Thou shalt not commit logical fallacies

Explanations wrote:One of the most important kinds of nonargument is the explanation. An explanation is an expression that purports to shed light on some event or phenomenon. The event or phenomenon in question is usually accepted as a matter of fact. Examples:

The sky appears blue from the earth's surface because light rays from the sun are scattered by particles in the atmosphere.

The AIDS virus causes sickness and death because it infects certain white blood cells called T cells, and these cells are essential to the body's immune system.

Naval oranges are called by that name because they have a growth that resembles a human naval on the end opposite the stem.

Every explanation is composed of two distinct components: the explanandum and explanans. The explanandum is the statement that describes the event or phenomenon to be explained, and the explanans is the statement or group of statements that purports to do the explaining. In the first example above, the explanandum is the statement "The sky appears blue from the earth's surface" and the explanans is "Light rays from the sun are scattered by particles in the atmosphere."



Explanations are sometimes mistaken for arguments because they often contain the indicator word "because." Yet explanations are not arguments, because in an explanation the purpose of the explanans is to shed light on, or to make sense of, the explanandum event—not to prove that it occurred. In other words, the purpose of the explanans is to show why something is the case, whereas in an argument, the purpose of the premises is to prove that something is the case.

In the first example given, the fact that the sky is blue is readily apparent to everyone. The statement that light rays from the sun are scattered by particles in the atmosphere is not intended to prove that the sky is blue, but rather to show why it is blue. In the second example, practically everyone knows that the AIDS virus causes sickness and death. The purpose of the passage is to explain why this happens—not to prove that it happens. Similarly, in the third example, it is obvious that naval oranges are called naval oranges. The purpose of the passage is to shed light on why they have this name.

Thus, to distinguish explanations from arguments, identify the statement that is either the explanandum or the conclusion (usually this is the statement that precedes the word "because"). If this statement describes an accepted matter of fact, and if the remaining statements purport to shed light on this statement, then the passage is an explanation.

This method usually works to distinguish arguments from explanations. However, some passages can be interpreted as both explanations and arguments. Example:

Women become intoxicated by drinking a smaller amount of alcohol than men because men metabolize part of the alcohol before it reaches the bloodstream, whereas women do not.

The purpose of this passage could be to prove the first statement to those people who do not accept it as fact, and to shed light on that fact to those people who do accept it. Alternately, the passage could be intended to prove the first statement to a single person who accepts its truth on blind faith or incomplete experience, and simultaneously to shed light on this truth. Thus, the passage can be correctly interpreted as both an explanation and an argument.

Perhaps the greatest problem confronting the effort to distinguish explanations from arguments lies in determining whether something is an accepted matter of fact. Obviously, what is accepted by one person may not be accepted by another. Thus, the effort often involves determining which person or group of people the passage is directed to—the intended audience. Sometimes the source of the passage (textbook, newspaper, technical journal, etc.) will decide the issue. But when the passage is taken totally out of context, ascertaining the source may prove impossible. In those circumstances the only possible answer may be to say that if the passage is an argument, then such-and-such is the conclusion and such-and-such are the premises.

Conditional Statements wrote:A conditional statement is an "if ... then ..." statement; for example:

If professional football games incite violence in the home, then the widespread approval given to this sport should be reconsidered.

If Lance Armstrong has won the Tour de France seven consecutive times, then he ranks as king of the hill in the world's most famous bicycle race.

Every conditional statement is made up of two component statements. The component statement immediately following the "if" is called the antecedent, and the one following the "then" is called the consequent. (Occasionally, the word "then" is left out, and occasionally the order of antecedent and consequent is reversed.) In the first example, the antecedent is "Professional football games incite violence in the home," and the consequent is "The widespread approval given to this sport should be reconsidered" In both of these examples, there is a meaningful relationship between antecedent and consequent. However, such a relationship need not exist for a statement to count as conditional. The statement "If Janet Jackson is a singer, then Denver is in Colorado" is just as much a conditional statement as those about professional football and Lance Armstrong.



Conditional statements are not arguments, because they fail to meet the criteria given earlier. In an argument, at least one statement must claim to present evidence, and there must be a claim that this evidence implies something. In a conditional statement, there is no claim that either the antecedent or the consequent presents evidence. In other words, there is no assertion that either the antecedent or the consequent is true. Rather, there is only the assertion that [/i]if[/i] the antecedent is true, then so is the consequent. Of course, a conditional statement as a whole may present evidence because it asserts a relationship between statements. Yet when conditional statements are taken in this sense, there is still no argument, because there is then no separate claim that this evidence implies anything.

Some conditional statements are similar to arguments, however, in that they express the outcome of a reasoning process. As such, they may be said to have a certain inferential content. Consider the following:

If Arnold Schwarzenegger was born a citizen of Austria, then he cannot be elected president of the United States.

If Jennifer Lopez is Marc Anthony's wife, then Marc Anthony is Jennifer Lopez's husband.

The link between the antecedent and consequent of these conditional statements resembles the inferential link between the premises and conclusion of an argument. Yet there is a difference because the premises of an argument are claimed to be true, whereas no such claim is made for the antecedent of a conditional statement. Accordingly, these conditional statements are not arguments.* Yet their inferential content may be reexpressed to form arguments:

Arnold Schwarzenegger was born a citizen of Austria.

Therefore, he cannot be elected president of the United States.

Jennifer Lopez is Marc Anthony's wife.

