Write expository essay for Critical Thinking Class (Philosophy 3) based on Hurley textbook

1.1Arguments, Premises, and Conclusions

How Logical Are You?

· After a momentary absence, you return to your table in the library only to find your smartphone is missing. It was there just minutes earlier. You suspect the student sitting next to you took it. After all, she has a guilty look. Also, there is a bulge in her backpack about the size of your phone, and one of the pouches has a loose strap. Then you hear a “ring” come from the backpack—and it’s the same ringtone that you use on your phone. Which of these pieces of evidence best supports your suspicion?

Answer

The best evidence is undoubtedly the “ring” you hear coming from her backpack, which is the same ringtone as the one on your phone. The weakest evidence is probably the “guilty look.” After all, what, exactly, is a guilty look? The bulge in the backpack and the loose strap are of medium value. The loose strap supports the hypothesis that something was quickly inserted into the backpack. In this section of the chapter you will learn that evidentiary statements form the premises of arguments.

Logic  may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study of logic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own.

An  argument , in its simplest form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose of logic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad.

As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one’s parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A  statement  is a sentence that is either true or false—in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:

Chocolate truffles are loaded with calories.

Melatonin helps relieve jet lag.

Political candidates always tell the complete truth.

No wives ever cheat on their husbands.

Tiger Woods plays golf and Maria Sharapova plays tennis.

The first two statements are true, the second two false. The last one expresses two statements, both of which are true. Truth and falsity are called the two possible  truth values  of a statement. Thus, the truth value of the first two statements is true, the truth value of the second two is false, and the truth value of the last statement, as well as that of its components, is true.

Unlike statements, many sentences cannot be said to be either true or false. Questions, proposals, suggestions, commands, and exclamations usually cannot, and so are not usually classified as statements. The following sentences are not statements:

Where is Khartoum?	(question)
Let’s go to a movie tonight.	(proposal)
I suggest you get contact lenses.	(suggestion)
Turn off the TV right now.	(command)
Fantastic!	(exclamation)

The statements that make up an argument are divided into one or more premises and exactly one conclusion. The  premises  are the statements that set forth the reasons or evidence, and the  conclusion  is the statement that the evidence is claimed to support or imply. In other words, the conclusion is the statement that is claimed to follow from the premises. Here is an example of an argument:

All film stars are celebrities.

Halle Berry is a film star.

Therefore, Halle Berry is a celebrity.

The first two statements are the premises; the third is the conclusion. (The claim that the premises support or imply the conclusion is indicated by the word “therefore.”) In this argument the premises really do support the conclusion, and so the argument is a good one. But consider this argument:

Some film stars are men.

Cameron Diaz is a film star.

Therefore, Cameron Diaz is a man.

In this argument the premises do not support the conclusion, even though they are claimed to, and so the argument is not a good one.

One of the most important tasks in the analysis of arguments is being able to distinguish premises from conclusions. If what is thought to be a conclusion is really a premise, and vice versa, the subsequent analysis cannot possibly be correct. Many arguments contain indicator words that provide clues in identifying premises and conclusion. Some typical  conclusion indicators  are

therefore	Accordingly	entails that
wherefore	we may conclude	hence
thus	it must be that	it follows that
consequently	for this reason	implies that
we may infer	So	as a result

Whenever a statement follows one of these indicators, it can usually be identified as the conclusion. By process of elimination the other statements in the argument are the premises. Example:

Tortured prisoners will say anything just to relieve the pain. Consequently, torture is not a reliable method of interrogation.

The conclusion of this argument is “Torture is not a reliable method of interrogation,” and the premise is “Tortured prisoners will say anything just to relieve the pain.”

If an argument does not contain a conclusion indicator, it may contain a premise indicator. Some typical  premise indicators  are

since	in that	seeing that
as indicated by	may be inferred from	for the reason that
because	As	inasmuch as
for	given that	owing to

Any statement following one of these indicators can usually be identified as a premise. Example:

Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the development of the fetus.

The premise of this argument is “The use of these drugs can jeopardize the development of the fetus,” and the conclusion is “Expectant mothers should never use recreational drugs.”

In reviewing the list of indicators, note that “for this reason” is a conclusion indicator, whereas “for the reason that” is a premise indicator. “For this reason” (except when followed by a colon) means for the reason (premise) that was just given, so what follows is the conclusion. On the other hand, “for the reason that” announces that a premise is about to be stated.

Sometimes a single indicator can be used to identify more than one premise. Consider the following argument:

It is vitally important that wilderness areas be preserved, for wilderness provides essential habitat for wildlife, including endangered species, and it is a natural retreat from the stress of daily life.

The premise indicator “for” goes with both “Wilderness provides essential habitat for wildlife, including endangered species,” and “It is a natural retreat from the stress of daily life.” These are the premises. By method of elimination, “It is vitally important that wilderness areas be preserved” is the conclusion.

Some arguments contain no indicators. With these, the reader/listener must ask such questions as: What single statement is claimed (implicitly) to follow from the others? What is the arguer trying to prove? What is the main point in the passage? The answers to these questions should point to the conclusion. Example:

We must get serious about modernizing our nation’s crumbling infrastructure. Many of our bridges are practically falling down, and our transit system is in dire need of repair. Furthermore, making these improvements would create jobs for millions of workers.

The conclusion of this argument is the first statement, and all of the other statements are premises. The argument illustrates the pattern found in most arguments that lack indicator words: The intended conclusion is stated first, and the remaining statements are then offered in support of this first statement. When the argument is restructured according to logical principles, however, the conclusion is always listed after the premises:

:	Many of our bridges are practically falling down.
:	Our transit system is in dire need of repair.
:	Making these improvements would create jobs for millions of workers.
C:	We must get serious about modernizing our nation’s crumbling infrastructure.

When restructuring arguments such as this, one should remain as close as possible to the original version, while at the same time attending to the requirement that premises and conclusion be complete sentences that are meaningful in the order in which they are listed.

Note that the first two premises are included within the scope of a single sentence in the original argument. For the purposes of this chapter, compound arrangements of statements in which the various components are all claimed to be true will be considered as separate statements.

Passages that contain arguments sometimes contain statements that are neither premises nor conclusions. Only statements that are actually intended to support the conclusion should be included in the list of premises. If, for example, a statement serves merely to introduce the general topic, or merely makes a passing comment, it should not be taken as part of the argument. Examples:

The claim is often made that malpractice lawsuits drive up the cost of health care. But if such suits were outlawed or severely restricted, then patients would have no means of recovery for injuries caused by negligent doctors. Hence, the availability of malpractice litigation should be maintained intact. Massive federal deficits push up interest rates for everyone. Servicing the debt gobbles up a huge portion of the federal budget, which lowers our standard of living. And big deficits also weaken the value of the dollar. For these reasons, Congress must make a determined effort to cut overall spending and raise taxes. Politicians who ignore this reality imperil the future of the nation.

In the first argument, the opening statement serves merely to introduce the topic, so it is not part of the argument. The premise is the second statement, and the conclusion is the last statement. In the second argument, the final statement merely makes a passing comment, so it is not part of the argument. The premises are the first three statements, and the statement following “for these reasons” is the conclusion.

Closely related to the concepts of argument and statement are those of inference and proposition. An  inference , in the narrow sense of the term, is the reasoning process expressed by an argument. In the broad sense of the term, “inference” is used interchangeably with “argument.” Analogously, a  proposition , in the narrow sense, is the meaning or information content of a statement. For the purposes of this book, however, “proposition” and “statement” are used interchangeably.

Note on the History of Logic

The person who is generally credited as the father of logic is the ancient Greek philosopher Aristotle (384–322 b.c.e.). Aristotle’s predecessors had been interested in the art of constructing persuasive arguments and in techniques for refuting the arguments of others, but it was Aristotle who first devised systematic criteria for analyzing and evaluating arguments.

