An Introduction to Reasoning

1 Reasoning and Argument

Section 1: Introduction

We spend a lot of time trying to figure things out, and we do so primarily by means of reason.  For example, we try to predict what will happen, explain what has already occurred, generalize from our experiences, and extrapolate from what we know.  While we are sometimes interested in abstract questions, most of the time we put our reasoning skills to work on entirely practical matters.  We have goals, plans, and interests, and being able to accurately predict, explain, generalize on, and extrapolate from, our experiences are crucial skills for achieving our goals.  Indeed, we all know how to reason.  We do it all the time, and it is something we are relatively good at doing.  Nevertheless, reasoning is also something that we can improve on, and sharpening our skills can have dramatic effects on our beliefs and decisions. In this chapter we will start by defining reasoning and explaining how it relates to arguments.  We will then briefly introduce two important skills: argument analysis and argument evaluation.  Along the way, we will begin building a vocabulary for thinking about and developing these skills.

Section 2: What is Reasoning?

We reason all the time, but what are we doing exactly?  This answer might not be immediately obvious, so let’s begin with some straightforward cases to see what they have in common.

  • Solving a math problem
  • Figuring out why your phone won’t work correctly
  • Deciding who to vote for
  • Working out why your friend is angry with you
  • Determining whether you can afford to buy a new car

What do these have in common?  We could pick out a number of features, but we will focus on two in particular.  First, in each case our thinking is driving toward a specific outcome or conclusion (e.g. “my phone won’t work because…”, or “the answer is…”, etc.).  Second, in each one of these cases this conclusion will be based on reasons.  That is, we will arrive at a specific conclusion because we think we have good reasons for doing so.  Let us take a closer look at each of these features.

Reasoning is a mental process that ends with a conclusion.  Sometimes this conclusion is a newly formed belief.  You might, for example, be asked to find the average of 88, 69, 94, and 77 and arrive at the new belief that the average of these numbers is 82.  Alternatively, you might troubleshoot your phone and arrive at the new belief that the operating system wasn’t properly installed. While reasoning always leads to a conclusion, that conclusion need not be a new belief.  In some cases, these processes lead us to be more (or less) confident in beliefs we already hold.  We can see both kinds of conclusion at work in the following example.

Ex. 1:

Talia wakes up one morning to discover that her car is missing.  As she thinks about it she quickly concludes that her brother has probably borrowed it.  Her reasons for drawing this conclusion are that he i) knows where her spare set of keys are, ii) has borrowed it without asking in the past, and iii) is supposed to pick up a cake at a bakery across town today.  Just after she has come to this conclusion the phone rings.  It is one of Talia’s friends who mentions that she saw Talia’s car parked at the bakery across town.

In the first part of Ex. 1 Talia is reasoning to a new belief, namely that her brother has borrowed her car.  When her friend calls, she gets a new piece of information.  However, this information does not lead her to any new belief; after all, this information is an additional reason for thinking that her brother has borrowed the car, and she already believes that.  Instead, as a result of this news, she is even more confident that her brother has borrowed the car.  In light of this distinction, we will say that reasoning is a process that leads to a change in a person’s system of belief, and we will understand a person’s system of belief to include not only their beliefs, but also the relationships between those beliefs, and the confidence with which they are held.

The second defining feature of reasoning is that it is a process whereby we change our system of beliefs because we have reasons for doing so.  In general, to have reasons for drawing some conclusion is to have some group of existing beliefs that indicate in one way or another that the conclusion in question is true.  In the example above, Talia has a variety of existing beliefs about her brother and his circumstances, and she takes this information to point toward the fact that her brother has borrowed the car.

