What Is Logic?

Image by Frits Ahlefeldt, Flickr, Creative Commons


By Dr. P.D. Magnus (left), Dr. Cathal Woods (right), and Dr. J. Robert Loftis (not pictured)
Magnus: Professor of Philosophy and Department Chair, University at Albany, SUNY
Woods: Professor of Philosophy, Virginia Weslayan College
Loftis: Associate Professor of Philosophy, Lorain County Community College


Logic is a part of the study of human reason, the ability we have think abstractly, solve problems, explain the things that we know, and infer new knowledge on the basis of evidence. Traditionally, logic has focused on the last of these items, the ability to make inferences on the basis of evidence. This is an activity you engage in every day. Consider, for instance, the game of Clue. (For those of you who have never played, Clue is a murder mystery game where players have to decide who committed the murder, what weapon they used, and where they were.) A player in the game might decide that the murder weapon was the candlestick by ruling out the other weapons in the game: the knife, the revolver, the rope, the lead pipe, and the wrench. This evidence lets the player know something know something they did not know previously, namely, the identify of the murderer.

In logic, we use the word “argument” to refer to the attempt to show that certain evidence supports a conclusion. This is very different from the sort of argument you might have with your family, which could involve screaming and throwing things. We are going to use the word “argument” a lot in this book, so you need to get used to thinking of it as a name for a rational process, and not a word that describes what happens when people disagree.

A logical argument is structured to give someone a reason to believe some conclusion. Here is the argument form the fi rst paragraph written out in a way that shows its structure.

P1: In a game of Clue, the possible murder weapons are the knife, the candlestick, the revolver, the rope, the lead pipe, and the wrench.
P2: The murder weapon was not the knife.
P3: The murder weapon was also not the revolver, rope, the lead pipe, or the wrench.
C: Therefore, the murder weapon was the candlestick.

In the argument above, statements P1{P3 are the evidence. We call these the premises. The word “therefore” indicates that the nal statement, marked with a C, is the conclusion of the argument. If you believe the premises, then the argument provides you with a reason to believe the conclusion. You might use reasoning like this purely in your own head, without talking with anyone else. You might wonder what the murder weapon is, and then mentally rule out each item, leaving only the candlestick. On the other hand, you might use reasoning like this while talking to someone else, to convince them that the murder weapon is the candlestick. (Perhaps you are playing as a team.) Either way the structure of the reasoning is the same.

We can defi ne Logic then more precisely as the part of the study of reasoning that focuses on argument. In more casual situations, we will follow ordinary practice and use the word “logic” to either refer to the business of studying human reason or the thing being studied, that is, human reasoning itself. While logic focuses on argument, other disciplines, like decision theory and cognitive science, deal with other aspects of human reasoning, like abstract thinking and problem solving more generally. Logic, as the study of argument, has been pursued for thousands of years by people from civilizations all over the globe. The initial motivation for studying logic is generally practical. Given that we use arguments and make inferences all the time, it only makes sense that we would want to learn to do these things better. Once people begin to study logic, however, they quickly realize that it is a fascinating topic in its own right. Thus the study of logic quickly moves from being a practical business to a theoretical endeavor people pursue for its own sake.

In order to study reasoning, we have to apply our ability to reason to our reason itself. This reasoning about reasoning is called metareasoning. It is part of a more general set of processes called metacognition , which is just any kind of thinking about thinking. When we are pursing logic as a practical discipline, one important part of metacognition will be awareness of your own thinking, especially its weakness and biases, as it is occurring. More theoretical metacognition will be about attempting to understand the structure of thought itself.

Whether we are pursuing logical for practical or theoretical reasons, our focus is on argument. The key to studying argument is to set aside the subject being argued about and to focus on the way it is argued for. The section opened with an example that was about a game of Clue. However, the kind of reasoning used in that example was just the process of elimination. Process of elimination can be applied to any subject. Suppose a group of friends is deciding which restaurant to eat at, and there are six restaurants in town. If you could rule out ve of the possibilities, you would use an argument just like the one above to decide where to eat. Because logic sets aside what an argument is about, and just look at how it works rationally, logic is said to have content neutrality. If we say an argument is good, then the same kind of argument applied to a different topic will also be good. If we say an argument is good for solving murders, we will also say that the same kind of argument is good for deciding where to eat, what kind of disease is destroying your crops, or who to vote for.

When logic is studied for theoretical reasons, it typically is pursued as formal logic. In formal logic we get content neutrality by replacing parts of the argument we are studying with abstract symbols. For instance, we could turn the argument above into a formal argument like this:

P1: There are six possibilities: A, B, C, D, E, and F.
P2: A is false.
P3: B, D, E, and F are also false.
C: The correct answer is C.

