Common Inductive Arguments
Section 1: Introduction
In the last unit we focused primarily on deductive arguments. In this unit, we will turn our attention to inductive arguments. Recall that in an inductive argument the truth of the premises does not guarantee the truth of the conclusion. Nevertheless, there are logically strong inductive arguments, and our primary goal will be to learn how to distinguish these arguments from the logically weak ones. We will start with a brief look at inductive arguments more generally. As it turns out, inductive arguments have two distinctive and important characteristics. First, inductive arguments are defeasible. Second, unlike deductive arguments, the logical strength of an inductive argument is not due solely to its form. As a result of these differences, the process of argument evaluation differs in important ways. In this chapter, we will discuss these distinctive features, show how they impact evaluation, and then take a close look at a particular argument form: Argument from Analogy. In the three chapters that follow we will look at other common forms. For each form, we will identify what makes it distinctive, learn the difference between logically strong and logically weak instances of that form, discuss some common pitfalls, and end with some questions that will help us to evaluate for logical strength.
Section 2: Defeasibility and The Rule of Total Evidence
Unlike deductive arguments, all inductive arguments are defeasible. That is, the logical strength of inductive arguments is sensitive to the introduction of new information. Recall the detective example from Chapter 10: a detective is investigating a murder, and has uncovered a number of important pieces of information. She has discovered that the murder weapon was owned by the victim’s sister, the sister’s fingerprints were found on the gun, and the sister had a strong motive. While these three facts strongly point to the sister, they do so in a defeasible way since the support they give to the conclusion might be undermined (or enhanced) by the addition of new information. Indeed, the detective did subsequently find new information, namely security camera footage showing the sister was 25 miles away at the time of the murder. This new information rightly changed the detective’s thinking because the body of evidence available to her no longer supported the sister’s guilt.
Let’s take this example in a different direction. Imagine the detective ignores the fact that the sister was 25 miles away at the time of the murder, and argues instead that the sister committed the crime. We can all agree that the detective has made a big mistake. But what, exactly, is the mistake? It is not a problem with factual correctness or logical weakness: the evidence the detective is drawing on (gun ownership, fingerprints, motive) is accurate and supports the conclusion that the sister is guilty. That is, the problem here is not internal to the argument as formulated. Instead, the problem is with the way the argument has been formulated in the first place. The detective has left something crucial out of the argument, so the conclusion is based on only part of the total available evidence. The same problem can crop up when we evaluate other people’s arguments. After all, if we fail to bring all the relevant facts to the table in deciding whether an argument is sound or not, we are guilty of precisely the same mistake. This kind of mistake is called a violation of The Rule of Total Evidence. This is a rule for evaluating and formulating arguments which tells us that we can’t leave out information. More specifically,
According to The Rule of Total Evidence, when evaluating and formulating an inductive argument, all available relevant evidence must be taken into account.
This rule tells us that in order to adequately evaluate inductive arguments we have to look outside or beyond the argument as stated. We have to think about the claim the conclusion is making, and consider whether there is any available information that would undermine (or enhance) the support the premises lend to the conclusion. Again, the issue here is that if there is available information, and you don’t take this into account, then any conclusion you draw about the argument’s soundness will be premature. Moreover, as premature, the conclusion will be more likely to be mistaken since it isn’t based on the total available evidence.
It is important to note a number of qualifications to The Rule. First, we almost never have “all” the evidence, and The Rule doesn’t say we have to. What The Rule says is that we shouldn’t set aside or ignore evidence that is relevant and available. Second, by ‘available’ we mean information that we know or have easy access to in some sense. Third, it can be difficult to spot violations of The Rule. In order to spot a violation of The Rule, you have to see that something is missing. That is, you have to see what is not in the argument, and this requires relevant background knowledge and the effort to sort through it, as we will see. Fourth, The Rule probably sounds like an obvious requirement—and it is. Nevertheless, people regularly violate this rule—both intentionally and unintentionally. People can unintentionally violate this rule for all kinds of reasons. Recall, for example, that myside bias can lead us to unintentionally leave out relevant evidence. Other times, we simply don’t think to check, or don’t know the right questions to ask. That said, people sometimes purposefully leave out information in order to make a conclusion look more plausible or appealing than it really is.
To intentionally violate The Rule in this way is called cherry-picking. Cherry picking is especially common in persuasive contexts. After all, a proposal, policy, or product can seem especially appealing when we can only see their positives. Here are a couple of recent examples to illustrate the point. In his State of the Union address in January of 2018, President Trump took credit for rising wages. Trump was correct in claiming that wages had risen during his presidency. What he didn’t say, and what undermines his claim, is that wages had been steadily increasing since at least 2014—2 years prior to his becoming president. In short, Trump cherry-picked statistics to make it sound as if his administration had been the chief cause of these gains in wages. Indeed, cherry picking is common in political contexts.