Importantly, our reasons can indicate the truth of the conclusion to different degrees.  When we take ourselves to have solved a math problem correctly, for example, we take ourselves to have shown that the conclusion is correct.  This is a bit different from Talia’s reasoning—she probably wouldn’t say that her reasons show or prove that her brother borrowed the car.  Nonetheless, she thinks that her reasons are good enough to draw the conclusion.  In general, reasons can support conclusions with different degrees of strength, and it should be no surprise that we have many different ways of talking about this support.  We can say, for example, that when we reason we take our existing beliefs to indicate, give good reason for, offer evidence on behalf of, establish, warrant, or demonstrate a change to our system of beliefs.  These differences will be important later, but for now we will simply say that when we reason, we take our existing beliefs to justify a particular change in our system of belief.

Now that we have taken a brief look at the reasoning process, we can return to the question we began with and define reasoning as follows:

Reasoning is the process whereby a person changes their system of belief on the basis of reasons which they take to justify this change.

Section 3: Types of Reasoning

We have just arrived at a definition of reasoning, but it is important to note that this definition captures only one kind of reasoning.  Over the last 20-30 years, psychologists and cognitive scientists have come to the conclusion that we use a variety of different methods and mechanisms to update our system of beliefs.  Some of these methods involve conscious directed attention, but many do not.  Here is the basic idea: many of the things that humans do are automatic and do not involve conscious control.  We do not, for example, need to tell ourselves to breathe or blink (although we can).  Moreover, it is not just physical activity that can be automatic; mental activities can occur automatically as well.  Take recognition for example.  You do not decide to recognize people—it is something you automatically do.  The same goes for laughing.  You do not need to think about laughing—it is often an automatic reaction (though sometimes events can become funny as you think about them).  Cognitive scientists and psychologists now think that, in addition, there are a variety of automatic and semi-automatic reasoning processes.  These processes update our systems of belief in ways that are often outside of any conscious effort or awareness.

In order to get a sense for different kinds of reasoning processes, consider the following example.[1]  In answering this question make sure to note the first answer that comes to mind.  Then stop and think about it a little more.

Ex. 2:

A bat and ball cost $1.10 in total.  The bat costs $1.00 more than the ball.  How much does the ball cost?

First Answer that Occurs to You: _________________.

Considered Answer:_________________.

baseball and bat
“National Baseball Hall of Fame: P. Waner’s 3000th Career Hit Ball and Bat” by IslesPunkFan CC BY-NC 2.0

Most people read this question and a particular answer just pops into their heads.  This answer appears immediately to them, without any particular effort.  However, if you take a closer look at this automatic answer, you will see that it can’t be right, and figuring out the actual answer to this question takes some work (follow this note if you need some help).[2]  The way the question in Ex. 2 is structured triggers in many people an automatic reasoning mechanism which gives an answer that our conscious reasoning system subsequently recognizes as wrong.

In this case, a largely automatic process leads us to make a mistake.  But this is not always the case; in fact, we rely on reasoning processes like this all of the time.  As we navigate through the world we automatically and reliably respond to our environment, and we will see that these kinds of reasoning processes naturally generate intuitive reactions to, and impressions of, people, places, circumstances, and ideas (among other things).  These intuitions and impressions contribute to our system of belief, and can thereby inform successive conscious forms of reasoning.

In this book, we will primarily address consciously directed reasoning, since this is the kind of reasoning over which we have the most control.  Nonetheless, we cannot ignore other types of reasoning processes.  These processes are pervasive features of our thinking and inform our conscious judgments and decisions both positively and negatively. Given this, it is important to know when to be skeptical of the impressions and intuitions that these processes give us.  As such, if we want to think more clearly and make better choices, we will have to take these kinds of processes into account.  Since we will be primarily discussing directed conscious reasoning, let us simply refer to this as “reasoning” in line with the definition given at the end of section 2.  When we need to talk about automatic reasoning processes we will explicitly identify them.