Here we have replaced the concrete possibilities in the rst argument with abstract letters that could stand for anything. We have also replaced the English word “therefore” with the symbol that means “therefore” (:_:). This lets us see the formal structure of the argument, which is why it works in any domain you can think of. In fact, we can think of formal logic as the method for studying argument that uses abstract notation to identify the formal structure of argument. Formal logic is closely allied with mathematics, and studying formal logic often has the sort of puzzle-solving character one associates with mathematics.

When logic is studied for practical reasons, it is typically called critical thinking. It is the study of reasoning with the goal of improving our reasoning in the real world. Sometimes people use the term “critical thinking” to simply refer to any time one is reasoning well. However, we will be using the term critical thinking more narrowly to refer to the use of metareasoning to improve our reasoning in practical situations. Critical thinking is generally pursued as informal logic, rather than formal logic. This means that we will keep arguments in ordinary language and draw extensively on your knowledge of the world to evaluate them. In contrast to the clarity and rigor of formal logic, informal logic is suffused with ambiguity and vagueness. There are problems problems with multiple correct answers, or where reasonable people can disagree with what the correct answer is. This is because you will be dealing with reasoning in the real world, which is messy.

Figure 1.1: The ob/ob mouse (left), a laboratory mouse which has been genetically engineered to be obese, and an ordinary mouse (right). Formal logic, which takes arguments out of their natural environment, often winds up studying arguments that look like the ob/ob mouse. They are huge, awkward, and unable to survive in the wild, but they tell us a lot about the limits of logic as a process. Photo from Wikimedia Commons (2006).

You can think of the difference between formal logic and informal logic as the difference between a laboratory science and a field science. If you are studying, say, mice, you could discover things about them by running experiments in a lab, or you can go go out into the field where mice live and observe them in their natural habitat. Informal logic is the fi eld science for arguments: you go out and study arguments in their natural habitats, like newspapers, courtrooms, and scientifi c journal articles. Like studying mice scurrying around a meadow, the process takes patience, and often doesn’t yield clear answers but it lets you see how things work in the real world. Formal logic takes arguments out of their natural habitat and performs experiments on them to see what they are capable of. The arguments here are like lab mice. They are pumped full of chemicals and asked to perform strange tasks, as it were. They live lives very different than their wild cousins. Some of the arguments we will wind up looking at the “ob/ob mouse”, a genetically engineered obese mouse scientists use to study type II diabetes. These arguments will be huge, awkward, and completely unable to survive in the wild. But they will tell us a lot about the limits of logic as a process.

Our main goal in studying arguments is to separate the good ones from the bad ones. The argument about Clue we saw earlier is a good one, based on the process of elimination. It is good because it leads to truth. If I’ve got all the premises right, the conclusion will also be right. The textbook Logic: Techniques of Formal Reasoning (Kalish et al., 1980) had a nice way of capturing the meaning of logic: \logic is the study of virtue in argument.” We accept this defi nition, with the caveat that an argument is virtuous if it helps us get to the truth.

Logic is different from rhetoric, which is the study of effective persuasion. Rhetoric does not look at virtue in argument. It only looks at the power of arguments, regardless of whether they lead to truth. An advertisement might convince you to buy a new truck by having a gravelly voiced announcer tell you it is \ram tough” and showing you a picture of the truck on top of a mountain, where it no doubt actually had to be airlifted. This sort of persuasion is often more effective at getting people to believe things than logical argument, but it has nothing to do with whether the truck is really the right thing to buy. Here, we will only be interested in rhetoric to the extent that it is we need to learn to defend ourselves against the misleading rhetoric of others. The sections on critical thinking will emphasize becoming aware of your biases and how others might use misleading rhetoric to exploit them. This will not, however, be anything close to a full treatment of the study of rhetoric.

Statement, Argument, Premise, Conclusion

So far we have de ned logic as the study of argument and outlined its relationship to related
fi elds. To go any farther, we are going to need a more precise de finition of what exactly an
argument is. We have said that an argument is not simply two people disagreeing; it is an
attempt to prove something using evidence. More specifi cally, an argument is composed of
statements. In logic, we de ne a statement as a unit of language that can be true or false. To
put it another way, it is some combination of words or symbols that have been put together in a way that lets someone agree or disagree with it. All of the items below are statements.

(a) Tyrannosaurus rex went extinct 65 million years ago.
(b) Tyrannosaurus rex went extinct last week.
(c) On this exact spot, 100 million years ago, a T. rex laid a clutch of eggs.
(d) George W. Bush is the king of Jupiter.
(e) Murder is wrong.
(f) Abortion is murder.
(g) Abortion is a woman’s right.
(h) Lady Gaga is pretty.
(i) The slithy toves did gyre and gimble in the wabe.
(j) The murder of logician Richard Montague was never solved.

