarify and understand ideas or to arrive at valid conclusions. Although it is thinking, it is not necessarily reasoning. Reasoning is thinking that is organized, systematic, and focused on clarifying ideas and arriving at conclusions. Everyone engages in reasoning. Every discussion with friends about politics, history, philosophy, society, art, college courses, religion, people, sports, and so on involves some degree of reasoning. However, not all reasoning is logical. Reasoning is often based on tenacity (It has always been that way, so it must be true.), authority (Freud said so; so it must be true.), intuition (I know it's true. I feel it.), or pseudo-sciences such as astrology. These approaches are fine for everyday, but for other decisions we need more formalized and systematic thinking. Would you want to drive across a two-mile bridge spanning a deep canyon if you knew the chief engineers had based their technical decisions on their "feelings" about things? Would you want to consult a physician who used astrology to guide his or her medical decisions? We expect these professionals to base their work on well-formulated procedures that are logically derived from the information available. Logic guides decisions by providing a systematic procedure that leads to both accurate and consistent decisions. Logic follows formal rules, much like mathematics.

It seems safe to say that all people think, much of our thinking is reasoning, but only some of our reasoning is logical.

Reasoning by Analogy

Much of everyday reasoning, and much of the reasoning that occurs in science, is reasoning by analogy. Analogy can be simple (You're just like your father!) or complex. In using analogy, we note that one thing is similar to another, and we conclude that some other aspects of the two things are therefore the similar. For example, we might reason by analogy as follows:

I know that when people are trying to solve a problem they often stop what they are doing, turn their heads to one side, and think for a moment about the problem. Then the solution occurs to them, and they solve the problem. I have noticed that my dog, when trying to get a ball out from some difficult place, will often stop, turn his head to one side, and remain still for a moment. Then, as if the solution occurred to him, he returns to his attempts to get the ball. Therefore, my dog, too, can stop and think about a problem.

In another example a naturalist might reason as follows:

I observe that alligators, to protect their young, will carry them in the mouth. This seems rather like the maternal instinctual behavior of mammals in caring for their young. Thus, there may be a similar maternal instinct even in the more primitive reptiles, such as alligators. Indeed, this instinct may have even been present in now-extinct reptiles, such as dinosaurs. If so, then the dinosaurs may have been far more complex and social animals than had been thought.

Analogy is often used to explain ideas. For example Lewis Thomas (1974) wrote

"…science is like an immense anthill; the individual almost vanishes into the mass of minds tumbling over each other, carrying information from place to place, passing it around at the speed of light."

Note that this reasoning by analogy does not establish the validity of the conclusion. What it does is to provide an argument about the possibility or probability that the conclusion might be valid, or it makes an idea more understandable. Nevertheless, reasoning by analogy is critical in science. It helps scientists to clarify ideas and to develop propositions about what might be possible.

Deductive Logic

In addition to the use of analogical, inductive logic, science also employs deductive logic. The logic of deduction guides systematic thinking that leads to valid conclusions. We use the term rationalism to refer to careful reasoning--inductive or deductive. Rationalism is rule-driven. The study of the rules that drive rationalism is what is meant by logic.

Science utilizes both inductive and deductive logic. It is an oversimplification, but still has merit, to note that in science inductive logic helps the scientist to create theories--our best guess about how some aspect of the world works. Reasoning by analogy is often employed in such induction. The major goal of deductive logic is to derive logical predictions from the theories. Induction helps to formulate our hypotheses; deduction helps to validate those hypotheses.

The logic that controls deductive thought in science follows the form of the syllogism. A syllogism is an arrangement of statements that lead deductively to a conclusion. In a deductive syllogism two statements are presented as premises, such as:

  • All autistic children have disrupted social relationships.
  • Joey is an autistic child.

A conclusion is inferred from the two premises:

  • Therefore, Joey has disrupted social relationships.

In the formal deductive syllogism, the conclusion is inferred from the two premises. The premises are assumed to be true and, if they are, the conclusion logically follows. Our expectation that Joey has disrupted social relationships follows from the logic of the argument, but at this point we are not sure that all of the premises of the argument are accurate. Therefore, we need to test this expectation; it becomes our research hypothesis. That is, each proposition and conclusion in science is checked against actual observations of nature. If the logical process and the empirical procedures are sound, but the hypothesis is not confirmed by empirical observations, then one or more of the premises must be false.

In science, whether a premise is true or false depends upon the empirical test of the premise; whether a conclusion is valid depends upon both the correctness of the logic and the empirical test of each premise.

False Conclusions and Logical Fallacies

Fallacies are errors in logic. They often lead to clearly inaccurate conclusions. We see them frequently in everyday usage such as in newspapers, political speeches, conversations, and so on. The conclusions asserted may be false, but they are often propounded with great belief and vigor. Fallacies can often be subtle, so that they may be convincing. Copi and Cohen (2002) note that erroneous arguments and conclusions can occur in either of two ways: the premise(s) might be incorrect or the logic might be faulty.

Incorrect premise

An argument can be erroneous and the conclusions false if one or more of the premises is (are) false. The truth or falsity of a premise can be determined by empirical test. We might hear someone cautioning another: "Stay away from that guy. He's from the South End, and all those people are untrustworthy." The advice (stay away from that guy) may be bad if any of the premises are false. The guy in question might not actually be from the South End or it may be that some South Enders are trustworthy. To formalize the logic in this simple statement, let's look at each of the elements.