Section 4: From Reasoning to Argument

In thinking about reasoning more generally, we will focus our attention primarily on the investigation of arguments.  In order to illustrate the difference between reasoning and argument, we will need to start by talking in more detail about beliefs.  Normally, we would agree that two people can share a belief.  Consider, for example, the fact that both Maria and Jackson are enrolled in Economics 101, and so share the belief that the course is taught on Tuesdays and Thursdays from 2-3:15.  In what sense do they share this belief?  As we’ve seen, a belief is part of an individual’s system of belief, and so is a psychological state of that individual.  Maria’s beliefs are hers, and Jackson’s are his, and this means that in an important sense, Maria and Jackson do not have the same belief.  Rather, they share the belief insofar as their distinct beliefs are about the same thing, or have the same content.  The sharable content of a belief is called a proposition, and we will say that Maria and Jackson believe the same proposition, namely that Economics 101 is on Tuesdays and Thursdays from 2-3:15.  Making the distinction between a belief and its content is useful, at least in part, because it allows us to talk about the truth of the proposition without talking about any individual person.

This is relevant because there is a similar distinction between reasoning and argument.  Suppose that Maria and Jackson are sitting in their Economics class; at 2:05 they both look out the window and see their friend Logan, who is also enrolled in the course, speeding away from the building on his bike.  They both conclude that Logan is not coming to class.  Let’s compare their thinking.  On the one hand, Maria and Jackson have engaged in distinct reasoning processes.  After all, Maria’s reasoning had led her to update her system of belief, and Jackson’s reasoning has led him to update his.  Nevertheless, there is something common to their distinct reasoning processes.  They have both updated their systems of belief to include the same proposition, namely ‘Logan is not coming to class,’ on the basis of the same reasons, namely their respective beliefs in the propositions that ‘It is 2:05’ and ‘Logan is speeding away from the building’.  These distinct reasoning processes share the same content, and we will call the content of a process of reasoning, an argument.  That is, we will say that an argument is a collection of propositions in which one is purportedly justified by the others.  When we reason, we take our existing belief that one or more propositions are true (our reasons), to justify our belief that some other proposition is also true (our conclusion).  That is, we reason by means of arguments. Like the distinction between beliefs and propositions, drawing the distinction between reasoning and argument is useful because it allows us to evaluate a reasoning processes independently of who is engaging in it.

Section 5: Arguments and their Parts

When it comes to arguments, it is important to make two terminological distinctions.  First, the term ‘argument’ as it is defined above differs from another common sense of the term.  We often use the term ‘an argument’ to refer to a disagreement or a dispute.  This is not how we will be using the term.  Here is an example of a dispute that is not an argument as this book uses the term.

Ex. 3:

Maria: Eating meat is irresponsible and unnecessary.

Jackson: Are you crazy?  No it is not.

Why isn’t this disagreement an example of an argument?  The answer, in short, is because neither person has tried to justify what they are saying.  Presumably each person has reasons for thinking they are right, but as conversation stands all that has been publically expressed is a disagreement.  Compare Ex. 3 to the following.

Ex. 4:

I bet the Phillies will win their game tonight since they are on a hot streak.

Ex. 5:

I needed to get at least 90% of the points in this class to earn an A-.  Because I got 84%, I didn’t earn an A-.

Ex. 6:

The choice for dinner is either lasagna or pizza.  The pizza is too gross to even consider eating.  I guess it’s lasagna for me!

Examples 4-6 are all arguments since, in each case, a reason is offered on behalf of a conclusion.  As these examples of argumentation show, arguments are common in everyday thinking and need not concern abstract or theoretical topics (although they certainly may).

A second terminological note is that all arguments have two parts—the premises and the conclusion.  The premises of an argument give reasons or evidence on behalf of the conclusion; put otherwise, premises are the pieces of information that back-up or justify the conclusion. The conclusion, on the other hand, is the proposition for which reasons or evidence are given, it is that proposition which is backed-up or justified.  We can label the parts of the arguments above accordingly:

Ex. 4:

Premise—The Phillies are on a hot streak

Conclusion—The Phillies will win their game tonight.

Ex. 5:

Premise—I needed to have gotten at least 90% of the points in this class to get an A-

Premise—I got 84%

Conclusion—I won’t get an A-

Ex. 6:

Premise—My choices are either lasagna or pizza.