Table 1.1: A statement in different contexts, or no context.

Because a statement is something that can be true or false, statements include truths like (a)
and falsehoods like (b). A statement can also be something that that must either be true or false, but we don’t know which, like (c). A statement can be something that is completely silly, like (d). Statements in logic include statements about morality, like (e), and things that in other contexts might be called “opinions,” like (f) and (g). People disagree strongly about whether (f) or (g) are true, but it is defi nitely possible for one of them to be true. The same is true about (h), although it is a less important issue than (f) and (g). Sentences can include nonsense words like (i), because we don’t really need to know what the sentence is about to see that it is the sort of thing that can be true or false. All of this relates back to the content neutrality of logic. The statements we study can be about dinosaurs, abortion, Lady Gaga, and even the history of logic itself, as in sentence (j), which is true.

We are treating statements primarily as units of language or strings of symbols, and most of the time the statements you will be working with will just words printed on a page. However, it is important to remember that statements are also what philosophers call “speech acts.” They are actions people take when they speak (or write). If someone makes a statement they are typically telling other people that they believe the statement to be true, and will back it up with evidence if asked to. When people make statements, they always do it in a context – they make statements at a place and a time with an audience. Often the context statements are made in will be important for us, so when we give examples statements or arguments we will sometimes include a description of the context. When we do that, we will give the context in italics. See Table 1.1 for examples. For the most part, the context for a statement or argument will be important on critical thinking, when we are pursing the study of logic for practical reasons.

“Statements” here does not include questions, commands, exclamations, or sentence fragments. Some who asks a question like “Does the grass need to be mowed?” is typically not claiming that anything is true or false. (Sometimes make statements and disguise them as questions, for instance if they were trying to hint that the lawn needs to be mowed. These are generally called rhetorical questions, and we will leave the study of them to the rhetoricians.) Generally, questions will not count as sentences, but answers will. “What is this course about?” is not a sentence. \No one knows what this course is about” is a sentence.

For the same reason commands do not count as statements for us. If someone bellows “Mow the grass, now!” they are not saying whether the grass has been mowed or not. You might infer that they believe the lawn has not been mowed, but then again maybe they think the lawn is fine and just want to see you exercise. Note, however, that commands are not always phrased as imperatives. “You will respect my authority” is either true or false – either you will or you will not – and so it counts as a statement in the logical sense.

An exclamation like “Ouch!” is also neither true nor false. On its own, it is not a statement. We will treat “Ouch, I hurt my toe!” as meaning the same thing as “I hurt my toe.” The “ouch” does not add anything that could be true or false.

Finally, a lot of possible strings of words will fail to qualify as statements simply because they don’t form a complete sentence. In your composition classes, these were probably referred to as sentence fragments. This includes strings of words that are parts of sentences, such as noun phrases like “The tall man with the hat” and verb phrases, like “ran down the hall.” Phrases like these are missing something they need to make an claim about the world. The class of sentence fragments also includes completely random combinations of words, like “The up if blender route,” which don’t even have the form of a statement about the world.

Other logic textbooks describe the components of argument as “propositions,” or “assertions,” and we will use these terms sometimes as well. There is actually a great deal of disagreement about what the differences between all of these things are and which term is best used to describe parts of arguments. However, none of that makes a difference here. We could have used any of the other terms here, and it wouldn’t change anything. Some textbooks will also use the term “sentence” here. We will not use the word “sentence” to mean the same thing as “statement.” Instead, we will use “sentence” the way it is used in ordinary grammar, to refer generally to statements, questions, and commands.

We use statements to build arguments. An argument is a connected series of statements designed to convince an audience of another statement. Here an audience might be a literal
audience sitting in front of you at some public speaking engagement. Or it might be the readers of a book or article. The audience might even by yourself as you reason your way through a problem. Let’s start with an example of an argument given to an external audience. This passage is from an essay by Peter Singer called “Famine, Affluence, and Morality” in which he tries to convince people in rich nations that they need to do more to help people in poor nations who are experiencing famine.

A contemporary philosopher writing in an academic journal: If it is in our power to prevent something bad from happening, without thereby sacri ficing anything of comparable moral importance, we ought, morally, to do so. Famine is something bad, and it can be prevented without sacri ficing anything of comparable moral importance. So, we ought to prevent famine. (Singer, 1972)

Singer wants his readers work to prevent famine. This is represented by the last statement of
the passage, \we ought to prevent famine,” which is called the conclusion of the passage. The
conclusion of an argument is the statement the argument is trying to convince the audience of.

Table 1.3: Premise and conclusion indicators.