Aristotle’s chief accomplishment is called  syllogistic logic , a kind of logic in which the fundamental elements are terms, and arguments are evaluated as good or bad depending on how the terms are arranged in the argument. Chapters 4 and 5 of this textbook are devoted mainly to syllogistic logic. But Aristotle also deserves credit for originating  modal logic , a kind of logic that involves such concepts as possibility, necessity, belief, and doubt. In addition, Aristotle catalogued several informal fallacies, a topic treated in Chapter 3 of this book.

After Aristotle’s death, another Greek philosopher, Chrysippus (280–206 b.c.e.), one of the founders of the Stoic school, developed a logic in which the fundamental elements were whole propositions. Chrysippus treated every proposition as either true or false and developed rules for determining the truth or falsity of compound propositions from the truth or falsity of their components. In the course of doing so, he laid the foundation for the truth-functional interpretation of the logical connectives presented in Chapter 6 of this book and introduced the notion of natural deduction, treated in Chapter 7.

For thirteen hundred years after the death of Chrysippus, relatively little creative work was done in logic. The physician Galen (c.e. 129–ca. 199) developed the theory of the compound categorical syllogism, but for the most part philosophers confined themselves to writing commentaries on the works of Aristotle and Chrysippus. Boethius (ca. 480–524) is a noteworthy example.

The first major logician of the Middle Ages was Peter Abelard (1079–1142). Abelard reconstructed and refined the logic of Aristotle and Chrysippus as communicated by Boethius, and he originated a theory of universals that traced the universal character of general terms to concepts in the mind rather than to “natures” existing outside the mind, as Aristotle had held. In addition, Abelard distinguished arguments that are valid because of their form from those that are valid because of their content, but he held that only formal validity is the “perfect” or conclusive variety. This textbook follows Abelard on this point.

After Abelard, the study of logic during the Middle Ages flourished through the work of numerous philosophers. A logical treatise by William of Sherwood (ca. 1200–1271) contains the first expression of the “Barbara, Celarent …” poem quoted in Section 5.1 of this book, and the Summulae Logicales of Peter of Spain (ca. 1205–1277) became the standard textbook in logic for three hundred years. However, the most original contributions from this period were made by William of Ockham (ca. 1285–1347). Ockham extended the theory of modal logic, conducted an exhaustive study of the forms of valid and invalid syllogisms, and further developed the idea of a metalanguage, a higher-level language used to discuss linguistic entities such as words, terms, and propositions.

Toward the middle of the fifteenth century, a reaction set in against the logic of the Middle Ages. Rhetoric largely displaced logic as the primary focus of attention; the logic of Chrysippus, which had already begun to lose its unique identity in the Middle Ages, was ignored altogether, and the logic of Aristotle was studied only in highly simplistic presentations. A reawakening did not occur until two hundred years later through the work of Gottfried Wilhelm Leibniz (1646–1716).

Leibniz, a genius in numerous fields, attempted to develop a symbolic language or “calculus” that could be used to settle all forms of disputes, whether in theology, philosophy, or international relations. As a result of this work, Leibniz is sometimes credited with being the father of symbolic logic. Leibniz’s efforts to symbolize logic were carried into the nineteenth century by Bernard Bolzano (1781–1848).

In the middle of the nineteenth century, logic commenced an extremely rapid period of development that has continued to this day. Work in symbolic logic was done by many philosophers and mathematicians, including Augustus De Morgan (1806–1871), George Boole (1815–1864), William Stanley Jevons (1835–1882), and John Venn (1834–1923). The rule bearing De Morgan’s name is used in Chapter 7 of this book. Boole’s interpretation of categorical propositions and Venn’s method for diagramming them are covered in Chapters 4 and 5. At the same time a revival in inductive logic was initiated by the British philosopher John Stuart Mill (1806–1873), whose methods of induction are presented in Chapter 10.

Across the Atlantic, the American philosopher Charles Sanders Peirce (1839–1914) developed a logic of relations, invented symbolic quantifiers, and suggested the truth-table method for formulas in propositional logic. These topics are covered in Chapters 6 and 8 of this book. The truth-table method was completed independently by Emil Post (1897–1954) and Ludwig Wittgenstein (1889–1951).

Toward the end of the nineteenth century, the foundations of modern mathematical logic were laid by Gottlob Frege (1848–1925). His Begriffsschrift sets forth the theory of quantification presented in Chapter 8 of this text. Frege’s work was continued into the twentieth century by Alfred North Whitehead (1861–1947) and Bertrand Russell (1872–1970), whose monumental Principia Mathematica attempted to reduce the whole of pure mathematics to logic. The Principia is the source of much of the symbolism that appears in Chapters 6, 7, and 8 of this text.

During the twentieth century, much of the work in logic focused on the formalization of logical systems and on questions dealing with the completeness and consistency of such systems. A now-famous theorem proved by Kurt Gödel (1906–1978) states that in any formal system adequate for number theory there exists an undecidable formula—that is, a formula such that neither it nor its negation is derivable from the axioms of the system. Other developments included multivalued logics and the formalization of modal logic. Most recently, logic has made a major contribution to technology by providing the conceptual foundation for the electronic circuitry of digital computers.

1.2Recognizing Arguments

How Logical Are You?

· Suppose a friend tells you that he believes life exists on other planets and it’s just a matter of time before someone proves it. You ask him why he believes this, and he replies, “This is my opinion, and I’m entitled to it. I have always held this view, and I have the right to think whatever I choose. You have your opinions, and I have mine. Yours are no better than mine.” Has your friend given you an argument? Why or why not?

Answer

Your friend has not given you an argument. Rather, what he has done is merely assert an opinion. In this section of the chapter you will learn the distinction between opinions and arguments.

Not all passages contain arguments. Because logic deals with arguments, it is important to be able to distinguish passages that contain arguments from those that do not. In general, a passage contains an argument if it purports to prove something; if it does not do so, it does not contain an argument.

In the previous section of this book we learned that every argument has at least one premise and exactly one conclusion. The premise or premises set forth the alleged evidence or reasons, and the conclusion asserts what is claimed to follow from the alleged evidence or reasons. This definition of an argument expresses what is needed for a passage to contain an argument:

1. At least one of the statements must claim to present evidence or reasons.

2. There must be a claim that the alleged evidence supports or implies something—that is, a claim that something follows from the alleged evidence or reasons.

It is not necessary that the premises present actual evidence or true reasons nor that the premises actually support the conclusion. But at least the premises must claim to present evidence or reasons, and there must be a claim that the evidence or reasons support or imply something. Also, you should recognize that the second claim is not equatable with the intentions of the arguer. Intentions are subjective and, as such, are usually not accessible to the evaluator. Rather, this claim is an objective feature of an argument grounded in its language or structure.

Eminent Logicians

Aristotle 384–322 b.c.e.

Aristotle was born in Stagira, a small Greek town situated on the northern coast of the Aegean Sea. His father was a physician in the court of King Amyntas II of Macedonia, and the young Aristotle was a friend of the king’s son Philip, who was later to become king himself and the father of Alexander the Great. When he was about seventeen, Aristotle was sent to Athens to further his education in Plato’s Academy, the finest institution of higher learning in the Greek world. After Plato’s death Aristotle left for Assos, a small town on the coast of Asia Minor, where he married the niece of the local ruler.

Six years later Aristotle accepted an invitation to return to Macedonia to serve as tutor of the young Alexander. When Alexander ascended the throne following his father’s assassination, Aristotle’s tutorial job was finished, and he departed for Athens where he set up a school near the temple of Apollo Lyceus. The school came to be known as the Lyceum, and Alexander supported it with contributions of money and specimens of flora and fauna derived from his far-flung conquests. After Alexander’s death, an anti-Macedonian rebellion forced Aristotle to leave Athens for Chalcis, about thirty miles to the north, where he died one year later at the age of sixty-two.