As another example, near the end of the 2020 Democratic Presidential primaries, Joe Biden tried to paint his chief opponent, Bernie Sanders, as against “common sense” gun-control measures like background checks for those purchasing firearms. In support of his contention, Biden pointed out that Sanders had voted against the Brady Bill 5 times. The Brady bill, which was passed into law in 1993 did, among other things, include a background check provision. Moreover, it is true that Sanders voted in this against this bill as it worked its way through Congress in the early 1990s. However, Biden was cherry-picking this statistic. In the intervening 25 years Sanders has voted in favor of a variety of gun control measures that have come before Congress. Taking all of these votes into consideration makes Biden’s claim that Sanders is against common sense gun-control measures more difficult to maintain.
The lesson from all of this for evaluating inductive arguments is that we need to be explicit about asking an another question. As we have seen, in evaluating an argument we need to check for factual correctness by asking: are the premises likely to be true? We also need to check for logical strength by asking: is the conclusion probable given the truth of the premises? While we need to take into account all the relevant evidence when we evaluate for logical strength, it can be easy to forget to do so. For this reason, we add to the Key Evaluative Questions first outlined in Chapter 7:
Three Key Evaluative Questions:
Are the premises likely to be true? (check for Factual Correctness)
Would the truth of the premises make the truth of the conclusion probable? (internal check for inductive strength)
Is there any other relevant information available? (external check for inductive strength)
This third question reminds us to look beyond the argument and to check its logical strength against what we know, or have access to, more broadly. For this reason, it is helpful to think of this third question as an external check on (inductive) logical strength, and the more straightforward consideration of the support lent by the premises themselves as an internal check.
Section 3: Determining Logical Strength for Inductive Argument Forms
In the last unit, we identified a number of deductive argument forms (e.g. Modus Ponens, Hypothetical Syllogism, etc). Identifying arguments by form is a useful way of classifying arguments, and we will continue to do so in this unit by identifying common inductive forms. However, there is an important difference between deductive and inductive argument forms, namely that while deductive forms guarantee logical strength, inductive forms do not. To illustrate, there are no logically weak arguments with the form of Modus Ponens. Any argument with this form will be logically strong because the form itself guarantees logical strength. In contrast, consider a common inductive form: Arguments from Analogy. While there are logically strong arguments with this form, there are logically weak Arguments from Analogy as well, and this is a because inductive forms do not guarantee logical strength. The upshot here is that when it comes to inductive forms, simply knowing an argument’s form won’t tell you whether it is logically strong or not. There are other relevant factors at work, and we’ll need to take these into account in determining logical strength.
What factors? There is no one-size-fits-all answer to this. Nevertheless, we will see that the relevant factors vary from one inductive form to another. Thus, the factors relevant to determining whether an Argument from Analogy is logically strong differ from the factors relevant to determining whether an Inductive Generalization is logically strong. Consequently, even though knowing an argument’s inductive form won’t automatically tell you whether it is logically strong or not, it will tell you what factors are relevant, and what questions to ask to figure it out. It is important to emphasize that in saying that evaluation differs from argument form to argument form, it is the process of evaluation that differs, not the criteria. We evaluate all arguments by the criteria of factual correctness and logical strength. The difference between evaluating an Argument from Analogy and an Inductive Generalization has to do with the appropriate steps to take for determining logical strength. So, what is an Argument from Analogy anyway, and how do we evaluate them? Let’s take a look.
Section 4: Identifying Arguments from Analogy
Observations of similarity and difference play a number of roles in everyday contexts. In many cases they are used as tools for explaining difficult concepts or relationships. For example, a science teacher might explain how electricity flows by comparing it to water. Moreover, judgments of similarity and difference underlie many other reasoning processes. To give just one example, think about categorization. To decide that two things belong in the same category is to decide they are similar in some important way. Our primary concern, however, will be arguments in which one or more similarities are used to infer the presence of a further similarity, and we will refer to arguments with this form as Arguments from Analogy.
Let us begin with some examples.
Sofia is a very good dancer, so I bet she has the potential to be very good at fencing, since fencing, like dance, requires excellent balance and fine motor skills.
You think it is fine to eat pork, and biologically speaking there are only minor differences between pigs and dogs, so you should be willing to eat dog too.
Let us take a closer look at these examples by standardizing them.
Surface-Level Standardization of Ex. 1:
- Sofia is a very good dancer.
- Fencing, like dance, requires excellent balance and fine motor skills.
- So, I bet Sofia has the potential to be a very good fencer.
Surface-Level Standardization of Ex. 2:
- You think it is fine to eat pork.
- Biologically, pigs and dogs are extremely similar.
- So, you should be willing to eat dog too.