The statements that do the convincing are called the premises. . In this case, the argument has three premises: (1) “If it is in our power to prevent something bad from happening, without thereby sacrifi cing anything of comparable moral importance, we ought, morally, to do so”; (2) “Famine is something bad”; and (3) “it can be prevented without sacrifi cing anything of comparable moral importance.”

Now let’s look at an example of internal reasoning.

Jack arrives at the track, in bad weather. There is no one here. I guess the race is not happening.

In the passage above, the words in italics explain the context for the reasoning, and the words in regular type represent what Jack is actually thinking to himself. This passage again has a premise and a conclusion. The premise is that no one is at the track, and the conclusion is that the race was canceled. The context gives another reason why Jack might believe the race has been canceled, the weather is bad. You could view this as another premise{it is very likely a reason Jack has come to believe that the race is canceled. In general, when you are looking at people’s internal reasoning, it is often hard to determine what is actually working as a premise and what is just working in the background of their unconscious.

When people give arguments to each other, they typically use words like “therefore” and “because.” These are meant to signal to the audience that what is coming is either a premise or a conclusion in an argument. Words and phrases like “because” signal that a premise is coming, so we call these premise indicators. Similarly, words and phrases like “therefore” signal a conclusion and are called conclusion indicators. The argument from Peter Singer above uses the conclusion indicator word, “so.” Table 1.3 is an incomplete list of indicator words and phrases in English.

The two passages we have looked at so far have been simply presented as quotations. But often it is extremely useful to rewrite arguments in a way that makes their logical structure clear. One way to do this is to use something called “canonical form.” An argument written in canonical form has each premise numbered and written on a separate line. Indicator words and other unnecessary material should be removed from the premises. Although you can shorten the premises and conclusion, you need to be sure to keep them all complete sentences with the same meaning, so that they can be true or false. The argument from Peter Singer, above, looks like this in canonical form:

P1: If we can stop something bad from happening, without sacri cing anything of comparable moral importance, we ought to do so.
P2: Famine is something bad.
P3: Famine can be prevented without sacri cing anything of comparable moral importance.
C: We ought to prevent famine.

Each statement has been written on its own line and given a number. The statements have been paraphrased slightly, for brevity, and the indicator word “so” has been removed. Also notice that the “it” in the third premise has been replaced by the word “famine,” so that statements reads naturally on its own.

Similarly, we can rewrite the argument Jack gives at the racetrack like this:

P: There is no one at the race track.
C: The race is not happening.

Notice that we did not include anything from the part of the passage in italics. The italics represent the context, not the argument itself. Also, notice that the “I guess” has been removed. When we write things out in canonical form, we write the content of the statements, ignore information about the speaker’s mental state, like “I believe” or “I guess.”

One of the first things you have to learn to do in logic is to identify arguments and rewrite
them in canonical form. The passage below is paraphrased from the ancient Greek philosopher Aristotle.

An ancient philosopher, writing for his students Again, our observations of the stars make it evident that the earth is round. For quite a small change of position to south
or north causes a manifest alteration in the stars which are overhead. (Aristotle, c.350 bce/1984c, 298a2-10)

The fi rst thing we need to do to put this argument in canonical form is to identify the conclusion. The indicator words are the best way to do this. The phrase “make it evident that” is a conclusion indicator phrase. He is saying that everything else is evidence for what follows. So we know that the conclusion is that the earth is round. “For” is a premise indicator word – it is sort of a weaker version of “because.” Thus the premise is that the stars in the sky change if you move north or south. In canonical form, Aristotle’s argument that the earth is round looks like this.

P: There are different stars overhead in the northern and southern parts of the earth.
C: The earth is spherical in shape.

That one is fairly simple, because it just has one premise. Here’s another example of an argument, this time from the book of Ecclesiastes in the Bible. The speaker in this part of the bible is generally referred to as The Preacher, or in Hebrew, Koheleth. In this verse, Koheleth uses both a premise indicator and a conclusion indicator to let you know he is giving reasons for enjoying life.

The words of the Preacher, son of David, King of Jerusalem There is something else meaningless that occurs on earth: the righteous who get what the wicked deserve, and the wicked who get what the righteous deserve. . . . So I commend the enjoyment of life, because there is nothing better for a person under the sun than to eat and drink and be glad. (Ecclesiastes 8:14-15, New International Version)

Koheleth begins by pointing out that good things happen to bad people and bad things happen
to good people. This is his rst premise. (Most Bible teachers provide some context here by
pointing that that the ways of God are mysterious and this is an important theme in Ecclesiastes.) Then Koheleth gives his conclusion, that we should enjoy life, which he marks with the word “so.” Finally he gives an extra premise, marked with a \because”, that there is nothing better for a person than to eat and drink and be glad. In canonical form, the argument would look like this.