Aristotle is universally recognized as the originator of logic. He defined logic as the study of the process by which a statement follows by necessity from one or more other statements. The most fundamental kind of statement, he thought, is the categorical proposition, and he classified the four kinds of categorical propositions in terms of their being universal, particular, affirmative, and negative. He also developed the square of opposition, which shows how one such proposition implies the truth or falsity of another, and he identified the relations of conversion, obversion, and contraposition, which provide the basis for various immediate inferences.

Mansell/Time Life Pictures/Getty Images

His crowning achievement is the theory of the categorical syllogism, a kind of argument consisting of three categorical propositions. He showed how categorical syllogisms can be catalogued in terms of mood and figure, and he developed a set of rules for determining the validity of categorical syllogisms. Also, he showed how the modal concepts of possibility and necessity apply to categorical propositions. In addition to the theory of the syllogism, Aristotle advanced the theory of definition by genus and difference, and he showed how arguments could be defective in terms of thirteen forms of informal fallacy.

Aristotle made profound contributions to many areas of human learning including biology, physics, metaphysics, epistemology, psychology, aesthetics, ethics, and politics. However, his accomplishments in logic were so extensive and enduring that two thousand years after his death, the great philosopher Immanuel Kant said that Aristotle had discovered everything that could be known about logic. His logic was not superseded until the end of the nineteenth century when Frege, Whitehead, and Russell developed modern mathematical logic.

In deciding whether a passage contains an argument, the claim that the alleged reasons or evidence supports or implies something is usually the more important of the two. Such a claim can be either explicit or implicit. An explicit claim is usually asserted by premise or conclusion indicator words (“thus,” “since,” “because,” “hence,” “therefore,” and so on). Example:

The Ebola virus has yet to be eradicated, and it kills on average 50 percent of those it infects. Thus, Ebola remains a threat to human health.

The word “thus” expresses the claim that something is being inferred, so the passage is an argument.

An implicit claim exists if there is an inferential relationship between the statements in a passage, but the passage contains no indicator words. Example:

The genetic modification of food is risky business. Genetic engineering can introduce unintended changes into the DNA of the food-producing organism, and these changes can be toxic to the consumer.

The inferential relationship between the first statement and the other two constitutes an implicit claim that evidence supports something, so we are justified in calling the passage an argument. The first statement is the conclusion, and the other two are the premises.

In deciding whether there is a claim that evidence supports or implies something, keep an eye out for

· (1)

premise and conclusion indicator words and

· (2)

the presence of an inferential relationship between the statements.

In connection with these points, however, a word of caution is in order. First, the mere occurrence of an indicator word by no means guarantees the presence of an argument. For example, consider the following passages:

Since Edison invented the phonograph, there have been many technological innovations. Since Edison invented the phonograph, he deserves credit for a major technological innovation.

In the first passage the word “since” is used in a temporal sense. It means “from the time that.” Thus, the first passage is not an argument. In the second passage “since” is used in a logical sense, and so the passage is an argument.

The second cautionary point is that it is not always easy to detect the occurrence of an inferential relationship between the statements in a passage, and one may have to review a passage several times before making a decision. In reaching such a decision, one may find it helpful to mentally insert the word “therefore” before the various statements to see whether it makes sense to interpret one of them as following from the others. Even with this mental aid, however, the decision whether a passage contains an inferential relationship (as well as the decision about indicator words) often involves a heavy dose of interpretation. As a result, not everyone will agree about every passage. Sometimes the only answer possible is a conditional one: “If this passage contains an argument, then these are the premises and that is the conclusion.”

To assist in distinguishing passages that contain arguments from those that do not, let us now investigate some typical kinds of nonarguments. These include simple noninferential passages, expository passages, illustrations, explanations, and conditional statements.

Simple Noninferential Passages

Simple noninferential passages are unproblematic passages that lack a claim that anything is being proved. Such passages contain statements that could be premises or conclusions (or both), but what is missing is a claim that any potential premise supports a conclusion or that any potential conclusion is supported by premises. Passages of this sort include warnings, pieces of advice, statements of belief or opinion, loosely associated statements, and reports.

A  warning  is a form of expression that is intended to put someone on guard against a dangerous or detrimental situation. Examples:

Watch out that you don’t slip on the ice. Whatever you do, never confide personal secrets to Blabbermouth Bob.

If no evidence is given to prove that such statements are true, then there is no argument.

A  piece of advice  is a form of expression that makes a recommendation about some future decision or course of conduct. Examples:

You should keep a few things in mind before buying a used car. Test drive the car at varying speeds and conditions, examine the oil in the crankcase, ask to see service records, and, if possible, have the engine and power train checked by a mechanic. Before accepting a job after class hours, I would suggest that you give careful consideration to your course load. Will you have sufficient time to prepare for classes and tests, and will the job produce an excessive drain on your energies?

As with warnings, if there is no evidence that is intended to prove anything, then there is no argument.

A  statement of belief  or  opinion  is an expression about what someone happens to believe or think about something. Examples:

We believe that our company must develop and produce outstanding products that will perform a great service or fulfill a need for our customers. We believe that our business must be run at an adequate profit and that the services and products we offer must be better than those offered by competitors.

(Robert D. Hay and Edmund R. Gray, “Introduction to Social Responsibility”)

When I can read the latte menu through the hole in my server’s earlobe, something is seriously out of whack. What happened to an earring, maybe two, in each lobe? Now any surface is game. Brow, lip, tongue, cheek, nose. I’ve adjusted to untied shoelaces and pants that make mooning irrelevant. But when it comes to piercings, I just can’t budge.

(Debra Darvick, “Service with a Smile, and Plenty of Metal”)

Because neither of these statements asserts any claim that a belief or opinion is supported by evidence, or that it supports some conclusion, there is no argument.

Loosely associated statements  may be about the same general subject, but they lack a claim that one of them is proved by the others. Example:

Not to honor men of worth will keep the people from contention; not to value goods that are hard to come by will keep them from theft; not to display what is desirable will keep them from being unsettled of mind.

(Lao-Tzu, Thoughts from the Tao Te Ching)

Because there is no claim that any of these statements provides evidence or reasons for believing another, there is no argument.

A  report  consists of a group of statements that convey information about some topic or event. Example:

The period of 1648–1789 was one of competition among the primary monarchs of Europe. Wars among the great powers were frequent but limited. France made major efforts to become paramount, but the balance of power operated to block French expansion.

(Steven L. Spiegel, World Politics in a New Era)

These statements could serve as the premises of an argument, but because the author makes no claim that they support or imply anything, there is no argument. Another type of report is the news report:

Witnesses said they heard a loud crack before a balcony gave way at a popular nightspot, dropping dozens of screaming people fourteen feet. At least eighty people were injured at the Diamond Horseshoe casino when they fell onto broken glass and splintered wood. Investigators are waiting for an engineer’s report on the deck’s occupancy load.

(Newspaper clipping)

Again, because the reporter makes no claim that these statements imply anything, there is no argument.

One must be careful, though, with reports about arguments:

“The Air Force faces a serious shortage of experienced pilots in the years ahead, because repeated overseas tours and the allure of high-paying jobs with commercial airlines are winning out over lucrative bonuses to stay in the service,” says a prominent Air Force official.

(Newspaper clipping)

Properly speaking, this passage is not an argument, because the author of the passage does not claim that anything is supported by evidence. Rather, the author reports the claim by the Air Force official that something is supported by evidence. If such passages are interpreted as “containing” arguments, it must be made clear that the argument is not the author’s but one made by someone about whom the author is reporting.

