Construct a Deductively Valid Argument/Deductive Logic

2.1 Arguments in Logic

Chapter 1 provisionally defined argument as a methodical defense of a position. We referred to this as the commonsense understanding of the way the word argument is employed in logic. The commonsense definition is very useful in helping us recognize a unique form of expression in ordinary human communication. It is part of the human condition to differ in opinion with another person and, in response, to attempt to change that person’s opinion. We may attempt, for example, to provide good reasons for seeing a particular movie or to show that our preferred kind of music is the best. Or we may try to show others that smoking or heavy drinking is harmful. As you will see, these are all arguments in the commonsense understanding of the term.

In Chapter 1 we also distinguished the commonsense understanding of argument from the meaning of argument in ordinary use. Arguments in ordinary use require an exchange between at least two people. As clarified in Chapter 1, commonsense arguments do not necessarily involve a dialogue and therefore do not involve an exchange. In fact, one could develop a methodical defense of a position—that is, a commonsense argument—in solitude, simply to examine what it would require to advocate for a particular position. In contrast, arguments, as understood in ordinary use, are characterized by verbal disputes between two or more people and often contain emotional outbursts. Commonsense arguments are not characterized by emotional outbursts, since unbridled emotions present an enormous handicap for the development of a methodical defense of a position.

In logic an argument is a set of claims in which some, called the premises, serve as support for another claim, called the conclusion. The conclusion is the argument’s main claim. For the most part, this technical definition of argument is what we shall employ in the remainder of this book, though we may use the commonsense definition when talking about less technical examples. Table 2.1 should help clarify which meanings are acceptable within logic. Take a moment to review the table and fix these definitions in your mind.

Table 2.1: Comparing meanings for the term argument

Meaning in ordinary use

Commonsense meaning

Technical meaning in logic

A verbal quarrel or disagreement, often characterized by raised voices and flaring emotions.

The methodical and well-researched defense of a position or point of view advanced in relation to a disputed issue.

A set of claims in which some, called premises, serve as support for another claim, called the conclusion.

Arguments in the technical sense are a primary way in which we can defend a position. Accordingly, we can find the structure of logical arguments in commonsense arguments all around us: in letters to the editor, social media, speeches, advertisements, sales pitches, proposals submitted for grant funds or bank loans, job applications, requests for a raise, communications of values to children, marriage proposals, and so on. Arguments often provide the basis on which most of our decisions are made. We read or hear an argument, and if we are convinced by it, then we accept its conclusion. For example, consider the following argument:

“I’m just not a math person.” We hear this all the time from anyone who found high school math challenging. . . . In high school math at least, inborn talent is less important than hard work, preparation, and self-confidence. This is what high school math teachers, college professors, and private tutors have observed as the pattern of those who become good in high school math. They point out that in any given class, students fall in a wide range of levels of math preparation. This is not due to genetic predisposition. What is rarely observed is that some children come from households in which parents introduce them to math early on and encourage them to practice it. These students will immediately obtain perfect scores while the rest do not. As a result, the students without previous preparation in math immediately assume that those with perfect scores have a natural math talent, without knowing about the preparation that these students had in their homes. In turn, the students who obtain perfect scores assume that they have a natural math talent given their scores relative to the rest of the class, so they are motivated to continue honing their math skills and, by doing this, they cement their top of the class standing. Thus, the belief that math ability cannot change becomes a self-fulfilling prophecy. (Kimball & Smith, 2013)

In this argument, the position defended by the authors is that the belief that math ability cannot change becomes a self-fulfilling prophecy. The authors support this claim with reasons that show good performance in math is not typically the result of a natural ability but of having a family support system for learning, a prior preparation in math from home, and continuous practice. It makes the case that it is hard work and preparation that lead to a person’s proficiency in math and other subjects, not genetic predisposition. This argument helps us recognize that we frequently accept oft-repeated information as fact without even questioning the basis. As you can see, an argument such as this can provide a solid basis for our everyday decisions, such as encouraging our children to work hard and practice in the subjects they find most difficult or deciding to obtain a university degree with confidence later in life.

To understand the more technical definition of an argument as a set of premises that support a conclusion, consider the following presentation of the reasoning from the commonsense argument we have just examined.

Good performance in math is not due to genetics.

Good performance in math only requires preparation and continuous practice.

Students who do well initially assume they have natural talent and practice more.

Students who do less well initially assume they do not have natural talent and practice less.

Therefore, believing that one’s math ability cannot change becomes a self-fulfilling prophecy.

