Phi 103 Week 3 Assignment

Learning Objectives After reading this chapter, you should be able to:1. Compare and contrast the advantages of deduction and induct ion.

2. Explain why one might choose an inductive argument over a de ductive argument.

3. Analyze an argument for its deductive and inductive compon ents.

4. Explain the use of induction within the hypothetico–deduct ive method.

5. Compare and contrast falsification and confirmation withi n scientific inquiry.

6. Describe the combined use of induction and deduction within scientific reasoning.

7. Explain the role of inference to the best explanation in sci ence and in daily life. 6 Deduction and Induction: Putting It All Together Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iSt ock/Thinkstock Now that you have learned something about deduction and induction, you may be wondering why we need both. This chapter is devoted to answering that qu estion. We will start by learning a bit more about the differences between deductive and inductive reaso ning and how the two types of reasoning can work together. After that, we will move on to explo re how scientific reasoning applies to both types of reasoning to achieve spectacular results. Arguments with both inductive and deductive elements are very common. Recognizing the advantages and disadvant ages of each type can help you build better arguments. We will also investigate another very useful type of inference, known as inference to the best explanation, and explore its advantages. Fuse/Thinkstock New information can have an impact on both deductive and inductive arguments. It can render deductive arguments unsound and can strengthen or weaken inductive arguments, such as arguments for buying one car over another. 6.1 Contrasting Deduction and Induction Remember that in logic, the difference between indu ction and deduction lies in the connection between the pre mises and conclusion. Deductive arguments aim for an absolut e connection, one in which it is impossible that the pre mises could all be true and the conclusion false. Arguments that achieve this aim are called valid. Inductive arguments aim for a probable connection, one in which, if all the premises are true, the conclusion is more likely to be true th an it would be otherwise. Arguments that achieve this aim ar e called strong. (For a discussion on common misconceptions about the meanings of induction and deduction , see A Closer Look: Doesn’t Induction Mean Going From Specific to General? ). Recall from Chapter 5 that inductive strength is the counterpart of deductive validity, and cogency is the inductive counterpart of deductive soundness. One of the purposes of this chapter is to properly understand the differences and connections between these two major ty pes of reasoning.

There is another important difference between deduct ive and inductive reasoning. As discussed in Chapter 5, if you add another premise to an inductive argument, the argument may become either stronger or weaker. For example, suppose you are thinking of buying a new cell phone. After looking at all yo ur options, you decide that one model suits your needs better than the others. New information about the ph one may make you either more convinced or less convinced that it is the right one for you—it depends on what the new information is. With deductive reasoning, by contrast, adding premises to a valid argu ment can never render it invalid. New information may show that a deductive argument is unso und or that one of its premises is not true after all, but it cannot undermine a valid connection bet ween the premises and the conclusion. For example, consider the following argument:

All whales are mammals.

Shamu is a whale.

Therefore, Shamu is a mammal.

This argument is valid, and there is nothing at all we could learn about Shamu that would change this. We might learn that we were mistaken about whales be ing mammals or about Shamu being a whale, but that would lead us to conclude that the argument is u nsound, not invalid. Compare this to an inductive argument about Shamu.

Whales typically live in the ocean.

Shamu is a whale.

Therefore, Shamu lives in the ocean.

Now suppose you learn that Shamu has been trained to d o tricks in front of audiences at an amusement park. This seems to make it less likely that Shamu lives in the ocean. The addition of this new information has made this strong inductive argument we aker. It is, however, possible to make it stronger again with the addition of more information. For example, we could learn that Shamu was part of a captive release program.

An interesting exercise for exploring this concept is to see if you can keep adding premises to make an inductive argument stronger, then weaker, then strong er again. For example, see if you can think of a series of premises that make you change your mind back and forth about the quality of the cell phone discussed earlier.

Determining whether an argument is deductive or indu ctive is an important step both in evaluating arguments that you encounter and in developing your own arguments. If an argument is deductive, there are really only two questions to ask: Is it val id? And, are the premises true? If you determine that the argument is valid, then only the truth of the pr emises remains in question. If it is valid and all of th e premises are true, then we know that the argument is so und and that therefore the conclusion must be true as well.