Premise—There is no way I can eat the pizza—it is always gross.

Conclusion—I will be having lasagna.

With these terminological issues out of the way we can focus on arguments themselves.  First, although we reason by means of arguments, it is important to recognize that we often think and reason about arguments as well.  Here is an example:

Ex. 7:

Maria says “I don’t buy the argument that since voting is a restricted activity, we should require IDs at the polls.”

Maria is considering the following argument:

Premise: Voting is a restricted activity.

Conclusion: We should require IDs at the polls.

In this instance Maria is talking about an argument, but not making one herself.  Maria is claiming that one reason people sometimes give for thinking that we should require IDs at the polls is not, to her mind, a good one.

“Vote for Nacho” by rikkis_refuge CC BY 2.0

This raises a second point.  Arguments can be good or bad.  When we come to believe a conclusion on the basis of the premises we do so because we have judged that the premises justify or establish the conclusion.  But we can be wrong about this.  Sometimes arguments that we take to be good, are not.  In general terms, good arguments are arguments in which the premises establish their conclusion, whereas bad arguments are those in which the premises do not.  Correspondingly, we reason well when our beliefs are based on good arguments and we reason poorly when they are not.  Thus, in order to improve our reasoning, we will have to learn how to properly evaluate arguments.  Doing so is a two-step process.  Most obviously, we will need to learn how to distinguish between good arguments and bad ones.  This information is useless, however, if we cannot accurately identify and analyze arguments.  Put otherwise, you cannot accurately assess whether an argument is good or bad, if you don’t know what the premises are, and how they are related to the conclusion.  Let us take an introductory look at these two steps.

Section 6: An Introduction to Spotting Arguments

There are a number of words that authors and speakers use to indicate that they are making an argument.  We will call these words indicator words, since they typically indicate the presence of an argument.  Some words and phrases, like ‘since’, ‘because’, ‘for’, ‘on account of’, and ‘given that…’, specifically indicate the presence of a premise.

Ex. 8:

There is no way the Spartans will make the playoffs this year, since they are 6 games back with less than two weeks to go.

Ex. 9:

Given the suspect’s blood/alcohol level at the time of the accident, it is clear that she was driving over the legal limit.

Other words and phrases specifically indicate the presence of an argument’s conclusion: ‘thus’, ‘therefore’, ‘hence’, ‘so’, ‘consequently’.

Ex. 10:

Malik doesn’t have any brothers or sisters; hence he is an only child.

Ex. 11:

The number 8 is even; consequently, it is not a prime number.

We need to keep two qualifications in mind.  First, these brief lists include the most common indicator words, but there are many ways that authors and speakers can indicate the presence of an argument without using these terms.  Thus, we cannot merely memorize the terms above and be done with it.  Second, unfortunately indicator words do not always indicate the presence of an argument.  Consider the following:

Ex. 12:

The marching band hasn’t gotten anything less than a #1 at contest since 2015.

In this case, the term ‘since’ is being used to refer to time, not to a premise.  Given that indicator words are not 100% reliable as indications of argumentation, we cannot infer that we have an argument merely because one of our indicator words shows up.  As we will see, we need to pay attention to the contexts in which these words are used.

There are a couple of common obstacles to spotting arguments we should note at the outset.  The first has to do with conditional claims.  As noted, an argument amounts to a set of propositions in which one proposition is supported by the others.  Propositions report a fact about the world and are either true or false, e.g. ‘Dogs are mammals’, ‘Yosemite is in California’, ‘Jordan’s mom is a lawyer’.  Presumably you get the point, but there is one kind of proposition that people often find confusing: conditionals.  What is a conditional?  To start off, let’s look at some examples:

Ex. 13:

You are legally eligible to purchase alcoholic beverages in this state only if you are 21 years of age or older.

Ex. 14:

If the candle is lit, then oxygen is present.