Expository Passages

An  expository passage  is a kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence. If the objective is not to prove the topic sentence but only to expand it or elaborate it, then there is no argument. Examples:

There are three familiar states of matter: solid, liquid, and gas. Solid objects ordinarily maintain their shape and volume regardless of their location. A liquid occupies a definite volume, but assumes the shape of the occupied portion of its container. A gas maintains neither shape nor volume. It expands to fill completely whatever container it is in.

(John W. Hill and Doris K. Kolb, Chemistry for Changing Times, 7th ed.)

There is a stylized relation of artist to mass audience in the sports, especially in baseball. Each player develops a style of his own—the swagger as he steps to the plate, the unique windup a pitcher has, the clean-swinging and hard-driving hits, the precision quickness and grace of infield and outfield, the sense of surplus power behind whatever is done.

(Max Lerner, America as a Civilization)

In each passage the topic sentence is stated first, and the remaining sentences merely develop and flesh out this topic sentence. These passages are not arguments, because they lack an inferential claim. However, expository passages differ from simple noninferential passages (such as warnings and pieces of advice) in that many of them can also be taken as arguments. If the purpose of the subsequent sentences in the passage is not only to flesh out the topic sentence but also to prove it, then the passage is an argument. Example:

Skin and the mucous membrane lining the respiratory and digestive tracts serve as mechanical barriers to entry by microbes. Oil-gland secretions contain chemicals that weaken or kill bacteria on skin. The respiratory tract is lined by cells that sweep mucus and trapped particles up into the throat, where they can be swallowed. The stomach has an acidic pH, which inhibits the growth of many types of bacteria.

(Sylvia S. Mader, Human Biology, 4th ed.)

In this passage the topic sentence is stated first, and the purpose of the remaining sentences is not only to show how the skin and mucous membranes serve as barriers to microbes but also to prove that they do this. Thus, the passage can be taken as both an expository passage and an argument.

In deciding whether an expository passage should be interpreted as an argument, try to determine whether the purpose of the subsequent sentences in the passage is merely to develop the topic sentence or also to prove that it is true. In borderline cases, ask yourself whether the topic sentence makes a claim that everyone accepts or agrees with. If it does, the passage is probably not an argument. In real-life situations authors rarely try to prove something is true when everyone already accepts it. However, if the topic sentence makes a claim that many people do not accept or have never thought about, then the purpose of the remaining sentences may be both to prove the topic sentence is true as well as to develop it. If this is so, the passage is an argument.

Finally, if even this procedure yields no definite answer, the only alternative may be to say that if the passage is taken as an argument, then the first statement is the conclusion and the others are the premises.

Illustrations

An  illustration  is an expression involving one or more examples that is intended to show what something means or how it is done. Illustrations are often confused with arguments because many illustrations contain indicator words such as “thus.” Examples:

Chemical elements, as well as compounds, can be represented by molecular formulas. Thus, oxygen is represented by “,” water by “,” and sodium chloride by “.” A deciduous tree is any tree that loses its leaves during the winter. For example, maples are deciduous. And so are elms, poplars, hawthorns, and alders.

These selections are not arguments, because they make no claim that anything is being proved. In the first selection, the word “thus” indicates how something is done—namely, how chemical elements and compounds can be represented by formulas. In the second, the examples cited are intended to illustrate the meaning of the word “deciduous.” It pins down the meaning by providing concrete instances.

However, as with expository passages, many illustrations can be taken as arguments. Such arguments are often called  arguments from example . Here is an instance of one:

Although most forms of cancer, if untreated, can cause death, not all cancers are life threatening. For example, basal cell carcinoma, the most common of all skin cancers, can produce disfigurement, but it almost never results in death.

In this passage the example given is intended to prove the truth of “Not all cancers are life threatening.” Thus, the passage is best interpreted as an argument.

In deciding whether an illustration should be interpreted as an argument, determine whether the passage merely shows how something is done or what something means, or whether it also purports to prove something. In borderline cases it helps to note whether the claim being illustrated is one that practically everyone accepts or agrees with. If it is, the passage is probably not an argument. As already noted, in real-life situations authors rarely attempt to prove what everyone already accepts. But if the claim being illustrated is one that many people do not accept or have never thought about, then the passage may be interpreted as an argument.

Thus, in reference to the first two examples we considered, most people are aware that elements and compounds can be expressed by formulas—practically everyone knows that water is —and most people have at least a vague idea of what a deciduous tree is. But they may not have ever considered whether some forms of cancer are not life threatening. This is one of the reasons for evaluating the first two examples as mere illustrations and the last one as an argument.

Explanations

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. Golf balls have a dimpled surface because the dimples reduce air drag, causing the ball to travel farther. Navel oranges are called by that name because they have a growth that resembles a human navel 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, 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 golf balls have a dimpled surface. The purpose of the passage is to explain why they have a dimpled surface—not to prove that they do. 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. Examples:

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. Household bleach should never be mixed with ammonia because the combination releases chlorine gas, which is highly poisonous.

The purpose of these passages could be to prove the first statement to those who do not accept it as fact, and to shed light on that fact to those who do accept it. Alternately, the passage could be intended to prove the first statement to a person who accepts its truth on blind faith or incomplete experience, and simultaneously to shed light on this truth. Thus, these passages 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

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 Roger Federer has played in more Grand Slam finals than any other contender, then he rightfully deserves the title of world’s greatest tennis player.

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 Taylor Swift is a singer, then Denver is in Colorado” is just as much a conditional statement as those about professional football and Roger Federer.

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 if 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 sugary drinks cause heart disease and diabetes, then sugary drinks should be regulated.

The link between the antecedent and consequent 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, conditional statements are not arguments. Yet their inferential content may be reexpressed to form arguments:

Sugary drinks cause heart disease and diabetes.

Therefore, sugary drinks should be regulated.

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 North Korea is developing nuclear weapons, then North Korea is a threat to world peace.

North Korea is developing nuclear weapons.

Therefore, North Korea is a threat to world peace.

If our borders are porous, then terrorists can enter the country at will.

If terrorists can enter the country at will, then all of us are less secure.

Therefore, if our borders are porous, then all of us are less secure.

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 (and many other fields) 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.

The difference between sufficient and necessary conditions is a bit tricky. So, to clarify the idea further, suppose you are given a large, closed cardboard box. Also, suppose you are told there is a dog in the box. Then you know for sure there is an animal in the box. No additional information is needed to draw this conclusion. This means that being a dog is sufficient for being an animal. However, being a dog is not necessary for being an animal, because if you are told that the box contains a cat, you can conclude with equal certainty that it contains an animal. In other words, it is not necessary for the box to contain a dog for it to contain an animal. It might equally well contain a cat, a mouse, a squirrel, or any other animal.

On the other hand, suppose you are told that whatever might be in the box, it is not an animal. Then you know for certain there is no dog in the box. The reason you can draw this conclusion is that being an animal is necessary for being a dog. If there is no animal, there is no dog. However, being an animal is not sufficient for being a dog, because if you are told that the box contains an animal, you cannot, from this information alone, conclude that it contains a dog. It might contain a cat, a mouse, a squirrel, and so on.

These ideas 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.

1.3Deduction and Induction

How Logical Are You?

· Recreational marijuana is not legal in your state, but there is a referendum coming up that would make it legal. You do some research and find that every state that has legalized recreational marijuana up to that date is a politically “blue” state. But your state is “red”—and becoming even more so. You conclude that your state will not be legalizing marijuana any time soon. Does your conclusion follow with certainty? If not, does it follow with probability?

Answer

Your conclusion does not follow with certainty, but it does follow with probability. The inference depends on the causal connection between being Republican and the tendency to resist the legalization of marijuana. In this section of the chapter, you will learn that causal inferences are probabilistic and are called inductive. On the other hand, arguments having conclusions that follow with certainty are deductive.