Presenting the reasoning this way can do a great deal to clarify the argument and allow us to examine its central claims and reasoning. This is why the field of logic adopts the more technical definition of argument for much of its work.

Regardless of what we think about math, an important contribution of this argument is that it makes the case that it is hard work and preparation that lead to our proficiency in math, and not the factor of genetic predisposition. Logic is much the same way. If you find some concepts difficult, don’t assume that you just lack talent and that you aren’t a “logic person.” With practice and persistence, anyone can be a logic person.

To help us properly identify logical arguments, we need clear criteria for what a logical argument is. Let us start unpacking what is involved in arguments by addressing their smallest element: the claim.

Claims

A claim is an assertion that something is or is not the case. Claims take the form of declarative sentences. It is important to note that each premise or conclusion consists of one single claim. In other words, each premise or conclusion consists of one single declarative sentence.

Claims can be either true or false. This means that if what is asserted is actually the case, then the claim is true. If the claim does not correspond to what is actually the case, then the claim is false. For example, the claim “milk is in the refrigerator” predicates that the subject of the claim, milk, is in the refrigerator. If this claim corresponds to the facts (if the refrigerator contains milk), then this claim is true. If it does not correspond to the facts (if the refrigerator does not contain milk), then the claim is false.

What factual claims can you make about this image?

Not all claims, however, can be easily checked for truth or falsity. For example, the truth of the claim “Jacob has the best wife in the world” cannot be settled easily, even if Jacob is the one asserting this claim (“I have the best wife in the world”). In order to understand what he could possibly mean by “best wife in the world,” we would have to propose the criteria for what makes a good wife in the first place, and as if this were not challenging enough, we would then have to establish a method or procedure to make comparisons among good wives. Of course, Jacob could merely mean “I like being married to my wife,” in which case he is not stating a claim about his wife being the best in the world but merely stating a feeling. It is not uncommon to hear people state things that sound like claims but are actually just expressions of preference or affection, and distinguishing between these is often challenging because we are not always clear in the way we employ language. Nonetheless, it is important to note that we often make claims from a particular point of view, and these claims are different from factual claims. Claims that advance a point of view, such as the example of Jacob’s wife—and especially claims about morality and ethicality—are indeed more challenging to settle as true or false than factual claims, such as “The speed limit here is 55.”

The important point is that both kinds of claims—the factual claim and the point-of-view claim—assert that something is or is not the case, affirm or deny a particular predicate of a subject, and can be either true or false. The following sentences are examples of claims that meet these criteria.

There is a full moon tonight.

Pecans are better than peanuts.

All flights to Paris are full.

BMWs are expensive to maintain.

Lola is my sister.

The following are not claims:

Is it raining? Why? Because questions are not, and cannot be, assertions that something is the case.

Oh, to be in Paris in the springtime! Why? Because this expresses a sentiment but does not state that anything might be true or false.

Buy a BMW! Why? Because a command is not an assertion that something is the case.

We often intend to advance claims in ways that do not present our claims clearly and properly—for example, by means of rhetorical questions, vague expressions of affection, and commands or metaphors that demand interpretation. But it is important to recognize that intention is not sufficient when communicating with others. In order for our intended claims to be identified as claims, they should meet the three criteria previously mentioned.

Claims are sometimes called propositions. We will use the terms claims and propositions interchangeably in this book. In this chapter we will stick to the word claim, but in subsequent chapters, we will move to the more formal terminology of propositions.

The Standard Argument Form

In informal logic the main method for identifying, constructing, or examining arguments is to extract what we hear or read as arguments and put this in what is known as the standard argument form. It consists of claims, some of which are called premises and one of which is called the conclusion. In the standard argument form, premises are listed first, each on a separate line, with the conclusion on the line after the last premise. There are various methods for displaying standard form. Some methods number the premises; others separate the conclusion with a line. We will generally use the following method, prefacing the conclusion with the word therefore:

Premise

Therefore, Conclusion

The number of premises can be as few as one and as many as needed. We must approach either extreme with caution given that, on the one hand, a single premise can offer only very limited support for the conclusion, and on the other hand, many premises risk error or confusion. However, there are certain kinds of arguments that, because of their formal structure, may contain only a limited number of premises.

In the standard argument form, each premise or conclusion should be only one sentence long, and premises and conclusions should be stated as clearly and briefly as possible. Accordingly, we must avoid premises or conclusions that have multiple sentences or single sentences with multiple claims. The following example shows what not to do:

I live in Boston, and I like clam chowder.