Ex. 15:

You are not permitted to play poker at the Platinum table if you are not willing to bet at least $20 per hand.

What do all of these propositions have in common?  While we might identify a number of features, the most important for our purposes is that each expresses a relationship between two things.  More specifically, each tells us that one thing is dependent or conditional in some way on another thing: a burning candle depends on oxygen, playing at the Platinum table is conditional on betting $20 per hand, and so forth.  In very general terms, this is what a conditional is—a proposition that says that one thing is dependent on another (more on this later though).  Part of what makes thinking about conditionals difficult is that we are used to thinking about objects and their characteristics, but less so about the relations between them.  Nevertheless, relations are just as much a part of the world as anything else.

There is a lot to say about conditionals, but for the time being we will focus on two noteworthy features of conditionals in particular.  First, as you can see there are many ways that conditionals can be expressed, though it is very common to use the word ‘if’.  Second, because conditional claims express a relation between two or more things, they commonly appear in arguments about the things they relate.   You might conclude, for example, that you are not permitted to play poker at the Platinum table, since you aren’t willing to bet $20 per hand, and this is a requirement for playing at that table.

A second obstacle to spotting arguments has to do with opinions.   Suppose somebody says “teens really shouldn’t be watching R-rated movies, since for the most part they  are not mature enough to handle the psychological and emotional effects of mature content.”  Is this an argument?  Many people are tempted to say ‘no’—this is just an opinion.  When we use ‘opinion’ in this way, we are identifying an idea or claim as particularly controversial, uncertain, or debatable.  Understood in this sense the claim that “teens really shouldn’t be watching R-rated movies” is an opinion, whereas something like “The bookshelf weighs 80 lbs.” is not.  After all, the weight of the bookshelf should not be controversial or debatable—we can use objective and commonly agreed upon methods to determine its weight.

Truck with many political bumper stickers
“Opinionated” by iceman9294 CC BY-NC 2.0

We need to be aware, however, that whether a statement is controversial or debatable is not relevant to whether there is an argument present.  Recall that anytime a speaker or author gives a reason to believe a conclusion, they have given an argument—regardless whether anything the author has said or written is controversial, uncertain, or debatable.  In the example above, the speaker uses the word ‘since’ to indicate the presence of a premise, and consequently, the presence of an argument.  So: whether somebody’s claim is an opinion won’t tell us anything about whether they have offered an argument.  In fact, often controversial, uncertain, and debatable claims are precisely the sort of thing that people offer arguments for!

Section 7: Evaluating Arguments

Last, let us turn to the most important topic this book will take up: argument evaluation.  To evaluate an argument is to decide whether it is good or bad.  We have an intuitive ability to evaluate arguments—we can usually distinguish good arguments from bad ones just by looking at them.  This native ability is not, however, infallible; in fact, there are certain contexts and kinds of cases where we tend to make mistakes.  Thus it is important to ask: what is the difference between a good argument and a bad one?  Put otherwise, we need to know what makes a good argument, good, and a bad argument, bad.  Let us start with an example.

Ex. 16:

Premise: The largest city in the U.S. is located in Nebraska.

Premise: New York City is the largest city in the U.S.

Conclusion:  So, New York City is located in Nebraska.

Clearly this is a bad argument.  The problem is that one of its premises is false—we know that the largest city in the U.S. is not in the state of Nebraska.  This example shows one way in which an argument can be bad: when it has false premises.  Let us say the following:

An argument is factually correct when (and only when) all of its premises are true.  It is factually incorrect otherwise.

Thus, the argument in Ex. 16 is factually incorrect because not all of its premises are true.  In addition, whether an argument is factually correct or not is solely a matter of whether the premises are true—an argument with all true premises but a false conclusion is still factually correct.  Factual correctness is not, however, the only feature of an argument relevant to its evaluation.  Consider the following case.

Ex. 17:

Premise: Selena passed her driver’s license exam.

Conclusion: So, Selena will pass her calculus exam.