The idea that arguments come in two forms, deductive and inductive, was first asserted by Aristotle. In the intervening centuries, deduction and induction have become a settled fixture not only in logic but in our intellectual culture. Countless books, both fiction and nonfiction, have referred to it. Einstein wrote a paper on it. And a huge number of textbooks ranging from philosophy to education, business to psychology, and chemistry to anthropology explore the subject. So what is the difference between a deductive and an inductive argument? Briefly we can say that deductive arguments are those that rest on necessary reasoning, while inductive arguments are those that rest on probabilistic reasoning.

Ruth Barcan Marcus 1921–2012

Ruth Barcan was born in New York City in 1921. Her mother was a homemaker, and her father a typesetter at, and contributor to, the Jewish Daily Forward. After completing her primary and secondary education at public schools, she enrolled in New York University, where, in addition to her academic pursuits, she won praise as an outstanding fencer. In 1941 she earned a bachelor’s degree in mathematics and philosophy, and five years later she received a PhD in philosophy from Yale University. In 1942 she married Jules Alexander Marcus, a physicist, and the couple had four children, two boys and two girls.

After graduating from Yale, Barcan Marcus’s early career was spent holding several postdoctoral fellowships (including a Guggenheim) and visiting professorships. In 1959 she accepted a position at Roosevelt University, followed by positions at the University of Illinois, Chicago (where she was founding department chair) and Northwestern University. In 1973 she returned to Yale as professor of philosophy.

Commencing early in her career, Barcan Marcus made pioneering contributions to the area of quantified modal logic. She proposed, as an axiom, the widely discussed Barcan formula, which asserts, in symbols, (x)□Fx ﬤ□(x)Fx. In English, this means that if everything is necessarily F, then it is necessary that everything is F. The formula is controversial because it implies that all objects that exist in every possible world exist in the actual world. This could be taken to imply that nothing new can be created.

Courtesy Michael Marsland

Personally, Ruth Barcan Marcus was fearless, down to earth, unpretentious, and a constant supporter of others. She had a great sense of humor—and she was also endearingly absentminded. On one occasion, while in the midst of a frantic search, she received a call from the local supermarket informing her that her final exams had been found amid the frozen meats.

Stated more precisely, a  deductive argument  is an argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. On the other hand, an  inductive argument  is an argument incorporating the claim that it is improbable that the conclusion be false given that the premises are true. Two examples:

The meerkat is closely related to the suricat.

The suricat thrives on beetle larvae.

Therefore, probably the meerkat thrives on beetle larvae.

The meerkat is a member of the mongoose family.

All members of the mongoose family are carnivores.

Therefore, it necessarily follows that the meerkat is a carnivore.

The first of these arguments is inductive, the second deductive.

In deciding whether an argument is inductive or deductive, we look to certain objective features of the argument. These features include

· (1)

the occurrence of special indicator words,

· (2)

the actual strength of the inferential link between premises and conclusion, and

· (3)

the form or style of argumentation.

However, we must acknowledge at the outset that many arguments in ordinary language are incomplete, and because of this, deciding whether the argument should best be interpreted as deductive or inductive may be impossible.

The occurrence of special indicator words is illustrated in the examples we just considered. The word “probably” in the conclusion of the first argument suggests that the argument should be taken as inductive, and the word “necessarily” in the conclusion of the second suggests that the second argument be taken as deductive. Additional inductive indicators are “improbable,” “plausible,” “implausible,” “likely,” “unlikely,” and “reasonable to conclude.” Additional deductive indicators are “certainly,” “absolutely,” and “definitely.” (Note that the phrase “it must be the case that” is simply a conclusion indicator that can occur in either deductive or inductive argments.)

Inductive and deductive indicator words often suggest the correct interpretation. However, if they conflict with one of the other criteria (discussed shortly), we should probably ignore them. Arguers often use phrases such as “it certainly follows that” for rhetorical purposes to add impact to their conclusion and not to suggest that the argument be taken as deductive. Similarly, some arguers, not knowing the distinction between inductive and deductive, will claim to “deduce” a conclusion when their argument is more correctly interpreted as inductive.

The second factor that bears on our interpretation of an argument as inductive or deductive is the actual strength of the inferential link between premises and conclusion. If the conclusion actually does follow with strict necessity from the premises, the argument is clearly deductive. In such an argument it is impossible for the premises to be true and the conclusion false. On the other hand, if the conclusion does not follow with strict necessity but does follow probably, it is often best to consider the argument inductive. Examples:

All entertainers are extroverts.

Stephen Colbert is an entertainer.

Therefore, Stephen Colbert is an extrovert.

The vast majority of entertainers are extroverts.

Stephen Colbert is an entertainer.

Therefore, Stephen Colbert is an extrovert.

In the first example, the conclusion follows with strict necessity from the premises. If we assume that all entertainers are extroverts and that Stephen Colbert is an entertainer, then it is impossible that Stephen Colbert not be an extrovert. Thus, we should interpret this argument as deductive. In the second example, the conclusion does not follow from the premises with strict necessity, but it does follow with some degree of probability. If we assume that the premises are true, then based on that assumption it is probable that the conclusion is true. Thus, it is best to interpret the second argument as inductive.

Occasionally, an argument contains no special indicator words, and the conclusion does not follow either necessarily or probably from the premises; in other words, it does not follow at all. This situation points to the need for the third factor to be taken into account, which is the character or form of argumentation the arguer uses.

Deductive Argument Forms

Many arguments have a distinctive character or form that indicates that the premises are supposed to provide absolute support for the conclusion. Five examples of such forms or kinds of argumentation are arguments based on mathematics, arguments from definition, and categorical, hypothetical, and disjunctive syllogisms.

An  argument based on mathematics  is an argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement. For example, a shopper might place two apples and three oranges into a paper bag and then conclude that the bag contains five pieces of fruit. Or a surveyor might measure a square piece of land and, after determining that it is 100 feet on each side, conclude that it contains 10,000 square feet. Since all arguments in pure mathematics are deductive, we can usually consider arguments that depend on mathematics to be deductive as well. However, arguments that depend on statistics are a noteworthy exception. As we will see shortly, such arguments are usually best interpreted as inductive.

An  argument from definition  is an argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion. For example, someone might argue that because Claudia is mendacious, it follows that she tells lies, or that because a certain paragraph is prolix, it follows that it is excessively wordy. These arguments are deductive because their conclusions follow with necessity from the definitions of “mendacious” and “prolix.”

A syllogism, in general, is an argument consisting of exactly two premises and one conclusion. Categorical syllogisms will be treated in greater depth in Chapter 5, but for now we will say that a  categorical syllogism  is a syllogism in which each statement begins with one of the words “all,” “no,” or “some.” Example:

All ancient forests are sources of wonder.

Some ancient forests are targets of the timber industry.

Therefore, some sources of wonder are targets of the timber industry.

Arguments such as these are nearly always best treated as deductive.

A  hypothetical syllogism  is a syllogism having a conditional (“if … then”) statement for one or both of its premises. Examples:

If estate taxes are abolished, then wealth will accumulate disproportionately.

If wealth accumulates disproportionately, then democracy will be threatened.

Therefore, if estate taxes are abolished, then democracy will be threatened.

If Fox News is a propaganda machine, then it misleads its viewers.

Fox News is a propaganda machine.

Therefore, Fox News misleads its viewers.

Later in this book, the first of these arguments will be given the more specific name of pure hypothetical syllogism because it is composed exclusively of conditional (hypothetical) statements. The second argument is called a mixed hypothetical syllogism because only one of its component statements is a conditional. Later in this book, the second argument will be given the more specific Latin name modus ponens.

A  disjunctive syllogism  is a syllogism having a disjunctive (“either … or…”) statement. Example:

Either global warming will be arrested, or hurricanes will become more intense.

Global warming will not be arrested.

Therefore, hurricanes will become more intense.