Therefore, Marc Anthony is Jennifer Lopez's husband.

Finally, while no single conditional statement is an argument, a conditional statement may serve as either the premise or the conclusion (or both) of an argument, as the following examples illustrate:

If Iran is developing nuclear weapons, then Iran is a threat to world peace.

Iran is developing nuclear weapons.

Therefore, Iran is a threat to world peace.

If borders are secure, then terrorists cannot enter the country.

If terrorists cannot enter the country, then acts of terrorism will be reduced.

Therefore, if borders are secure, then acts of terrorism will be reduced.

The relation between conditional statements and arguments may now be summarized as follows:

1. A single conditional statement is not an argument.
2. A conditional statement may serve as either the premise or the conclusion (or both) of an argument.
3. The inferential content of a conditional statement may be reexpressed to form an argument.

The first two rules are especially pertinent to the recognition of arguments. According to the first rule, if a passage consists of a single conditional statement, it is not an argument. But if it consists of a conditional statement together with some other statement, then, by the second rule, it may be an argument, depending on such factors as the presence of indicator words and an inferential relationship between the statements.

Conditional statements are especially important in logic because they express the relationship between necessary and sufficient conditions. A is said to be a sufficient condition for B whenever the occurrence of A is all that is needed for the occurrence of B. For example, being a dog is a sufficient condition for being an animal. On the other hand, B is said to be a necessary condition for A whenever A cannot occur without the occurrence of B. Thus, being an animal is a necessary condition for being a dog. These relationships are expressed in the following conditional statements:

If X is a dog, then X is an animal.

If X is not an animal, then X is not a dog.

The first statement says that being a dog is a sufficient condition for being an animal, and the second that being an animal is a necessary condition for being a dog. However, a little reflection reveals that these two statements say exactly the same thing. Thus, each expresses in one way a necessary condition and in another way a sufficient condition. The terminology of sufficient and necessary conditions will be used in later chapters to express definitions and causal connections.

*In saying this we are temporarily ignoring the possibility of these statements being enthymemes. As we shall see in Chapter 5, an enthymeme is an argument in which a premise or conclusion (or both) is implied but not stated. If, to the second example, we add the premise "Jennifer Lopez is Marc Anthony's wife" and the conclusion "Therefore, Marc Anthony is Jennifer Lopez's husband," we have a complete argument. To decide whether a conditional statement is an enthymeme, we must be familiar with the context in which it occurs.

Summary wrote:In deciding whether a passage contains an argument, you should look for three things: (1) indicator words such as "therefore" "since" "because," and so on; (2) an inferential relationship between the statements; and (3) typical kinds of nonarguments. But remember that the mere occurrence of an indicator word does not guarantee the presence of an argument. You must check to see that the statement identified as the conclusion is claimed to be supported by one or more of the other statements. Also keep in mind that in many arguments that lack indicator words, the conclusion is the first statement. Furthermore, it helps to mentally insert the word "therefore" before the various statements before deciding that a statement should be interpreted as a conclusion. The typical kinds of nonarguments that we have surveyed are as follows:

warnings pieces of advice statements of belief statements of opinion loosely associated statements

reports expository passages illustrations explanations conditional statements

Keep in mind that these kinds of nonargument are not mutually exclusive, and that, for example, one and the same passage can sometimes be interpreted as both a report and a statement of opinion, or as both an expository passage and an illustration. The precise kind of nonargument a passage might be is nowhere near as important as correctly deciding whether or not it is an argument.

Counterexample Method wrote:

Being able to identify the form of an argument with ease requires a familiarity with the basic deductive argument forms. The first task consists in distinguishing the premises from the conclusion. Always write the premises first and the conclusion last. The second task involves distinguishing what we may call "form words" from "content words." To reduce an argument to its form, leave the form words as they are, and replace the content words with letters. For categorical syllogisms, the words "all," "no," "some," "are," and "not" are form words, and for hypothetical syllogisms the words "if," "then," and "not" are form words. Additional form words for other types of arguments are "either," "or," "both," and "and." For various kinds of hybrid arguments, a more intuitive approach may be needed. Here is an example:

All movie stars are actors who are famous, because all movie stars who are famous are actors.

If we replace "movie stars," "actors," and "famous" with the letters M, A, and F, this argument has the following form:

All M who are F are A.

All M are A who are F.

Here is one possible substitution instance for this form:

All humans who are fathers are men.

Therefore, all humans are men who are fathers.

Because the premise is true and the conclusion false, the form is invalid and so is the original argument.

Using the counterexample method to prove arguments invalid requires a little ingenuity because there is no rule that will automatically produce the required term or statement to be substituted into the form. Any term or statement will work, of course, provided that it yields a substitution instance that has premises that are indisputably true and a conclusion that is indisputably false. Ideally, the truth value of these statements should be known to the average individual; otherwise, the substitution instance cannot be depended on to prove anything. If, for example, P in the earlier hypothetical syllogism had been replaced by the statement "George Wilson is dead," the substitution instance would be useless, because nobody knows whether this statement is true or false.

The counterexample method is useful only for proving invalidity, because the only arrangement of truth and falsity that proves anything is true premises and false conclusion. If a substitution instance is produced having true premises and a true conclusion, it does not prove that the argument is valid. Furthermore, the method is useful only for deductive arguments because the strength and weakness of inductive arguments is only partially dependent on the form of the argument. Accordingly, no method that relates exclusively to the form of an inductive argument can be used to prove the argument weak.