P1: Good things happen to bad people and bad things happen to good people.
P2: There is nothing better for people than to eat, to drink and to enjoy life.
C: You should enjoy life.

Notice that in the original passages, Aristotle put the conclusion in the fi rst sentence, while Koheleth put it in the middle of the passage, between two premises. In ordinary English, people can put the conclusion of their argument where ever they want. However, when we write the argument in canonical form, the conclusion goes last.

Unfortunately, indicator words aren’t a perfect guide to when people are giving an argument. Look at this passage from a newspaper:

From the general news section of a national newspaper: The new budget underscores the consistent and paramount importance of tax cuts in the Bush philosophy. His first term cuts affected more money than any other initiative undertaken in his presidency, including the costs thus far of the war in Iraq. All told, including tax incentives for health care programs and the extension of other tax breaks that are likely to be taken up by Congress, the White House budget calls for nearly $300 billion in tax cuts over the next ve years, and $1.5 trillion over the next 10 years. (Toner, 2006)

Although there are no indicator words, this is in fact an argument. The writer wants you to believe something about George Bush: tax cuts are his number one priority. The next two sentences in the paragraph give you reasons to believe this. You can write the argument in
canonical form like this.

P1: Bush’s first term cuts affected more money than any other initiative undertaken in his presidency, including the costs thus far of the war in Iraq.
P2: The White House budget calls for nearly $300 billion in tax cuts over the next five years, and $1.5 trillion over the next 10 years.
C: Tax cuts are of consistent and paramount importance of in the Bush philosophy.

The ultimate test of whether something is an argument is simply whether some of the sentences provide reason to believe another one of the sentences. If some sentences support others, you are looking at an argument. The speakers in these two cases use indicator phrases to let you know they are trying to give an argument.

Under our defi nition, something counts as an argument if the speaker is simply trying to support the conclusion with the premises, even if she doesn’t do a very good job. In fact, for our purposes, even something like this counts as an argument:

P1: There is coffee in the coffee pot.
P2: There is a dragon playing bassoon on the armoire.
C: Salvador Dali was a poker player.

It may seem odd to call this an argument, but that is because it would be a terrible argument. The two premises have nothing at all to do with the conclusion. Nevertheless, given our de finition, it still counts as an argument|albeit a bad one.

A final bit of terminology here. An inference is the act of coming to believe a conclusion on the basis of some set of premises. When Jack in the example above saw that no one was at the track, and came to believe that the race was not on, he was making an inference. We also use the term inference to refer to the connection between the premises and the conclusion of an argument. If your mind moves from premises to conclusion, you make an inference, and the premises and the conclusion are said to be linked by an inference. In that way inferences are like argument glue: they hold the premises and conclusion together.

Arguments and Nonarguments

We just saw that arguments are made of statements. However, there are lots of other things you can do with statements. Part of learning what an argument is involves learning what an argument is not, so we are going to look at some other things you can do with statements besides make arguments.

The list below of kinds of nonarguments is not meant to be exhaustive: there are all sorts of things you can do with statements that are not discussed. Nor are the items on this list meant to be exclusive. One passage may function as both, for instance, a narrative and a statement of belief. Right now we are looking at real world reasoning, so you should expect a lot of ambiguity and imperfection.

Simple Statements of Belief

An argument is an attempt to persuade an audience to believe something, using reasons. Often, though, when people try to persuade others to believe something, they skip the reasons, and give a simple statement of belief. This is kind of nonargumentative passage where the speaker simply asserts what they believe without giving reasons. Sometimes simple statements of belief are prefaced with the words “I believe,” and sometimes they are not. A simple statements of belief can be a profoundly inspiring way to change people’s hearts and minds. Consider this passage from Dr. Martin Luther King’s Nobel acceptance speech.

I believe that even amid today’s mortar bursts and whining bullets, there is still hope for a brighter tomorrow. I believe that wounded justice, lying prostrate on the blood-flowing streets of our nations, can be lifted from this dust of shame to reign supreme among the children of men. I have the audacity to believe that peoples everywhere can have three meals a day for their bodies, education and culture for their minds, and dignity, equality and freedom for their spirits. (King, 1964)

This actually is a part of a longer passage that consists almost entirely of statements that begin with some variation of “I believe.”It is incredibly powerful oration, because the audience, feeling the power of King’s beliefs, comes to share in those beliefs. The language King uses to describe how he believes is important, too. He says his belief in freedom and equality requires audacity, making the audience feel his courage and want to share in this courage by believing the same things.