  • Premise #1: All people from the South End are untrustworthy.
  • Premise #2: He is from the South End.
  • Conclusion: Therefore, he is untrustworthy.
  • Advice: Stay away from him.

Many everyday conversations end in false conclusions because the premises are false, which may well be what is going on in the above example. The logic may be fine, but logic alone is not sufficient. Focusing on the logic of such statements will not correct the falsity of the premises.

Faulty Logic

The term fallacy is usually reserved for arguments in which the logic is faulty. Logical fallacies are often subtle and hard to detect, making them particularly dangerous when important decisions have to be made. For example, consider the following argument:

That guy says he's from the North Side, but he's really from the South Side. I happen to know that he is very untrustworthy--he cheats all the time. Every single person I have known who is from the South Side is untrustworthy.

If we can unravel that bit of thinking the underlying reasoning would look like this:

  • Premise #1: Everyone I know from the South Side is untrustworthy.
  • Premise #2: He is untrustworthy.
    Conclusion: Therefore, he is from the South Side.

The two premises might be absolutely correct; but the logic is erroneous and the conclusion may be wrong. Can you see the error? One good way to spot such errors is to maintain the form but substitute patently clear statements and erroneous conclusions. For example, while looking at a black cat you might say:

  • Premise #1: All crows are black.
  • Premise #2: This cat is black.
  • Conclusion: Therefore, this cat is a crow.

There are many types of logical fallacies. Copi and Cohen (2002) noted that Aristotle identified 13 types. Since then many have been described and the list is now over 100. These authors discuss a number of common fallacies, some of which are noted below.

Arguing from ignorance. Arguing from ignorance involves shifting the focus from proof for a proposition to proof against it. If you assert something, it is your responsibility to provide the evidence. We have all been in arguments in which someone asserts a conclusion such as "ghosts exist." When we challenge them, they might retort "Can you prove that ghosts do not exist?" Of course we cannot prove a negative. All we can do is examine cases of supposed ghostly visitations and find acceptable alternative explanations for the phenomena. The argument that something is true because it has not yet been proven to be untrue is a logical fallacy. Likewise, it is not logically correct to assert that if something has not been proved, it is untrue. All we can say is that it might or might not be true, weigh the empirical evidence, and draw tentative conclusions about its probabilities of being true.

Arguing by inappropriate authority. In a complex world, we cannot always rationally decide every issue. There simply is not enough time. Therefore, we frequently rely on the advice of authorities--people who are experts on a topic--as a basis for deciding what to do. That is fine, provided the authority really is an expert and is not motivated to give bad advice. Basing an argument on an authority presupposes expertise in the authority figure. If the authority figure is not an expert, the argument is weakened substantially. 

Unfortunately, arguments based on inappropriate authority occur frequently, especially in politics. A person may justify strong opinions on the nature and causes of alcoholism, poverty, AIDS, homelessness, unemployment, or homosexuality because they are also held by a well-respected authority--a Senator who has been chair of the prestigious Senate Medical Policy Committee. 

Basing the validity of propositions on an authority is reasonable, but the authority must be appropriate. Sometimes it is difficult to tell who is an appropriate authority. A U.S. Senator, who may be an appropriate authority on public policy, may not be an authority on medical or social research. A more obvious inappropriate authority is the movie star, who tells us in television commercials that the new Superhoncho V-8 is the best automobile in the country. He may be a good actor, but he may know nothing about cars or, for that matter, on what may be best for each of the millions of people watching the commercial.

Posing complex propositions. Often a question or a conclusion is presented in a complex statement that presupposes the truth of the proposition. For example:

What do average Americans think of the failure of elected officials to improve education by supporting the superior private schools over public schools, which have clearly failed to educate our children?

Perhaps that statement is so blatant it does not need much discussion. Obviously, it states the question in such way that it presupposes the truth of critical beliefs (i.e., public officials have failed, private schools are superior to public schools). In essence, it is a complex statement in the guise of a question.

Ad hominem arguments. Ad hominem arguments are made, not against the logic or validity of a position, but against the person who holds the position. To argue that a position is wrong because the person arguing it is a radical, a communist, a conservative, a Republican, or a Democrat is irrelevant for the logic of the position. Ad hominem arguments can be abusive or circumstantial. The abusive form disparages the opponent's character (e.g., This idea is wrong because it is proposed by a communist.). In the circumstantial form, one ought to accept or reject a proposition because of one's status or group membership (e.g., As an Italian, you should know that Columbus never abused the Indians.). In either case, the person's identity or association has nothing to do with the logic of the position.

Arguments by emotion. Perhaps the most obvious fallacies are those involving arguments that appeal to emotion. The emotional arguments might be bombastic or subtle, but in either case, the impact is to convince people of some proposition by the force of the emotions that are stimulated. Those emotions have nothing to do with the adequacy of the logic of the argument. Television commercials and advertisements of all kinds are virtually all emotion-based, and politicians commonly resort to emotional-based arguments.

These and other fallacies are discussed in detail in Copi and Cohen (2002).

Copi, I. M. & Cohen, C. (2002). Introduction to Logic (11th ed). New York: Macmillan.