My family also lives in Boston. They also like clam chowder.

My friends live in Boston. They all like clam chowder, too.

Therefore, everyone I know in Boston likes clam chowder.

If you want to make more than one claim about the same subject, then you can break your declarative sentences into several sentences that each contain only one claim. The clam chowder argument can then be rewritten as follows:

I live in Boston.

I like clam chowder.

My family lives in Boston.

My family likes clam chowder.

My friends live in Boston.

My friends like clam chowder.

Therefore, everyone I know in Boston likes clam chowder.

The relationship between premises and the conclusion is that of inference—the process of drawing a claim (the conclusion) from the reasons offered in the premises. The act of reasoning from the premises serves as the glue connecting the premises with the conclusion.

2.2 Putting Arguments in the Standard Form

Presenting arguments in the standard argument form is crucial because it provides us with a dispassionate method that will allow us to find out whether the argument is good, regardless of how we feel about the subject matter. The first step is to identify the fundamental argument being presented.

At first it might seem a bit daunting to identify an argument, because arguments typically do not come neatly presented in the standard argument form. Instead, they may come in confusing and unclear language, much like this statement by Special Prosecutor Francis Schmitz of Wisconsin regarding Governor Scott Walker:

Governor Walker was not a target of the investigation. At no time has he been served with a subpoena. . . . While these documents outlined the prosecutor’s legal theory, they did not establish the existence of a crime; rather, they were arguments in support of further investigation to determine if criminal charges against any person or entity are warranted. (Crocker, 2014, para. 7 & 10)

This was a position presented in regard to the investigation of an alleged illegal campaign finance coordination during the 2011–2012 recall elections (Stein, 2014). Does it claim a vindication of Walker? Or does it suggest that there may be sufficient evidence to make Walker a central figure in the investigation? How would you even begin to make heads or tails of such a confusing argument? Do not despair. The remainder of this section will show you exactly what to look for in order to make sense of the most complicated argument. With a little practice, you will be able to do this without much effort.

Find the Conclusion First

Punctuation, parentheses, and conclusion indicators all serve as signposts to assist us when deconstructing an argument. They provide important clues about where to find the conclusion as well as supporting claims.

Although the conclusion is last in the standard form, the conclusion is the first thing to find because the conclusion is the main claim in an argument. The other claims—the premises—are present for the sole purpose of supporting the conclusion. Accordingly, if you are able to find the conclusion, then you should be able to find the premises.

The good news is that language is not only a means for expressing ideas; it also offers a road map for the ideas presented. Chapter 1 underscored the fundamental importance of clear, precise, and correct language in logical reasoning. When used properly, language also offers structures and directions for communicating meaning, thus facilitating our understanding of what others are saying. One punctuation mark—the question mark—tells us that we are confronting a question. A different punctuation mark—the parentheses—tells us that we are being given relevant information but only as an aside or afterthought to the main point; if removed, the parenthetical information would not alter the main point. In the case of arguments, some words serve as signposts identifying conclusions. Take the following example of an argument in the standard argument form:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

The word therefore indicates that the sentence is a conclusion. In fact, the word therefore is the standard conclusion indicator we will use when constructing arguments in the standard argument form. However, there are other conclusion indicators that are used in ordinary arguments, including:

Consequently . . .

So . . .

Hence . . .

Thus . . .

Wherefore . . .

As a result . . .

It follows that . . .

For these reasons . . .

We may conclude that . . .

When a conclusion indicator is present, it can help identify the conclusion in an argument. Unfortunately, many arguments do not come with conclusion indicators. In such cases start by trying to identify the main point. If you can clearly identify a single main point, then that is likely to be the conclusion. But sometimes you will have to look at a passage closely to find the conclusion. Suppose you encounter the following argument:

Don’t you know that driving without a seat belt is dangerous? Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one. Besides, in our state you can get fined $100 if you are caught not wearing one. You ought to wear one even if you are driving a short distance.

Arguments are often longer and more complicated than this one, but let us work with this simple case before trying more complicated examples. You know that the first thing you need to do is to look for the conclusion. The problem is that the author of the argument does not use a conclusion indicator. Now what? Nothing to worry about. Just remember that the conclusion is the main claim, so the thing to look for is what the author may be trying to defend. Although the first sentence is stated as a question—remember, punctuation marks give us important clues—the author seems to intend to assert that driving without a seat belt is dangerous. In fact, the second sentence offers evidence in support of this claim. On the other hand, the third sentence seems to be important, yet it does not speak to driving without a seat belt being dangerous, only expensive. In the final sentence, we find a claim that is supported by all the others. Because of this, the final sentence presents the conclusion.