On the other hand, because inductive arguments can go from strong to weak with the addition of more information, there are more questions to consider rega rding the connection between the premises and conclusion. In addition to considering the truth of t he premises and the strength of the connection between the premises and conclusion, you must also consid er whether relevant information has been left out of the premises. If so, the argument may beco me either stronger or weaker when the relevant information is included.

Later in this chapter we will see that many argument s combine both inductive and deductive elements. Learning to carefully distinguish between these elemen ts will help you know what questions to ask when evaluating the argument. A Closer Look : Doesn’t Induction Mean Going From Specific to General?

A common misunderstanding of the meanings of induction and deduction is that deduction goes from the general to the specific, whereas induction g oes from the specific to the general. This definition is used by some fields, but not by logic or philosophy. It is true that some deductive arguments go from general premises to specific conclusio ns, and that some inductive arguments go from the specific premises to general conclusions. Ho wever, neither statement is true in general.

First, although some deductive arguments go from gener al to specific, there are many deductive arguments that do not go from general to specific. So me deductive arguments, for example, go from general to general, like the following:

All S are M.

All M are P.

Therefore, all S are P.

Propositional logic is deductive, but its arguments do not go from general to specific. Instead, arguments are based on the use of connectives ( and, or , not , and if . . . then ). For example, modus ponens (discussed in Chapter 4) does not go from the general to the specific, but it is deductively valid. When it comes to inductive arguments, some—for e xample, inductive generalizations—go Use this video to review deductive and inductive arguments. from specific to general; others do not. Statistical sy llogisms, for example, go from general to specific, yet they are inductive.

This common misunderstanding about the definitions of induction and deduction is not surprising given the different goals of the fields in which the terms are used. However, the definitions used by logicians are especially suited for the classificati on and evaluation of different types of reasoning.

For example, if we defined terms the old way, then t he category of deductive reasoning would include arguments from analogy, statistical syllogisms, and some categorical syllogisms. Inductive reasoning, on the other hand, would includ e only inductive generalizations. In addition, there would be other types of inference that would f it into neither category, like many categorical syllogisms, inferences to the best explanation, appeals to authority, and the whole field of propositional logic.

The use of the old definitions, therefore, would not clear up or simplify the categories of logic at all but would make them more confusing. The current di stinction, based on whether the premises are intended to guarantee the truth of the conclusion, does a much better job of simplifying logic’s categories, and it does so based on a very important and relevant d istinction.

Deductive and Inductive Arguments   Deductive and Inductive Arguments From Title: Logic: The Structure of Reason (https://fod.infobase.com/PortalPlaylists.aspx?wID= 100753&xtid=32714) Critical Thinking Questions 1. What does it mean when we say that validity is independent of the truth of the premises and conclusions in an argument? 2. What are the differences between deductive and inductive arguments? What is the relationship between truth and the structure of a deductive versus an inductive argument? Practice Problems 6.1 Click here (https://ne.edgecastcdn.net/0004BA/constellation/PD Fs/PHI103_2e/Answers_PracticeProblems6.1.pdf) to check your answers.

1. A deductive argument that establishes an absolute connecti on between the premises and conclusion is called a __________. a. strong argument b. weak argument c. invalid argument d. valid argument 2. An inductive argument whose premises give a lot of support for t he truth of its conclusion is said to be __________. a. strong b. weak c. valid d. invalid 3. Inductive arguments always reason from the specific to the gen eral. a. true b. false 4. Deductive arguments always reason from the general to the spec ific. a. true b. false Alistair Scott/iStock/Thinkstock Despite knowing that a helium­filled balloon will rise when we let go of it, we still hold our belief in gravity due to strong inductive reasoning and our reliance on observation. 6.2 Choosing Between Induction and Deduction You might wonder why one would choose to use inductive reasoning over deductive reasoning. After all, why would you want to show that a conclusion was only probably true rather than guaranteed to be true? There are several reasons, which will be discussed in this section. First, there may not be an available deductive argument based on agreeable premises. Seco nd, inductive arguments can be more robust than deductive arguments. Third, inductive argument s can be more persuasive than deductive arguments.