These statements are moving, but they do not form an argument. None of these statements provide evidence for any of the other statements. In fact, they all say roughly the same thing, that good will triumph over evil. So the study of this kind of speech belongs to the discipline of rhetoric, not of logic.

Expository Passages

Perhaps the most basic use of a statement is to convey information. Often if we have a lot of information to convey, we will sometimes organize our statements around a theme or a topic. Information organized in this fashion can often appear like an argument, because all of the
statements in the passage relate back to some central statement. However, unless the other
statements are given as reasons to believe the central statement, the passage you are looking at is not an argument. Consider this passage:

From a college psychology textbook. Eysenck advocated three major behavior techniques that have been used successfully to treat a variety of phobias. These techniques are modeling, flooding, and systematic desensitization. In modeling phobic people watch nonphobics cope successfully with dreaded objects or situations. In flooding clients are exposed to dreaded objects or situations for prolonged periods of time in order to extinguish their fear. In contrast to flooding, systematic desensitization involves gradual, client-controlled exposure to the anxiety eliciting object or situation. (Adapted from Ryckman 2007)

We call this kind of passage an expository passage. In an expository passage , statements are organized around a central theme or topic statement. The topic statement might look like a conclusion, but the other statements are not meant to be evidence for the topic statement.
Instead, they elaborate on the topic statement by providing more details or giving examples. In the passage above, the topic statement is “Eysenck advocated three major behavioral techniques . . . .” The statements describing these techniques elaborate on the topic statement, but they are not evidence for it. Although the audience may not have known this fact about Eysenk before reading the passage, they will typically accept the truth of this statement instantly, based on the textbook’s authority. Subsequent statements in the passage merely provide detail.

The name \expository passage” might make it sound like we are only talking about formal
writing, but really people give information organized around topic sentences all the time.
Consider this:

Your friend Bea is on the phone: Kelly is driving me insane. First she told Michael that I was out when I was right there in my room, and then she ate the leftover food I was keeping for lunch today.

In this passage, “Kelly is driving me insane” acts as a topic sentence, and the other two
statements provide details illustrating the topic sentence. This doesn’t really count as an
argument, though, because Bea probably doesn’t need to convince you that Kelly is driving her
insane. You take your friends word for it as soon as she says it. Most human communication is
actually like this. We assume people are telling the truth until we are giving reason to doubt
them. Societies that lack this basic level of trust can quickly break down because no one can
cooperate enough to get basic tasks accomplished.

Deciding whether a passage is an argument or an expository passage is complicated by the fact that sometimes people argue by example:

Steve: Kenyans are better distance runners than everyone else.
Monica: Oh come on, that sounds like an exaggeration of a stereotype that isn’t even true.
Steve: What about Dennis Kimetto, the Kenyan who set the world record for running the marathon? And you know who the previous record holder was: Emmanuel Mutai, also Kenyan.

Here Steve has made a general statement about all economists. Monica clearly doubts this claim, so Steve backs it up with some examples that seem to match his generalization. This isn’t a very strong way to argue: moving from two examples to statement about all Kenyans is
probably going to be a kind of bad argument known as a hasty generalization. The point here however, is that Steve is just offering it as an argument.

The key to telling the difference between expository passages and arguments by example is
whether there is a conclusion that they audience needs to be convinced of. In the passage from the psychology textbook, “Eysenck advocated three major behavioral techniques” doesn’t really work as a conclusion for an argument. The audience, students in an introductory psychology course, aren’t likely to challenge this assertion, the way Steve challenges Emerson’s broad, dismissive claim.

Context is very important here, too. The Internet is a place where people argue in the ordinary sense of exchanging angry words and insults. In that context, people are likely to actually give some arguments in the logical sense of giving reasons to believe a conclusion.


Statements can also be organized into descriptions of events and actions, as in this snippet from book V of Harry Potter.

But she [Hermione] broke off; the morning post was arriving and, as usual, the Daily Prophet was soaring toward her in the beak of a screech owl, which landed perilously close to the sugar bowl and held out a leg. Hermione pushed a Knut into its leather pouch, took the newspaper, and scanned the front page critically as the owl took off again. (Rowling, 2003)

We will use the term narrative loosely to refer to any passage that gives a sequence of events or actions. A narrative can be fictional or non fictional. It can be told in regular temporal
sequence or it can jump around, forcing the audience to try to reconstruct a temporal sequence. A narrative can describe a short sequence of actions, like Hermione taking a newspaper from an owl, or a grand sweep of events, like this passage about the fall rise and fall of an empire in the ancient near east:

The Guti were finally expelled from Mesopotamia by the Sumerians of Erech (c. 2100), but it was left to the kings of Ur’s famous third dynasty to re-establish the Sargonoid frontiers and write the final chapter of the Sumerian History. The dynasty lasted through the twenty first century at the close of which the armies of Ur were overthrown by the Elamites and Amorites (McEvedy and Woodcock, 1967).