Now, it so happens that in this case, the conclusion is at the end of this short argument, but keep in mind that conclusions can be found in various places in essays, such as the beginning or sometimes in the middle. Now that you have identified your first piece of the puzzle, we have this:

Premise 1: ?

Premise 2: ?

Premise 3: ?

Therefore, you ought to wear a seat belt whenever you drive.

You might have noticed that the conclusion does not appear as it did in the essay. The original sentence is “You ought to wear one even if you are driving a short distance.” Why did we modify it? Once again, clarity is of the essence in logical reasoning. Conclusions should make the subject clear, so the pronoun one was replaced with the actual subject to which the author is referring: seat belt. In addition, the predicate “even if you are driving a short distance” was rewritten to reflect the more inclusive point that the author seems to be making: that you should wear a seat belt whenever you drive.

This modification of language, known as paraphrasing, is part of the construction of arguments in the standard argument form. The act of extracting an argument from a longer piece to its fundamental claims in the standard argument form necessarily involves paraphrasing the original language to the clearest and most precise form possible. This concept will be addressed in greater detail later in this section.

Find the Premises Next

After identifying the conclusion, the next thing to do is look for the reasons the author offers in defense of his or her position. These are the premises. As with conclusions, there are premise indicators that serve as signposts that reasons are being offered for the main claim or conclusion. Some examples of premise indicators are:

Since . . .

For . . .

Given that . . .

Because . . .

As . . .

Owing to . . .

Seeing that . . .

May be inferred from . . .

To practice identifying premises, let us return to our seat belt example:

Much like a map will get you from point A to point B, putting an argument into the standard argument form will help you navigate from the conclusion to the premises and vice versa.

Notice again that this argument starts with a question: “Don’t you know that driving without a seat belt is dangerous?” The author is not really asking whether you know that driving without a seat belt is dangerous. Rather, the author seems to be asking a rhetorical question—a question that does not actually demand an answer—to assert that driving without a seat belt is dangerous. You should avoid asking rhetorical questions in the essays that you write, because the outcome can be highly uncertain. The success of a rhetorical question depends on the reader or listener first understanding the hidden meaning behind the rhetorical question and then correctly articulating the answer you have in mind. This does not always work.

For the sake of this example, however, let us do our best to try to get at the author’s intention. We could paraphrase the first premise to the following claim: Driving without a seat belt is dangerous. Does this paraphrased claim serve as a premise in support of the conclusion? In order to answer this, we need to put the conclusion in the form of a question. Again, premises are reasons offered in support of the conclusion, so if we have a well-constructed argument, then the premises should answer why the conclusion is the case. This is what we would have:

Question: Why must you wear a seat belt whenever you drive?

Answer: Because driving without a seat belt is dangerous.

This works, so the paraphrased claim that we drew from the author’s rhetorical question is indeed a reason in defense of the conclusion. So now we have one more piece of the puzzle:

Premise 1: Driving without a seat belt is dangerous.

Premise 2: ?

Premise 3: ?

Therefore, you ought to wear a seat belt whenever you drive.

Let us now move to the next sentence: “Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.” Is this a claim that can be a support for the conclusion? In other words, if we put the conclusion in the form of a question again as we did before, would this sentence be an adequate reason in response? Let us see.

Question: Why must you wear a seat belt whenever you drive?

Answer: Because statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.

The answer provides a reason in support of the conclusion, and thus, we have another premise. Now we have most of the puzzle completed, as follows:

Premise 1: Driving without a seat belt is dangerous.

Premise 2: Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.

Premise 3: ?

Therefore, you ought to wear a seat belt whenever you drive.

We have one more sentence left in the argument, which reads: “Besides, in our state you can get fined $100 if you are caught not wearing one.” Is this a premise? Well, it is uncertain, since the sentence is not presented in the form of a claim. So let us paraphrase it as a claim as follows: “Not wearing a seat belt can result in a $100 fine.” This is now a claim, and the paraphrasing has not altered the meaning, so we can proceed to our question: Is this a premise for the argument that we are examining? Once again, let us put the conclusion into a question:

Question: Why must you wear a seat belt whenever you drive?

Answer: Because not wearing a seat belt can result in a $100 fine.

This is a claim that can be a support for the conclusion, and thus, we have another premise. We can now see the argument presented more formally as follows:

Driving without a seat belt is dangerous.