Availability Sometimes the best evidence available does not lend it self to a deductive argument. Let us consider a readily accepted fact: Gravity is a force that pulls everything toward the earth. How would you provide an argument for that claim? You would probably pick something up, let go of it, and note that it falls toward the earth. For added effect, you might pick up several things and show that each of them falls. Put in premise–conclusion form, your argument looks something like t he following:

My coffee cup fell when I let go of it.

My wallet fell when I let go of it.

This rock fell when I let go of it.

Therefore, everything will fall when I let go of it.

When we put the argument that way, it should be clea r that it is inductive. Even if we grant that the premises are true, it is not guaranteed that everything will fall when you let go of it. Perhaps gravity does not aff ect very small things or very large things. We could do more ex periments, but we cannot check every single thing to make sure that it is affected by gravity. Our belief in gravity is the result of extremely stron g inductive reasoning. We therefore have great reasons to believe in gravity , even if our reasoning is not deductive.

All subjects that rely on observation use inductive rea soning: It is at least theoretically possible that future observations may be totally different than past ones. Therefore, our inferences based on observatio n are at best probable. It turns out that there are very few subjec ts in which we can proceed entirely by deductive reasoning. These tend t o be very abstract and formal subjects, such as mathematics. Although other fie lds also use deductive reasoning, they do so in combination with i nductive reasoning. The result is that most fields rely heavily on inductive reasoning .

Robustness Inductive arguments have some other advantages over d eductive arguments. Deductive arguments can be extremely persua sive, but they are also fragile in a certain sense. When something goes wro ng in a deductive argument, if a premise is found to be false or if it is found to be invalid, th ere is typically not much of an argument left. In co ntrast, inductive arguments tend to be more robust. The robust ness of an inductive argument means that it is less fragile; if there is a problem with a premise, the argument may become weaker, but it can still be quite persuasive. Deductive arguments, by contrast, tend to be completely unconvincing once they are shown not to be sound. Let us work through a couple of examples to see what this means in practice.

Consider the following deductive argument: All dogs are mammals.

Some dogs are brown.

Therefore, some mammals are brown.

As it stands, the argument is sound. However, if we chan ge a premise so that it is no longer sound, then we end up with an argument that is nearly worthless. F or example, if you change the first premise to “Most dogs are mammals,” you end up with an invalid argument . Validity is an all­or­nothing affair; there is no such thing as “sort of valid” or “more valid.” Th e argument would simply be invalid and therefore unsound; it would not accomplish its purpose of demonstr ating that the conclusion must be true. Similarly, if you were to change the second premise t o something false, like “Some dogs are purple,” then the argument would be unsound and therefore would supply no rea son to accept the conclusion.

In contrast, inductive arguments may retain much of their strength even when there are problems with them. An inductive argument may list several reasons in support of a conclusion. If one of those reasons is found to be false, the other reasons continue to supp ort the conclusion, though to a lesser degree. If an argument based on statistics shows that a particular con clusion is extremely likely to be true, the result of a problem with the argument may be that the conc lusion should be accepted as only fairly likely. The argument may still give good reasons to accept the conclusion.

Fields that rely heavily on statistical arguments often have some threshold that is typically required in order for results to be publishable. In the social scien ces, this is typically 90% or 95%. However, studies that do not quite meet the threshold can still be instr uctive and provide evidence for their conclusions. If we discover a flaw that reduces our confidence in an argument, in many cases the argument may still be strong enough to meet a threshold.

As an example, consider a tweet made by President Barack Obama re garding climate change. Twitter/Public Domain Although the tweet does not spell out the argument fully, it seems to have the following structure:

A study concluded that 97% of scientists agree that clim ate change is real, man­made, and dangerous.

Therefore, 97% of scientists really do agree that clima te change is real, man­made, and dangerous.