As with hypothetical syllogisms, such arguments are usually best taken as deductive. Hypothetical and disjunctive syllogisms will be treated in greater depth in Chapter 6.

Inductive Argument Forms

In general, inductive arguments are such that the content of the conclusion is in some way intended to “go beyond” the content of the premises. The premises of such an argument typically deal with some subject that is relatively familiar, and the conclusion then moves beyond this to a subject that is less familiar or that little is known about. Such an argument may take any of several forms: predictions about the future, arguments from analogy, inductive generalizations, arguments from authority, arguments based on signs, and causal inferences, to name just a few.

A  prediction  is an argument that proceeds from our knowledge of the past to a claim about the future. For example, someone might argue that because certain meteorological phenomena have been observed to develop over a certain region of central Missouri, a storm will occur there in six hours. Or again, one might argue that because certain fluctuations occurred in the prime interest rate on Friday, the value of the dollar will decrease against foreign currencies on Monday. Nearly everyone realizes that the future cannot be known with certainty; thus, whenever an argument makes a prediction about the future, one is usually justified in considering the argument inductive.

An  argument from analogy  is an argument that depends on the existence of an analogy, or similarity, between two things or states of affairs. Because of the existence of this analogy, a certain condition that affects the better-known thing or situation is concluded to affect the similar, lesser-known thing or situation. For example, someone might argue that because Christina’s Porsche is a great-handling car, it follows that Angela’s Porsche must also be a great-handling car. The argument depends on the existence of a similarity, or analogy, between the two cars. The certitude attending such an inference is probabilistic at best.

A  generalization  is an argument that proceeds from the knowledge of a selected sample to some claim about the whole group. Because the members of the sample have a certain characteristic, it is argued that all the members of the group have that same characteristic. For example, one might argue that because three oranges selected from a certain crate were especially tasty and juicy, all the oranges from that crate are especially tasty and juicy. Or again, one might argue that because six out of a total of nine members sampled from a certain labor union intend to vote for Johnson for union president, two-thirds of the entire membership intend to vote for Johnson. These examples illustrate the use of statistics in inductive argumentation.

An  argument from authority  is an argument that concludes something is true because a presumed expert or witness has said that it is. For example, a person might argue that earnings for Hewlett-Packard Corporation will be up in the coming quarter because of a statement to that effect by an investment counselor. Or a lawyer might argue that Mack the Knife committed the murder because an eyewitness testified to that effect under oath. Because the investment counselor and the eyewitness could be either mistaken or lying, such arguments are essentially probabilistic.

An  argument based on signs  is an argument that proceeds from the knowledge of a sign to a claim about the thing or situation that the sign symbolizes. The word “sign,” as it is used here, means any kind of message (usually visual) produced by an intelligent being. For example, when driving on an unfamiliar highway one might see a sign indicating that the road makes several sharp turns one mile ahead. Based on this information, one might argue that the road does indeed make several sharp turns one mile ahead. Because the sign might be misplaced or in error about the turns, the conclusion is only probable.

A  causal inference  is an argument that proceeds from knowledge of a cause to a claim about an effect, or, conversely, from knowledge of an effect to a claim about a cause. For example, from the knowledge that a bottle of wine had been accidentally left in the freezer overnight, someone might conclude that it had frozen (cause to effect). Conversely, after tasting a piece of chicken and finding it dry and tough, one might conclude that it had been overcooked (effect to cause). Because specific instances of cause and effect can never be known with absolute certainty, one may usually interpret such arguments as inductive.

Further Considerations

It should be noted that the various subspecies of inductive arguments listed here are not intended to be mutually exclusive. Overlaps can and do occur. For example, many causal inferences that proceed from cause to effect also qualify as predictions. The purpose of this survey is not to demarcate in precise terms the various forms of induction but rather to provide guidelines for distinguishing induction from deduction.

Keeping this in mind, we should take care not to confuse arguments in geometry, which are always deductive, with arguments from analogy or inductive generalizations. For example, an argument concluding that a triangle has a certain attribute (such as a right angle) because another triangle, with which it is congruent, also has that attribute might be mistaken for an argument from analogy. Similarly, an argument that concludes that all triangles have a certain attribute (such as angles totaling two right angles) because any particular triangle has that attribute might be mistaken for an inductive generalization. Arguments such as these, however, are always deductive, because the conclusion follows necessarily and with complete certainty from the premises.

One broad classification of arguments not listed in this survey is scientific arguments. Arguments that occur in science can be either inductive or deductive, depending on the circumstances. In general, arguments aimed at the discovery of a law of nature are usually considered inductive. Suppose, for example, that we want to discover a law that governs the time required for a falling body to strike the earth. We drop bodies of various weights from various heights and measure the time it takes them to fall. Comparing our measurements, we notice that the time is approximately proportional to the square root of the distance. From this we conclude that the time required for any body to fall is proportional to the square root of the distance through which it falls. Such an argument is best interpreted as an inductive generalization.

Another type of argument that occurs in science has to do with the application of known laws to specific circumstances. Scientific laws are widely considered to be generalizations that hold for all times and all places. As so understood, their application to a specific situation is always deductive, even though it might relate to the future. Suppose, for example, that we want to apply Boyle’s law for ideal gases to a container of gas in our laboratory. Boyle’s law states that the pressure exerted by a gas on the walls of its container is inversely proportional to the volume. Applying this law, we conclude that when we reduce the volume of our laboratory sample by half, the pressure will double. This application of Boyle’s law is deductive, even though it pertains to the future.

A final point needs to be made about the distinction between inductive and deductive arguments. There is a tradition extending back to the time of Aristotle that holds that inductive arguments are those that proceed from the particular to the general, while deductive arguments are those that proceed from the general to the particular. (A  particular statement  is one that makes a claim about one or more particular members of a class, while a  general statement  makes a claim about all the members of a class.) It is true, of course, that many inductive and deductive arguments do work in this way; but this fact should not be used as a criterion for distinguishing induction from deduction. As a matter of fact, there are deductive arguments that proceed from the general to the general, from the particular to the particular, and from the particular to the general, as well as from the general to the particular; and there are inductive arguments that do the same. For example, here is a deductive argument that proceeds from the particular to the general:

Three is a prime number.

Five is a prime number.

Seven is a prime number.

Therefore, all odd numbers between two and eight are prime numbers.

And here is one that proceeds from the particular to the particular:

Gabriel is a wolf.

Gabriel has a tail.

Therefore, Gabriel’s tail is the tail of a wolf.

Here is an inductive argument that proceeds from the general to the particular:

All emeralds previously found have been green.

Therefore, the next emerald to be found will be green.

The other varieties are easy to construct. Thus, the progression from particular to general, and vice versa, cannot be used as a criterion for distinguishing induction from deduction.

1.4Validity, Truth, Soundness, Strength, Cogency

How Logical Are You?

· Instagram does not allow the posting of photos. Therefore, you will not be allowed to post any of your selfies on Instagram, and you will not be able to see any photos of your friends on Instagram. Does this conclusion follow from the premise? Why or why not?

Answer

The conclusion does follow from the premise. If you assume the premise is true, the conclusion follows with certainty. However, the premise is actually false. Instagram does allow the posting of photos. In this section of the chapter you will learn how to analyze and classify arguments such as this one.

This section introduces the central ideas and terminology needed to evaluate arguments—to distinguish good arguments from bad arguments. Regardless of the type of argument, whether deductive or inductive, the evaluation of any argument involves answering two distinct questions:

· (1)

Do the premises support the conclusion?

· (2)

Are all the premises true?

The answer to the first question is the more important one, because if the premises fail to support the conclusion (that is, if the reasoning is bad), the argument is worthless. The material that follows first considers deductive arguments and then inductive.