Statistics show that you are 10 times more likely to be injured in an accident if you are not wearing one.

Not wearing a seat belt can result in a $100 fine.

Therefore, you ought to wear a seat belt whenever you drive.

The Necessity of Paraphrasing

As we have discussed, extracting the fundamental claims from a written or a spoken argument often involves paraphrasing. Paraphrasing is not merely an option but rather a necessity in order to uncover the intended argument in the best way possible. Most other arguments presented to you (especially those in the media) will not consist of only premises and the conclusion in clearly identifiable language. Furthermore, many arguments will be much longer and complicated than the seat belt argument example. Often, arguments are presented with many other sentences that do not serve the purposes of an argument, such as empty rhetorical devices, filler sentences that aim to manipulate your emotions, and so on. So your task in extracting an argument from such sources is akin to that of a surgeon—removing all those linguistic tumors that obscure the argument in order to reveal the basic claims presented and their supporting evidence. In other words, you should expect to do paraphrasing as a necessary task when you attempt to draw an argument in the standard form from almost any source.

It is important to recognize that not everyone who advances an argument does so clearly or even coherently. This is precisely why the structure of the standard argument form is such a powerful tool to command. It offers you the machinery to distinguish arguments from what are not arguments. It also helps you unearth the elements of an argument that are buried under complicated prose and rhetoric. And it helps you evaluate the worthiness of the argument presented once it has been fully clarified. You should paraphrase all claims when presenting them in the standard argument form, whether the claims are implied in a long argumentative essay or speech or in shorter arguments that may be ambiguous or unclear. (To understand the added benefits, see Everyday Logic: Modesty and Charity.)

Everyday Logic: Modesty and Charity

The goal of paraphrasing is to find the best presentation of the premises and conclusions intended. By presenting the argument offered in its best possible light, this will help you see not only how far off the argument is from an optimal defense, but also how good it is despite its bad presentation. Why should you be so charitable?

First we must keep in mind that ideas are important, even if the ideas are not ours. So we must always give our utmost due diligence to the examination of ideas. Sometimes even the roughest presentation of ideas can contain the most impressive pearls of insight. If we are not charitable to the ideas of others, then we might miss out on hidden wisdom.

Second, modesty is a good intellectual habit to develop. It is very easy to fall into the trap of thinking that our thoughts are the best ones around. This is generally far from the truth. The most fruitful innovations of mankind have been quite unexpected, often as the result of someone paying attention to others’ ideas and coming up with a new way of putting them to use. This applies to all sorts of things, including everything from the ways in which cooking methods turned into regional cuisines, to scientific discoveries, product innovations, and the emergence of the Internet.

That modesty has advantages is not a new idea. In the 1980s Peter Drucker wrote the book Innovation and Entrepreneurship, in which he recounts, among many other stories, the story of how Ray Kroc founded the burger chain McDonald’s®. As the well-known story goes, Kroc bought a hamburger stand from the McDonald brothers, along with their invention of a milkshake machine. Although Kroc never invented anything, his entrepreneurial genius was in seeing the potential of a hamburger, fries, and milkshake business that catered to mothers with little children and turning this vision into a billion-dollar standardized operation (Drucker, 1985/2007).

Even if you dislike McDonald’s, the point is that Kroc noticed the potential for something that many, including the McDonald brothers themselves, had overlooked. Gems are everywhere in the world of ideas, but we often have to dust them off, remove all the excess baggage, and extract what is good in them. Intellectual modesty allows us to do this; we don’t blind ourselves by assuming our own ideas are best. Once we seek to fully understand others’ ideas and allow them to challenge our own, we can do all sorts of good things: understand an idea more clearly, understand someone better, and understand ourselves (our values, what we find important, and so on) better as well.

Given that our human social world is characterized by diversity of ideas, modesty also marks the path of cooperation, harmony, and respect among human beings. This is one of the many small ways in which the application of logical reasoning can help us all have better lives and better relations with other people. If we could all use logical reasoning on a regular basis, perhaps we would not have as many wars and atrocities as we have today.

Thinking Analytically

Identifying an argument’s components as we have just done is an example of analytical thinking. When we analyze something, we examine its architectural structure—that is, the relation of the whole to its parts—to identify its parts and to see how the parts fit together as a whole.