This passage does not feature individual people performing speci c actions, but it is still united by character and action. Instead of Hermione at breakfast, we have the Sumarians in Mesopotamia. Instead of retrieving a message from an owl, the conquer the Guti, but then are
conquered by the Elamites and Amorites. The important thing is that the statements in a
narrative are not related as premises and conclusion. Instead, they are all events which are united common characters acting in speci fic times and places.

Arguments and Explanations

Explanations are are not arguments, but they they share important characteristics with arguments, so we should devote a separate section to them. Both explanations and arguments are parts of reasoning, because both feature statements that act as reasons for other statements. The difference is that explanations are not used to convince an audience of a conclusion.

Let’s start with workplace example. Suppose you see your co-worker, Henry, removing a
computer from his office. You think to yourself “Gosh, is he stealing from work?” But when you ask him about it later, Henry says, “I took the computer because I believed that it was scheduled for repair.” Henry’s statement looks like an argument. It has the indicator word “because” in it, which would mean that the statement \I believed it was scheduled for repairs” would be a premise. If it was, we could put the argument in canonical form, like this:

P: I believed the computer was scheduled for repair
C: I took the computer from the office.

But this would be awfully weird as an argument. If it were an argument, it would be trying to
convince us of the conclusion, that Henry took the computer from the office. But you don’t need to be convinced of this. You already know it|that’s why you were talking to him in the fi rst place.

Henry is giving reasons here, but they aren’t reasons that try to prove something. They are
reasons that explain something. When you explain something with reasons, you increase your understanding of the world by placing something you already know in a new context. You already knew that Henry took the computer, but now you know why Henry took the computer, and can see that his action was completely innocent (if his story checks out).

Both arguments and explanations both involve giving reasons, but the reasons function differently in each case. An explanation is defi ned as a kind of reasoning where reasons are used to provide a greater understanding of something that is already known.

Because both arguments and explanations are parts of reasoning, we will use parallel language to describe them. In the case of an argument, we called the reasons “premises.” In the case of an explanation, we will call them explainers. Instead of a “conclusion,” we say that the explanation has an explainee. We can use the generic term reasons to refer to either premises or explainers and the generic term target proposition to refer to either conclusions or explainees. Figure 1.2 shows this relationship.

We can put explanations in canonical form, just like arguments, but to distinguish the two, we will simply number the statements, rather than writing Ps and Cs, and we will put an E next to
the line that separates explainers and exaplainee, like this:

1. Henry believed the computer was scheduled for repair
2. Henry took the computer from the office.

Often the same piece of reasoning can work as either an argument or an explanation, depending on the situation where it is used. Consider this short dialogue

Monica visits Steve’s cubical.
Monica: All your plants are dead.
Steve: It’s because I never water them.

In the passage above, Steve uses the word “because,” which we’ve seen in the past is a premise indicator word. But if it were a premise, the conclusion would be \All Steve’s plants are dead.” But Steve can’t possibly be trying to convince Monica that all his plants are dead. It is something that Monica herself says, and that they both can see. The \because” here indicates a reason, but here Steve is giving an explanation, not an argument. He takes something that Steve and Monica already know|that the plants are dead|and puts it in a new light by explaining how it came to be. In this case, the plants died because they didn’t get water, rather than dying because they didn’t get enough light or were poisoned by a malicious co-worker. The reasoning is best represented like this:

1. Steve never waters his plants.
2. All the plants are dead.

But the same piece of reasoning can change form an explanation into an argument simply by putting it into a new situation:

Monica and Steve are away from the office.
Monica: Did you have someone water your plants while you were away?
Steve: No.
Monica: I bet they are all dead.

Here Steve and Monica do not know that Steve’s plants are dead. Monica is inferring this idea based on the premise which she learns from Steve, that his plants are not being watered. This
time “Steve’s plants are not being watered” is a premise and “The plants are dead” is a conclusion. We represent the argument like this:

P. Steve never waters his plants.
C. All the plants are dead.

In the example of Steve’s plants, the same piece of reasoning can function either as an argument or an explanation, depending on the situation context where it is given. This is because the reasoning in the example of the plants is causal: the causes of the plants dying are given as reasons for the death, and we can appeal to causes either to explain something that we know happened or to predict something that we think might have happened.

Not all kinds of reasoning are flexible like that, however. Reasoning from authority can be used in some kinds of argument, but often makes a lousy explanation. Consider another conversation between Steve and Monica:

Monica: I saw on a documentary last night that the universe is expanding and probably will keep expanding for ever.
Steve: Really?
Monica: Yeah, Steven Hawking said so.