Therefore, climate change is real, man­made, and dangerous. Given the politically charged nature of the discussion of climate change, it is not surprising that the president’s argument and the study it referred to rece ived considerable criticism. (You can read the study at http://iopscience.iop.org/1748–9326/8/2/024024/pdf/174 8 –9326_8_2_024024.pdf (http://iopscience.iop.org/1748­9326/8/2/024024/pdf/1748­9326_8_2_024024.pdf) .) Looking at the effect some of those criticisms have on the argument is a good way to see how inductive arguments can be more robust than deductive ones.

One criticism of Obama’s claim is that the study he ref erenced did not say anything about whether climate change was dangerous, only about whether it w as real and man­made. How does this affect the argument? Strictly speaking, it makes the first premise false. But notice that even so, the argument can still give good evidence that climate change is real and man­made. Since climate change, by its nature, has a strong potential to be dangerous, the argument i s weakened but still may give strong evidence for its conclusion.

A deeper criticism notes that the study did not find o ut what all scientists thought; it just looked at those scientists who expressed an opinion in their published work or in response to a voluntary survey. This is a significant criticism, for it may expose a bias in the sampling m ethod (as discussed in Chapters 5, 7, and 8). Even granting the criticism, the argument can re tain some strength. The fact that 97% of scientists who expressed an opinion on the issue said that climate change is real and man­made is still some reason to think that it is real and man­made. Of cour se, some scientists may have chosen not to voice an opposing opinion for reasons that have nothing to do w ith their beliefs about climate change; they may have simply wanted to keep their views private, for e xample. Taking all of this into account, we get the following argument:

A study found that 97% of scientists who stated their op inion said that climate change is real and man­made.

Therefore, 97% of scientists agree that climate change is real an d man­made.

Climate change, if real, is dangerous.

Therefore, climate change is real, man­made, and dangerous.

This is not nearly as strong as the original argument, b ut it has not collapsed entirely in the way a purely deductive argument would. There is, of course, much m ore that could be said about this argument, both in terms of criticizing the study and in terms of respo nding to those criticisms and bringing in other considerations. The point here is merely to highlight the difference between deductive and inductive arguments, not to settle issues in climate science or public polic y.

Persuasiveness A final point in favor of inductive reasoning is that it can often be more persuasive than deductive reasoning. The persuasiveness of an argument is based on h ow likely it is to convince someone of the truth of its conclusion. Consider the following classic argumen t:

All Greeks are mortal.

Socrates was a Greek.

Therefore, Socrates was mortal.

Is this a good argument? From the standpoint of logic, it is a perf ect argument: It is deductively valid, and its premises are true, so it is sound (therefore, its conc lusion must be true). However, can you persuade anyone with this argument? Imagine someone wondering whether Socrates was mortal. Could you use this argument to convince him or her that Socrates was mortal? Probably not. Th e argument is so simple and so obviously valid that anyone who accepts the premises likely already ac cepts the conclusion. So if someone is wondering about the conclusion, it is unlikely that he or she will be persuaded by these premises. He or she may, for example, remember that some legendary Greeks, such as Hercules, were granted immortality and wonder whether Socrates was one of these. The deductive approach, therefore, is unlikely to win anyone over to the conclusion here. On the other hand, consider a very si milar inductive argument.

Of all the real and mythical Greeks, only a few were considered t o be immortal.

Socrates was a Greek.

Therefore, it is extremely unlikely that Socrates was immortal .

Again, the reasoning is very simple. However, in this case, we can imagine someone who had been wondering about Socrates’s mortality being at least som ewhat persuaded that he was mortal. More will likely need to be said to fully persuade her or him, but this simple argument may have at least some persuasive power where its deductive version likely does not.