Deductive Arguments

The previous section defined a deductive argument as one incorporating the claim that it is impossible for the conclusion to be false given that the premises are true. If this claim is true, the argument is said to be valid. Thus, a  valid deductive argument  is an argument in which it is impossible for the conclusion to be false given that the premises are true. In these arguments the conclusion follows with strict necessity from the premises. Conversely, an  invalid deductive argument  is a deductive argument in which it is possible for the conclusion to be false given that the premises are true. In these arguments the conclusion does not follow with strict necessity from the premises, even though it is claimed to.

An immediate consequence of these definitions is that there is no middle ground between valid and invalid. There are no arguments that are “almost” valid and “almost” invalid. If the conclusion follows with strict necessity from the premises, the argument is valid; if not, it is invalid.

To test an argument for validity we begin by assuming that all the premises are true, and then we determine if it is possible, in light of that assumption, for the conclusion to be false. Here is an example:

All television networks are media companies.

NBC is a television network.

Therefore, NBC is a media company.

In this argument both premises are actually true, so it is easy to assume that they are true. Next we determine, in light of this assumption, if it is possible for the conclusion to be false. Clearly this is not possible. If NBC is included in the group of television networks (second premise) and if the group of television networks is included in the group of media companies (first premise), it necessarily follows that NBC is included in the group of media companies (conclusion). In other words, assuming the premises to be true and the conclusion false entails a strict contradiction. Thus, the argument is valid.

Here is another example:

All automakers are computer manufacturers.

United Airlines is an automaker.

Therefore, United Airlines is a computer manufacturer.

In this argument, both premises are actually false, but it is easy to assume that they are true. Every automaker could have a corporate division that manufactures computers. Also, in addition to flying airplanes, United Airlines could make cars. Next, in light of these assumptions, we determine if it is possible for the conclusion to be false. Again, we see that this is not possible, by the same reasoning as the previous example. Assuming the premises to be true and the conclusion false entails a contradiction. Thus, the argument is valid.

Another example:

All banks are financial institutions.

Wells Fargo is a financial institution.

Therefore, Wells Fargo is a bank.

As in the first example, both premises of this argument are true, so it is easy to assume they are true. Next we determine, in light of this assumption, if it is possible for the conclusion to be false. In this case it is possible. If banks were included in one part of the group of financial institutions and Wells Fargo were included in another part, then Wells Fargo would not be a bank. In other words, assuming the premises to be true and the conclusion false does not involve any contradiction, and so the argument is invalid.

In addition to illustrating the basic idea of validity, these examples suggest an important point about validity and truth. In general, validity is not something that is uniformly determined by the actual truth or falsity of the premises and conclusion. Both the NBC example and the Wells Fargo example have actually true premises and an actually true conclusion, yet one is valid and the other invalid. The United Airlines example has actually false premises and an actually false conclusion, yet the argument is valid. Rather, validity is something that is determined by the relationship between premises and conclusion. The question is not whether the premises and conclusion are true or false, but whether the premises support the conclusion. In the examples of valid arguments the premises do support the conclusion, and in the invalid case they do not.

Nevertheless, there is one arrangement of truth and falsity in the premises and conclusion that does determine the issue of validity. Any deductive argument having actually true premises and an actually false conclusion is invalid. The reasoning behind this fact is fairly obvious. If the premises are actually true and the conclusion is actually false, then it certainly is possible for the premises to be true and the conclusion false. Thus, by the definition of invalidity, the argument is invalid.

The idea that any deductive argument having actually true premises and a false conclusion is invalid may be the most important point in all of deductive logic. The entire system of deductive logic would be quite useless if it accepted as valid any inferential process by which a person could start with truth in the premises and arrive at falsity in the conclusion.

Table 1.1 presents examples of categorical syllogisms (deductive arguments) that illustrate the various combinations of truth and falsity in the premises and conclusion. In the examples having false premises, both premises are false, but it is easy to construct other examples having only one false premise. When examining this table, note that the only combination of truth and falsity that does not allow for both valid and invalid arguments is true premises and false conclusion. As we have just seen, any argument having this combination is necessarily invalid.

Table 1.1

Deductive Arguments

	Valid	Invalid
True premises	All flowers are plants. All daisies are flowers.	All flowers are plants. All daisies are plants.
True conclusion	Therefore, all daisies are plants. [sound]	Therefore, all daisies are flowers. [unsound]
True premises	None exist	All roses are flowers. All daisies are flowers.
False conclusion		Therefore, all daisies are roses. [unsound]
False premises	All flowers are dogs. All poodles are flowers.	All dogs are flowers. All poodles are flowers.
True conclusion	Therefore, all poodles are dogs. [unsound]	Therefore, all poodles are dogs. [unsound]
False premises	All flowers are dogs. All tigers are flowers.	All roses are cats. All daisies are cats.
False conclusion	Therefore, all tigers are dogs. [unsound]	Therefore, all daisies are roses. [unsound]

The relationship between the validity of a deductive argument and the truth or falsity of its premises and conclusion, as illustrated in Table 1.1, is summarized as follows:

Premises	Conclusion	Validity
T	T	?
T	F	Invalid
F	T	?
F	F	?

This short summary table reinforces the point that merely knowing the truth or falsity of the premises and conclusion tells us nothing about validity except in the one case of true premises and false conclusion. Any deductive argument having true premises and a false conclusion is necessarily invalid.

A  sound argument  is a deductive argument that is valid and has all true premises. Both conditions must be met for an argument to be sound; if either is missing the argument is unsound. Thus, an  unsound argument  is a deductive argument that is invalid, has one or more false premises, or both. Because a valid argument is one such that it is impossible for the premises to be true and the conclusion false, and because a sound argument does in fact have true premises, it follows that every sound argument, by definition, will have a true conclusion as well. A sound argument, therefore, is what is meant by a good, or successful, deductive argument in the fullest sense of the term.

In connection with this definition of soundness, a single proviso is required: For an argument to be unsound, the false premise or premises must actually be needed to support the conclusion. An argument having a conclusion that is validly supported by true premises but having a superfluous false premise would still be sound. By similar reasoning, no addition of a false premise to an originally sound argument can make the argument unsound. Such a premise would be superfluous and should not be considered part of the argument. Analogous remarks, incidentally, extend to induction.

Since (at least from the standpoint of logic) every premise is either true or false, and every deductive argument is either valid or invalid, it follows that every deductive argument is either sound or unsound. However, given that many, if not most, premises have truth values that are unknown or impossible to determine, it is not always possible to determine the soundness of a deductive argument. But that does not mean that soundness is unimportant in logic. It is crucially important that soundness be recognized as a criterion of evaluation that is distinct from validity and that the evaluator be ever vigilant never to confuse soundness with validity.

Inductive Arguments

Section 1.3 defined an inductive argument as one incorporating the claim that it is improbable that the conclusion be false given that the premises are true. If this claim is true, the argument is said to be strong. Thus, a  strong inductive argument  is an inductive argument in which it is improbable that the conclusion be false given that the premises are true. In such arguments, the conclusion does in fact follow probably from the premises. Conversely, a  weak inductive argument  is an argument in which the conclusion does not follow probably from the premises, even though it is claimed to.

All inductive arguments depend on what philosophers call the uniformity of nature. According to this principle, the future tends to replicate the past, and regularities that prevail in one spatial region tend to prevail in other regions. For example, in the past, sugar has always tasted sweet. According to the uniformity of nature, sugar will continue to taste sweet in the future. Also, just as sugar tastes sweet in Los Angeles, so does it in New York, London, and everywhere else. The uniformity of nature is the ultimate basis for our judgments about what we naturally expect to occur. Good inductive arguments are those that accord with the uniformity of nature. They have conclusions that we naturally expect to turn out true. If the conclusion of such an argument should turn out to be false, in violation of our expectations, this occurrence would cause us to react with surprise.