Let us say that it is true that Selena passed her driver’s license exam.  Even so, clearly this is a bad argument.  This is a poor argument because the premise does not support the truth of the conclusion.  That is, the premise, though true, does not give us good or sufficient reason to believe the conclusion is true.  We will refer to this feature of arguments as logical strength and say:

An argument is logically strong when (and only when) the premises—if true—provide strong support for the truth of the conclusion.  An argument is logically weak otherwise.

It is crucial to see that these features of arguments are independent of one another.  An argument may be factually incorrect, but logically strong (see, e.g. Ex. 16), factually correct, but logically weak (Ex. 17), both correct and strong, or both incorrect and weak.  In light of these distinctions we can distinguish good arguments from bad ones in the following way.  Let us say that:

An argument is good, henceforth sound, when (and only when) it is both factually correct and logically strong.  An argument is unsound otherwise.

Ideally, all of our reasoning would proceed by means of sound arguments.  However, we are always working with limited information, and this means that we all sometimes endorse unsound arguments.  Nevertheless, as we will see in this text, we can take steps to limit these kinds of cases.

Exercises

Exercise Set 1A:

Directions: For each of the following passages, determine whether either speaker is giving an argument or whether the speakers are merely having a dispute.

#1:

A: We should go to Drew’s place tonight.

B: Um, no.  We should avoid Drew’s place like the plague.

#2:

A: Obama is our worst president!

B: What are you talking about?  Our “worst president”?  Do you even know what that means?

#3:

A: Many peer-reviewed studies have shown that asbestos is a carcinogen.

B: These studies can’t be right, since my uncle worked in an asbestos mine for 40 years and didn’t get cancer.

#4:

A: Minneapolis has about the same population as Indianapolis.

B: No it doesn’t, my dad told me that Indianapolis is much bigger.

Exercise Set 1B:

Directions: For each of the following passages, determine whether there is an indicator word(s) present and if so, identify it.

#1:

People who can’t speak Russian are excluded from this opportunity, so you can’t come.

#2:

The first inhabitants of the island were Dutch settlers.  The next wave of settlers were mainly from Italy and Greece.

#3:

There are two main reasons for rejecting this option—first, it is immoral; second, it doesn’t achieve what we are actually trying to do!

#4:

Seeing as it has air conditioning, I think you should count yourself lucky to live in that dorm.

Exercise Set 1C:

Directions: Determine whether each of the following arguments is sound or not.  If unsound, then say whether it is factually incorrect, logically weak, or both.

#1:

Premise: There are exactly 52 states that make up the United States.

Conclusion: So, if I’ve only been to 50 states, then I haven’t been to them all.

#2:

Premise: All squares are rectangles.

Premise: No rectangles are circles.

Conclusion: So some squares are circles.

#3:

Premise: The word ‘since’ always indicates the presence of an argument.

Conclusion: So, the claim “the marching band hasn’t gotten anything less than a #1 at contest since 2015” is an argument.

#4:

Premise: If an argument is sound, then it is logically strong.

Premise: If an argument is logically strong, then the premises—if true—provide  strong support for the truth of the conclusion.

Conclusion: So, if an argument is sound, then the premises—if true—provide strong support for the truth of the conclusion.

Exercise Set 1D:

#1:

Our systems of belief change all the time.  Give a brief example of a time your system of belief changed.

#2:

What is the difference between reasoning and argument as we are using the terms in this book.

#3:

List 1 true conditional claim.  List 1 false conditional claim.

#4:

Describe the experience of playing scrabble, or bananagrams, or some other similar word game.  How might automatic reasoning processes be at work in this kind of experience?

 

 


  1. Frederick, Shane. (2005) “Cognitive Reflection and Decision Making.” Journal of Economic Perspectives 19 (4), 25-42.
  2. On first glance most people think the answer is that the ball costs $.10.  However, that can’t be right.  The bat costs $1.00 more than the ball, so if the ball costs $.10, the bat costs $1.10, and together they cost $1.20.

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