What these arguments have in common is that each draws its conclusion on the basis of a comparison between two objects or situations (note the underlined terms), and indeed this is what is distinctive about arguments from analogy. It is important to remember that just because an argument contains an analogy or comparison does not mean it is an argument from analogy. Again, arguments from analogy are inferences in which the conclusion is drawn on the basis of a comparison.
We will refer to the objects or situations that are compared in an argument from analogy as the analogues. Thus, the analogues in Ex. 1 are fencing and dancing, and the analogues in Ex. 2 are pigs and dogs. People are creative and draw comparisons between all kinds of things; in some cases, people offer arguments from analogy in which the analogues are themselves arguments! Consider the following:
Sometimes people argue that we should not take prescription drugs because they contain unnatural substances and unnatural substances may be harmful to the body. But this is a poor argument since by similar reasoning we could conclude that you should not consume ice cream (since it is an unnatural substance and may be harmful to the body). Since this is a bad argument, so too is the first one.
This argument draws a comparison between arguments. Let us call the first argument the Prescription Drug Argument and standardize it as follows:
- Prescription drugs contain unnatural substances.
- Unnatural substances may be harmful to the body.
- So, we should not take prescription drugs.
Let us call the second argument the Ice Cream Argument and standardize it as follows:
- Ice cream contains unnatural substances.
- Unnatural substances may be harmful to the body.
- So, we should not (eat) ice cream.
In short, the argument in Ex. 3 is claiming that the Prescription Drug Argument is like the Ice Cream Argument in that both draw their conclusions on the basis of the fact that their subjects contain unnatural substances, and that unnatural substances may be harmful to the body. Given these similarities and that the Ice Cream Argument is a bad argument (the author is assuming that you will agree that it is not wrong to eat ice cream), the author concludes that the Prescription Drug Argument is a bad one too.
Section 5: Evaluating Arguments from Analogy
What is the difference between logically strong Arguments from Analogy and logically weak ones? Let us begin with a weak Argument from Analogy. We will modify the argument in Ex. 1 to make it uncontroversially weak.
Sofia is a very good fencer, so I bet she has the potential to be very good at throwing the shot put, since fencing, like throwing the shot put, is an Olympic sport.
We can agree that this is a weak argument, but what makes it weak? The problem is that the noted similarity is irrelevant to the similarity that is inferred in the conclusion. The fact that both fencing and shot put are Olympic events has nothing to do with whether Sofia would be a good shot putter. There are many different Olympic events, and the skill and expertise required for one may not translate to another. Since all Arguments from Analogy rely on a comparison, this is a point we can generalize upon. We can say that in a logically strong Argument from Analogy, the noted similarity or similarities are relevant to the inferred similarity.
Two brief notes about this requirement. First, a noted similarity is relevant to the inferred similarity when (and only when) the presence of the noted similarity makes the presence of the inferred similarity more probable. Second, this is only one condition for logical strength. Even if the noted similarities are relevant, it does not follow that the argument is logically strong. After all, arguments from analogy are defeasible, and so in accordance with The Rule of Total Evidence, we have to consider whether there is relevant available information that bolsters or undermines the support the noted similarities give to the inferred similarities. To illustrate, let’s modify the example above again.
Sofia is a very good fencer, so I bet she has the potential to be very good at throwing the shotput, since fencing, like throwing the shot put, requires quickness and agility.
This argument does not have the same problem as Ex. 4. In this case, the author is noting that both fencing and the shot put require quickness and agility, and these characteristics are relevant to the inferred similarity. Knowing that somebody is quick and agile would give you some positive reason to think that they would be good at throwing the shot put. Nevertheless, this argument is problematic, since even a passing familiarity with the two sports reveals fundamental differences. For example, body mass and power are crucial for success in throwing the shot put, but are less so in fencing. Similarly, fine hand-eye coordination and physical endurance are crucial for success in fencing, but less so for shot put. Thus, although the noted similarities are relevant to the inferred similarity, there are relevant differences between the two that undermine the logical strength of the existing argument. Again, since all arguments from analogy depend on a comparison, we can generalize on this example and say that the presence of relevant differences between the analogues weakens the strength of the analogy—sometimes decisively.
One last note: it is important to recognize that not all differences are relevant differences. What makes a difference relevant is that it makes the inferred similarity less probable, but there will always be differences that do not tell us anything about the probability of the inferred similarity. For example, in fencing you wear a mask, and in the shot put you do not. This difference doesn’t really tell us anything about whether Sofia would be a good at the shot put or not. Again, there will always be many differences between analogues, and the task is not to identify differences, but relevant differences.