Let us examine an excerpt from President Barack Obama’s (2014) speech on Ebola as a way of bringing the new skills from this section all together:

In West Africa, Ebola is now an epidemic of the likes that we have not seen before. It’s spiraling out of control. It is getting worse. It’s spreading faster and exponentially. Today, thousands of people in West Africa are infected. That number could rapidly grow to tens of thousands. And if the outbreak is not stopped now, we could be looking at hundreds of thousands of people infected, with profound political and economic and security implications for all of us. So this is an epidemic that is not just a threat to regional security—it’s a potential threat to global security if these countries break down, if their economies break down, if people panic. That has profound effects on all of us, even if we are not directly contracting the disease. (para. 8)

We have identified “The West African Ebola epidemic is a potential threat to global security” as the conclusion. What are the premises? Read the passage a few times while asking yourself, “Why should I think the epidemic is a global threat?” Obama says that the epidemic is not like others, that it is growing faster and exponentially. He moves from there being thousands of people infected, to tens of thousands, to the possibility of hundreds of thousands. So far, everything is about how fast the epidemic is growing.

In the middle of the seventh sentence, the president switches from talking about the growth of the epidemic to claiming that it has profound economic and security implications. What is the basis for the claim that the growth will have these effects? Notice that it is not in the seventh sentence, at least not explicitly. However, the last part of the eighth sentence does address this. In that sentence, Obama suggests three conditions that might lead to a global security threat: “if these countries break down, if their economies break down, if people panic.” So the extreme growth of the epidemic may lead to the breakdown of economies or countries, or it may lead to widespread panic. If any of these things happen, there are “profound effects on all of us.” Therefore, the epidemic is a potential threat to global security. We can now list the premises, and indeed the entire argument, in standard form as follows:

The West African Ebola epidemic is growing extremely fast.

If the growth isn’t stopped, the countries may break down.

If the growth isn’t stopped, the economies may break down.

If the growth isn’t stopped, people may panic.

Any of these things would have profound effects on people outside of the region.

Therefore, the West African Ebola epidemic is a potential threat to global security.

Notice that putting the argument in standard form may lose some of the fluidity of the original, but it more than makes up for it in increased clarity.

2.4 Classifying Arguments

There are many ways of classifying arguments. In logic, the broadest division is between deductive and inductive arguments. Recall that Section 2.1 introduced the notion of inference, the process of drawing a judgment from the reasons offered in the premises. The distinction between deductive and inductive arguments is based on the strength of that inference. A conclusion can follow from the premises very tightly or very loosely, and there is a wide range in between. For deductive arguments, the expectation is that the conclusion will follow from the premises necessarily. For inductive arguments, the expectation is that the conclusion will follow from the premises probably but not necessarily. We shall explore these two kinds of arguments in greater depth in subsequent chapters. In this section our goal is to achieve a basic grasp of their respective definitions and understand how the two types differ from one another. Finally, we will improve our understanding of the concept of an argument by comparing arguments to explanations, which are often mistaken for arguments.

Deductive Arguments

A cartoon that shows a woman asking a man a question. He asks, “Can I get input from the guys at the bar on this one?” He then asks, “Multiple choice guys. Wainscoting is: A. a style of body painting at Mardi Gras, B. the second baseman for the 1953 Red Sox, C. a type of paneling.” The guys at the bar shout all As and Bs for answers. The man asking the question then says, “The consensus is C.” The woman who originally asked the question says, “I’ll give you that one for using sound deductive reasoning.”

In logic the terms deductive and inductive are used in a technical sense that is somewhat different than the way the terms may be used in other contexts. For example, Sherlock Holmes, the protagonist in Sir Arthur Conan Doyle’s detective novels, often referred to his own style of reasoning as deductive. In fact, the popularity of Sherlock Holmes introduced deductive reasoning into ordinary speech and made it a commonplace term. Unfortunately, deductive reasoning is often misunderstood, and in the case of Sherlock Holmes, his clever style of reasoning is actually more inductive than deductive. For example, in The Adventure of the Cardboard Box, he says:

Let me run over the principal steps. We approached the case, you remember, with an absolutely blank mind, which is always an advantage. We had formed no theories. We were simply there to observe and to draw inferences from our observations. (Doyle, 1892/2008, para. 114)

The foregoing does not describe deductive reasoning as it is employed in logic. In fact, Sherlock Holmes mostly uses inductive rather than deductive reasoning. For now, the simplest way to present deductive arguments is to say that deductive reasoning is the sort of reasoning that we normally encounter in mathematical proofs. In a mathematical proof, as long as you do not make a mistake, you can count on the conclusion being true. If the conclusion is not true, you have either made an error in the proof or assumed something that was false. The same is true of deductive reasoning, because good deductive arguments are characterized by their truth-preserving nature—if the premises are true, then the conclusion is guaranteed to be true also. Consider the following deductive argument:

All married men are husbands.