There aren’t any indicator words here, but it looks like Monica is giving an arguments. She states that the universe is expanding, and Steve gives a skeptical “really?” Monica then replies by saying that she got this information from the famous physicist Steven Hawking. It looks like Steve is supposed to believe that the universe will expand inde finitely because Hawking, an authority in the relevant fi eld, said so. This makes for an ok argument:

P: Steven Hawking said that the universe is expanding and will continue to do so indefi nitely.
C: The universe is expanding and will continue to do so inde finitely.

Arguments from authority aren’t very reliable, but for very many things they are all we have to go on. We can’t all be experts on everything. But now try to imagine this argument as an explanation. What would it mean to say that the expansion of the universe can be explained by
the fact that Steven Hawking said that it should expand. It would be as if Hawking were a god,
and the universe obeyed his commands! Arguments from authority are acceptable, but not ideal. Explanations from authority, on the other hand, are completely illegitimate.

In general, arguments that appeal to how the world works are is more satisfying than one which appeals to the authority or expertise of others. Compare the following pair of arguments:

(a) Jack says traffic will be bad this afternoon. So, traffic will be bad this afternoon.
(b) Oh no! Highway repairs begin downtown today. And a bridge lift is scheduled for the middle of rush hour. Traffic is going to be terrible

Even though the second passage is an argument, the reasons used to justify the conclusion
could be used in an explanation. Someone who accepts this argument will also have an explanation ready to offer if someone should later ask “Traffic was terrible today! I wonder why?”. This is not true of the fi rst passage: bad traffic is not explained by saying “Jack said it would be bad.” The argument that refers to the drawbridge going up is appealing to a more powerful sort of reason, one that works in both explanations and arguments. This simply makes for a more satisfying argument, one that makes for a deeper understanding of the world, than one that merely appeals to authority.

Although arguments based on explanatory premises are preferred, we must often rely on other
people for our beliefs, because of constraints on our time and access to evidence. But the other people we rely on should hopefully hold the belief on the basis of an empirical understanding. And if those people are just relying on authority, then we should hope that at some point the chain of testimony ends with someone who is relying on something more than mere authority.

We just have seen that they same set of statements can be used as an argument or an explanation depending on the context. This can cause confusion between speakers as to what is going on. Consider the following case:

Bill and Henry have just nished playing basketball.
Bill: Man, I was terrible today.
Henry: I thought you played fi ne.
Bill: Nah. It’s because I have a lot on my mind from work.

Bill and Henry disagree about what is happening|arguing or explaining. Henry doubts Bill’s
initial statement, which should provoke Bill to argue. But instead, he appears to plough ahead
with his explanation. What Henry can do in this case, however, is take the reason that Bill offers as an explanation (that Bill is preoccupied by issues at work) and use it as a premise in an argument for the conclusion \Bill played terribly.” Perhaps Henry will argue (to himself) something like this: “It’s true that Bill has a lot on his mind from work. And whenever a person is preoccupied, his basketball performance is likely to be degraded. So, perhaps he did play poorly today (even though I didn’t notice).”

In other situations, people can switch back and forth between arguing and explaining. Imagine
that Jones says “The reservoir is at a low level because of several releases to protect the
down-stream ecology.” Jones might intend this as an explanation, but since Smith does not share the belief that the reservoir’s water level is low, he will first have to be given reasons for believing that it is low. The conversation might go as follows:

Jones: The reservoir is at a low level because of several releases to protect the down-stream ecology.
Smith: Wait. The reservoir is low?
Jones: Yeah. I just walked by there this morning. You haven’t been up there in a while?
Smith: I guess not.
Jones: Yeah, it’s because they’ve been releasing a lot of water to protect the ecology lately.

When challenged, Smith o ers evidence from his memory: he saw the reservoir that morning.
Once Smith accepts that the water level is low, Jones can restate his explanation.

Some forms of explanation overlap with other kinds of nonargumentative passages. We are
dealing right now with thinking in the real world, and as we mentioned on page 4 the real world is full of messiness and ambiguity. One effect of this is that all the categories we are discussing will wind up overlapping. Narratives and expository passages, for instance, can also function as explanations. Consider this passage

From an article on espn.go.com Duke beat Butler 61-59 for the national championship Monday night. Gordon Hayward’s half-court, 3-point heave for the win barely missed to leave tiny Butler one cruel basket short of the Hollywood ending.

On the one hand, this is clearly a narrative|retelling a sequence of events united by time,
place, and character. But it also can work as an explanation about how Duke won, if the audience immediately accepts the result. ‘The last shot was a miss and then Duke won’ can be understood as ‘the last shot was a miss and so Duke won’.

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