There are a number of other features relevant to the evaluation of Arguments from Analogy. For example, the more relevant similarities there are between the analogues, the stronger the argument. Furthermore, relevant similarity and difference are a matter of degree; that is, one similarity (or difference) might be more relevant than another. Nevertheless, the relevance of the noted similarity to the inferred similarity, and whether there are relevant differences are by far the most important issues when it comes to evaluating Arguments from Analogy. Thus, after having identified an argument as an Argument from Analogy, and having identified the noted similarity and the inferred similarity, you will always want to ask yourself two questions.
Two Questions to Ask of Any Argument from Analogy:
Are the similarities relevant?
Are there relevant differences?
The first question asks about the argument as stated. The second question asks about whether there is other available information that is relevant to the conclusion. While we could ask the question more broadly to look for similarities as well, looking for differences is especially important. After all, the person giving the argument has already identified similarities that purportedly support the conclusion. If they’ve left something important out, it is likely to be in the form of a difference, and so it makes sense to focus your thinking on them.
In general, it is worth observing that people tend to find it much easier to detect weak Arguments from Analogy when the noted similarity is not relevant to the inferred similarity, than it is to detect arguments that are weak due to relevant differences. One plausible explanation for this is that taking up the first question above is relatively easy—the similarities in question are right there in front of you, and all you need to do is determine whether one is relevant to the other. Taking up the second question above requires more effort, since whether there are relevant differences is not right there in front of you. If there are relevant differences, they are missing; to find them we have to look beyond the argument itself, thinking about what else we know of the analogues. Thus, it takes extra work to identify differences, and this is worth keeping in mind when evaluating Arguments from Analogy.
Exercise Set 12A:
Have you ever noticed or suspected that somebody was cherry-picking their evidence? When? If not, make up a realistic example of cherry-picking.
Invent an argument from analogy in which the noted similarity is not relevant to the inferred similarity.
Think about the last time you felt you were treated unfairly. How might your judgment that you were treated unfairly rely on an argument from analogy?
In law the concept of a legal precedent is very important. What is a legal precedent and how might its use in legal proceedings be related our discussion of arguments from analogy?
Exercise Set 12B:
Directions: Each of the following is an argument from analogy. Assume each argument is factually correct, and evaluate each argument’s logical strength. Explain your evaluation.
You wouldn’t think eating a person is okay, would you? A cow is a living breathing being just like a person is, so why do you think that eating a cow is fine?
Last week I sold my 2012 Toyota Camry for $5000. The body was in good shape and so was the engine, and the mileage on the car was pretty low. Your 2013 Camry is in about the same condition, and the mileage is about the same, so I’d guess you could get at least $5000 for it.
Blaming guns for the mass shooting at Columbine is like blaming spoons for America’s obesity epidemic!
Having children is just like buying a house. Like buying a house, raising a child properly is an expensive prospect, and just as you shouldn’t take on a mortgage you can’t afford, so too you shouldn’t have children unless you can afford to do so.
Covid-19 is an easily spreadable virus just like the flu. But we don’t lock down the country or take extreme measures to prevent the spread of the flu, so we shouldn’t do so for Covid-19 either.
I am completely on board with the proposed law to require voters to present valid ID before they can vote. I mean you have to present ID to buy alcohol or cigarettes, to board a plane, legally drive a car, and to get into an R-rated movie, so why should voting be any different?
You wouldn’t commit to buying a car without test driving it first, so why would you commit to marrying someone without living together first?
Copy machine repair person: Your copy machine is pretty good—I mean it only breaks down on average once a month.
Copy machine owner: You think that is good? I have a dishwasher and it has never broken down!
Comedian George Carlin:
I don’t understand this notion of ethnic pride. “Proud to be Irish,” “Puerto Rican pride,” “Black pride.”…Being Irish isn’t a skill; it’s genetic. You wouldn’t say. “I’m proud to have brown hair,” or “I’m proud to be short and stocky.” So why…would you say you’re proud to be Irish? I’m Irish, but I’m not particularly proud of it. Just glad!…[G]lad to be Irish!
Hydraulic fracking produces, as a waste product, a lot of salty chemical-laden water. The EPA prefers that when the water cannot be recycled that it be put into injection wells which deposit the waste far underground. However, in Ohio this process may be responsible for a recent spate of earthquakes. This had led to a moratorium on permits on new injection wells. In response the owner of a company that runs inspection wells says:
- “If you’ve got a car that has a problem with it, does that mean we should take all the cars off the road and go back to horse and buggy?”
- See Fetzer, James (Ed.). (2001). The Philosophy of Carl Hempel. Oxford: Oxford University Press, 114. ↵
- Jacobson, Louis. (2018, Feb. 5). "The Age of Cherry Picking." Politifact. https://www.politifact.com/truth-o-meter/article/2018/feb/05/age-cherry-picking/ ↵
- Source: Detrow, Scott. (2012, Apr. 11). “From Pa. Waste To Ohio Quakes” NPR. https://www.npr.org/2012/04/11/150445837/from-pa-waste-to-ohio-quakes ↵