Jacob is a married man.

Therefore, Jacob is a husband.

In this example, the conclusion necessarily follows from the given premises. In other words, if it is true that all married men are husbands and, moreover, that Jacob is a married man, then it must be necessarily true that Jacob is a husband.

But suppose that Jacob is a 3-year-old boy, so he is not a married man. Would the argument still be a good deductive argument and, thereby, truth preserving? The answer is yes, because deductive reasoning reflects the relations between premises and the conclusion such that if it were to be the case that the premises were true, then it would be impossible for the conclusion to be false. If it so happens that Jacob is a 3-year-old boy, then the second premise would not be true, and thus, the necessity for the conclusion to be true is broken.

However, this does not mean that all we need are true premises and a true conclusion. Good deductive arguments are not free form; rather, they use specific patterns that must be followed strictly in the inferential operation. Although this might sound rigid, the greatest advantage of good deductive arguments is that their precise structure guides us into grasping a truth that we might not otherwise have recognized with the same certainty. The use of deductive reasoning is quite broad—in science, mathematics, and the examination of moral problems, to name a few examples. Subsequent chapters will demonstrate more about the powerful machinery of deductive arguments.

Inductive Arguments

In contrast to deductive arguments, good inductive arguments do not need to be truth preserving. Even those that have true premises do not guarantee the truth of their conclusion. At best, true premises in inductive arguments make the conclusion highly probable. The premises of good inductive arguments offer good grounds for accepting the conclusion, but they do not guarantee its truth. Consider the following example:

The produce at my corner store is stocked by local farmers every day.

They have a bakery, too, and they refill their shelves with fresh-baked bread twice a day.

I have been shopping at my corner store continuously for 5 years, and every day is the same.

Therefore, my corner store will have fresh produce and baked goods every day of the week.

Let us suppose that all the premises are true. After 5 years of going to the corner store and getting to know its practices and the quality of its daily offerings, the conclusion would seem to be highly probable. But is it necessarily true? At some point the store may change hands, close, or experience something else that interrupts its normal operations. Such cases show that even though the reasoning is good, the conclusion is not guaranteed to be true just because the premises are true.

Another way to think of what is going on here is to address a likely familiar fact of the human condition: Past experience does not guarantee that the future will be the same. Think of that great car you loved that did not require any expensive maintenance—and then suddenly one day it started to break down bit by bit with age. Time changes the performance of things. Or think of the great quality of a clothing brand you counted on year after year that one day was no longer as good. Products also change with time as the leaders of the manufacturing company change or the standards become somewhat relaxed. Things change. Sometimes the changes are for the better, sometimes for the worse. But our observation of how things are now and have been in the past does not guarantee that things will remain the same in the future. Accordingly, even if the conclusion in our corner store example seems sufficiently justified for us to venture saying that it is true, the fact is that at some point it could change. At best, we can say that the premises give us good grounds to assert that it is probably true that the store will have good produce and baked goods this coming week.

Despite having a weaker connection between premises and conclusion, inductive arguments are more widely used than deductive arguments. In fact, you have likely been using inductive reasoning your entire life without knowing it. Think about the expectation you have that your car, house, or other object will be in the location you last left it. This expectation is based on good inductive reasoning. You have good reasons for expecting your car to be sitting in the parking space where you left it. We can represent your reasoning as follows:

I left my car in that spot.

I have always found my car in the same parking spot I left it in.

Therefore, my car will be in that spot when I return.

Of course, having good reason is not the same as having a guarantee, as anyone who has experienced having their vehicle stolen can attest. This is the difference between deductive and inductive arguments. Because inductive arguments only establish that their conclusions are probable, the conclusions can turn out to be false even when the premises are all true. The chance may be small, but there is always a chance. By contrast, a good deductive argument is airtight; it is absolutely impossible for the conclusion to be false when the premises are true. Of course, if one of the premises is false, then neither kind of argument can establish its conclusion. If you misremember which spot you parked in, then you are not likely to find your car immediately, even if it is right where you left it.

Arguments Versus Explanations

Mastering logical reasoning requires not only understanding what arguments are, but also being able to distinguish arguments from their closest conceptual neighbors. Although it might be clear by now why news articles, debates, and commands are not considered arguments, we should take a closer look at explanations, because they are commonly mistaken for arguments and present a similar framework. Arguments provide a methodical defense of a position, presenting evidence by means of premises in support of a conclusion that is disputed. Explanations, in contrast, tell why or how something is the case.