The procedure for testing the strength of inductive arguments runs parallel to the procedure for deduction. First we assume the premises are true, and then we determine whether, based on that assumption, the conclusion is probably true. This determination is accomplished by linking up the premises with regularities that exist in our experiential background. For example, if the argument is a causal inference, we link the information in the premises with known causal patterns. If the argument is an argument from signs, we connect the information in the premises with what we know about signs: some kinds of signs are trustworthy, others are not. If the argument is a generalization, we connect the information in the premises with what we know about a sample being representative of a population. All of these regularities are instances of the uniformity of nature. Here is an example of a prediction:

All dinosaur bones discovered to this day have been at least 50 million years old. Therefore, probably the next dinosaur bone to be found will be at least 50 million years old.

In this argument the premise is actually true. Given that all dinosaur bones discovered to date have been over 50 million years old (and that thousands of such bones have been discovered), the uniformity of nature dictates that the next one to be discovered will also be over 50 million years old. This is what we would naturally expect, and anything to the contrary would be highly surprising. Thus, the conclusion is probably true, and so the argument is strong.

Here is another example:

All meteorites found to this day have contained salt. Therefore, probably the next meteorite to be found will contain salt.

The premise of this argument is clearly false; but if we assume it to be true, then we would naturally expect that the next meteorite to be found would contain salt. Thus, the argument is strong.

The next example is an argument from analogy:

Dom Pérignon champagne, which is made in France, sells for over $100 per bottle. Marquis de la Tour is also a French champagne. Therefore probably it, too, sells for over $100 per bottle.

In this argument the premises are actually true, but our background experience tells us that the mere fact that two wines come from the same country does not imply that they sell for the same price. Thus, the argument is weak. The conclusion, incidentally, happens to be false.

Another example:

During the past fifty years, inflation has consistently reduced the value of the American dollar. Therefore, industrial productivity will probably increase in the years ahead.

In this argument, the premise is actually true and the conclusion is probably true in the actual world, but the probability of the conclusion is in no way based on the assumption that the premise is true. Because there is no direct connection between inflation and increased industrial productivity, the premise is irrelevant to the conclusion and it provides no probabilistic support for it. The conclusion is probably true independently of the premise. As a result, the argument is weak.

This last example illustrates an important distinction between strong inductive arguments and valid deductive arguments. As we will see in later chapters, if the conclusion of a deductive argument is necessarily true independently of the premises, the argument is still considered valid. But if the conclusion of an inductive argument is probably true independently of the premises, the argument is weak.

These four examples show that in general the strength or weakness of an inductive argument results not from the actual truth or falsity of the premises and conclusion, but from the probabilistic support the premises give to the conclusion. The dinosaur-bone argument has a true premise and a probably true conclusion, and the meteorite argument has a false premise and a probably false conclusion; yet both are strong because the premise of each provides probabilistic support for the conclusion. The industrial productivity argument has a true premise and a probably true conclusion, but the argument is weak because the premise provides no probabilistic support for the conclusion. As in the evaluation of deductive arguments, the only arrangement of truth and falsity that establishes anything is true premises and probably false conclusion (as in the Dom Pérignon argument). Any inductive argument having true premises and a probably false conclusion is weak.

Before proceeding further, however, we must qualify and explain this last statement. When we speak of the premises being true, we mean “true” in a complete sense. The premises must not exclude or overlook some crucial piece of evidence that undermines the stated premises and requires a different conclusion. This proviso is otherwise called the total evidence requirement. If the total evidence requirement is not met, an argument might have literally true premises and a probably false conclusion and still be strong. Also, when we speak of the conclusion being probably false, we mean probably false in the actual world in light of all the known evidence.

Table 1.2 presents several predictions (inductive arguments) that illustrate the various combinations of truth and falsity in the premises and conclusion. Note that the only arrangement of truth and falsity that is missing for strong arguments is true premises and probably false conclusion.

Table 1.2

Inductive Arguments

	Strong	Weak
True premise	Every previous U.S. president was older than 40.	A few U.S. presidents were lawyers.
Probably true conclusion	Therefore, probably the next U.S. president will be older than 40. [cogent]	Therefore, probably the next U.S. president will be older than 40. [uncogent]
True premise	None exist	A few U.S. presidents were unmarried.
Probably false conclusion		Therefore, probably the next U.S. president will be unmarried. [uncogent]
False premise	Every previous U.S. president was a TV debater.	A few U.S. presidents were dentists.
Probably true conclusion	Therefore, probably the next U.S. president will be a TV debater. [uncogent]	Therefore, probably the next U.S. president will be a TV debater. [uncogent]
False premise	Every previous U.S. president died in office.	A few U.S. presidents were dentists.
Probably false conclusion	Therefore, probably the next U.S. president will die in office. [uncogent]	Therefore, probably the next U.S. president will be a dentist. [uncogent]

The relationship between the strength of an inductive argument and the truth or falsity of its premises and conclusion, as illustrated in Table 1.2, is summarized as follows:

Premises	Conclusion	Strength
T	probably T	?
T	probably F	Weak
F	probably T	?
F	probably F	?

Like the summary table for deduction, this brief table reinforces the point that merely knowing the truth values of the premises and conclusion tells us nothing about the strength of an argument except in the one case of true premises and probably false conclusion. Any inductive argument having true premises (in the sense just explained) and a probably false conclusion is weak.

Unlike the validity and invalidity of deductive arguments, the strength and weakness of inductive arguments allow for degrees. To be considered strong, an inductive argument must have a conclusion that is more probable than improbable. In other words, given that the premises are true, the likelihood that the conclusion is true must be more than 50 percent, and as the probability increases, the argument becomes stronger. For this purpose, consider the following pair of arguments:

This barrel contains 100 apples.

Three apples selected at random were found to be ripe.

Therefore, probably all 100 apples are ripe.

This barrel contains 100 apples.

Eighty apples selected at random were found to be ripe.

Therefore, probably all 100 apples are ripe.

The first argument is weak and the second is strong. However, the first is not absolutely weak nor the second absolutely strong. Both arguments would be strengthened or weakened by the random selection of a larger or smaller sample. For example, if the size of the sample in the second argument were reduced to seventy apples, the argument would be weakened. The incorporation of additional premises into an inductive argument will also generally tend to strengthen or weaken it. For example, if the premise “One unripe apple that had been found earlier was removed” were added to either argument, the argument would be weakened.

A  cogent argument  is an inductive argument that is strong and has all true premises. Also, the premises must be true in the sense of meeting the total evidence requirement. If any one of these conditions is missing, the argument is uncogent. Thus, an uncogent argument is an inductive argument that is weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these. A cogent argument is the inductive analogue of a sound deductive argument and is what is meant by a good, or successful, inductive argument without qualification. Because the conclusion of a cogent argument is genuinely supported by true premises, it follows that the conclusion of every cogent argument is probably true in the actual world in light of all the known evidence.

As an illustration of the need for the total evidence requirement, consider the following argument:

Swimming in the Caribbean is usually lots of fun. Today the water is warm, the surf is gentle, and on this beach there are no dangerous currents. Therefore, it would be fun to go swimming here now.

If the premises reflect all the important factors, then the argument is cogent. But if they ignore the fact that several large dorsal fins are cutting through the water (suggesting sharks), then obviously the argument is not cogent. Thus, for cogency the premises must not only be true but also not overlook some important fact that requires a different conclusion.

Finally, just as it is not always possible to determine the soundness of a deductive argument, it is not always possible to determine the cogency of an inductive argument. And this follows for two reasons. Many inductive arguments, especially those about complex real-life subjects, are not susceptible to being evaluated as clearly strong or clearly weak. And many premises have truth values that are unknown or impossible to determine. Yet, it remains important that cogency be recognized as a criterion for evaluating inductive arguments and that it not be confused with strength and weakness.