Suppose that we have the following claim:

We have to travel by train instead of by plane.

If you disagree with this decision, then you might question this claim, thus presenting a request for evidence. Accordingly, an argument would be the appropriate response. We could then have the following:

The total cost for plane tickets is $2,000.

The total cost for train tickets is $1,000.

We have a budget of $1,200 for this trip.

Therefore, we have to travel by train instead of by plane.

Now, suppose that you do not question the claim, but you still want to know why we have to travel by train. This is not a request for evidence for the conclusion. Rather, this is a request for the cause that leads to the conclusion. This is thus a request for an explanation, which may be as simple as this:

Because we do not have enough money for plane tickets.

The point of an argument is to establish its main claim as true. The point of an explanation is to say how or why its main claim is true. In arguments, the premises will likely be less controversial than the conclusion. It is difficult to convince someone that your conclusion is true if they are even less likely to agree with your premises. In explanations, the thing being explained is likely to be less controversial than the explanation given. There is little reason to explain why or how something is true if the listener does not already accept that it is true. Unlike arguments, then, explanations do not involve contested conclusions but, instead, accepted ones. Their point is to say why or how the primary claim is true, not to provide reasons for believing that it is true. This explanation might be fairly straightforward, but distinguishing between arguments and explanations in real life may seem a bit more blurry.

As an example, suppose you try to start your car one morning and it will not start. You recall that your son drove the car last night and know that he has a bad habit of leaving the lights on. You see the light switch is on. You now understand why the car will not start. In our scenario, you found out your car would not start and then looked around for the reason. After noticing that the light switch was on, you came up with the following explanation:

Your son left the lights on.

Leaving the lights on will drain the battery.

A drained battery will prevent the car from starting.

That’s why your car won’t start.

It is an explanation because you already know that your car will not start; you just want to know why.

On the other hand, suppose that after your son got home last night, you noticed that he left the lights on. Rather than turn them off or tell him to do it, you decide to teach him a lesson by letting the battery go dead. In the morning you have the following conversation with your son:

You: I hope you don’t need to go anywhere with the car this morning.

Son: Why?

You: You left the car’s lights on last night.

Son: So?

You: The lights will have completely drained the battery. The car won’t start with a dead battery, so it’s not going to start this morning.

In this case the thing you are most sure of is that your son left the lights on. You reason from that to the conclusion that the car will not start. In this scenario, knowing that the lights were left on is a reason for believing that the car will not start. You are trying to convince your son that the car will not start, and the fact that he left the lights on last night is the starting point for doing so. We can show the structure of your argument as follows:

Your son left the lights on.

Leaving the lights one will drain the battery.

A drained battery will prevent the car from starting.

Therefore, your car won’t start.

Notice that the structure of this argument is the same as the structure of the explanation example. The only difference is whether you are trying to show that the car will not start or to understand why it will not start after already realizing that it will not. Finding the structure will help you understand the details of the argument or explanation, but it will not, by itself, help you determine which one you are dealing with. For that, you have to determine what the author is trying to accomplish and what the author sees as common ground with the reader. Understanding the structure of what is said can help you become clearer about what the author is doing, so it is a good thing to look for, but understanding the structure is not enough.

Determining whether a passage is an argument or an explanation is thus often a matter of interpreting the intention of the speaker or writer of the claim. A good first step is to identify the main point or central focus of the passage. What you are looking for is the sentence that will be either the conclusion to the argument or the claim being explained. If the author has not done so, paraphrase the main claim as a single, simple sentence. Try to avoid including words like because or therefore in your paraphrase. Ask yourself, if this is an argument, what is its conclusion? Once you have identified the potential conclusion, try to determine whether the author is attempting to convince you that that sentence is true, or whether the author assumes you agree with the sentence and is trying to help you understand why or how the sentence is true. If the author is trying to convince you, then the author is advancing an argument. If the author is trying to help you get a deeper understanding, the author is providing an explanation.

It is important to be able to tell the difference between arguments and explanations both when listening to others and when crafting our own arguments and explanations. This is because arguments and explanations are trying to accomplish different goals; what makes an effective argument may not make an effective explanation.

Moral of the Story: Arguments Versus Explanations

If the main claim is accepted as true from the beginning, then the speaker or writer may be advancing an explanation, not an argument. If the point of a passage is to convince the reader that the main claim is true, then it is most likely an argument. Of course, you may question an explanation, thus requesting an argument that the explanation is correct.