Of course, deductive arguments can be persuasive, but t hey generally need to be more complicated or subtle in order to be so. Persuasion requires that a per son change his or her mind to some degree. In a deductive argument, when the connection between pre mises and conclusion is too obvious, the argument is unlikely to persuade because the truth of the premises will be no more obvious than the truth of the conclusion. Therefore, even if the argu ment is valid, someone who questions the truth of the conclusion will often be unlikely to accept the truth of the premises, so she or he may be unpersuaded by the argument. Suppose, for example, that we wanted t o convince someone that the sun will rise tomorrow morning. The deductive argument may look like this:

The sun will always rise in the morning.

Therefore, the sun will rise tomorrow morning.

One problem with this argument, as with the Socrates a rgument, is that its premise seems to assume the truth of the conclusion (and therefore commits the fa llacy of begging the question, as discussed in Chapter 7), making the argument unpersuasive. Additio nally, however, the premise might not even be true . What if, billions of years from now, the earth is swa llowed up into the sun after it expands to become a red giant? At that time, the whole concept of morning may be out the window. If this is true then the first premise may be technically false. That means that the argument is unsound and therefore fairly worthless deductively.

The inductive version, however, does not lose much stre ngth at all after we learn of this troubling information:

The sun has risen in the morning every day for millions of years.

Therefore, the sun will rise again tomorrow morning.

This argument remains extremely strong (and persuasive) regardless of what will happen billions of years in the future. Practice Problems 6.2 Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.2.pdf) to check your answers.

1. Which form of reasoning is taking place in this example? The sun has risen every day of my life.

The sun rose today.

Therefore, the sun will rise tomorrow.

a. inductive b. deductive 2. Inductive arguments __________. a. can retain strength even with false premises b. collapse when a premise is shown to be false c. are equivalent to deductive arguments d. strive to be valid 3. Deductive arguments are often __________. a. less persuasive than inductive arguments b. more persuasive than inductive arguments c. weaker than inductive arguments d. less valid than inductive arguments 4. Inductive arguments are sometimes used because __________. a. the available evidence does not allow for a deductive argum ent b. they are more likely to be sound than deductive ones c. they are always strong d. they never have false premises 6.3 Combining Induction and Deduction You may have noticed that most of the examples we have explored have been fairly short and simple. Real­life arguments tend to be much longer and more complicated. They also tend to mix inductive and deductive elements. To see how this might work, let us revisit an example from the previous section.

All Greeks are mortal.

Socrates was Greek.

Therefore, Socrates was mortal.

As we noted, this simple argument is valid but unlikely to convince anyone. So suppose now that someone questioned the premises, asking what reasons there are for thinking that all Greeks are mortal or that Socrates was Greek. How might we respond?

We might begin by noting that, although we cannot c heck each and every Greek to be sure he or she is mortal, there are no documented cases of any Greek, o r any other human, living more than 200 years. In contrast, every case that we can document is a case in which the person dies at some point. So, although we cannot absolutely prove that all Greeks are mortal , we have good reason to believe it. We might put our argument in standard form as follows:

We know the mortality of a huge number of Greeks.

In each of these cases, the Greek is mortal.

Therefore, all Greeks are mortal.

This is an inductive argument. Even though it is theor etically possible that the conclusion might still be false, the premises provide a strong reason to accept th e conclusion. We can now combine the two arguments into a single, larger argument:

We know the mortality of a huge number of Greeks.

In each of these cases, the Greek is mortal.

Therefore, all Greeks are mortal.

Socrates was Greek.

Therefore, Socrates was mortal.

This argument has two parts. The first argument, leading to the subconclusion that all Greeks are mortal, is inductive. The second argument (whose conclusion is “ Socrates was mortal”) is deductive. What about the overall reasoning presented for the conclusion th at Socrates was mortal (combining both arguments); is it inductive or deductive?

The crucial issue is whether the premises guarantee the truth of the conclusion. Because the basic premise used to arrive at the conclusion is that all of the Greeks who se mortality we know are mortal, the overall reasoning is inductive. This is how it generally works. As noted ear lier, when an argument has both inductive and deductive components, the overall argument is generally induct ive. There are occasional exceptions to this general rule, so in particular cases, you still have to check whether the premises guarantee the conclusion. But, almost always, t he longer argument will be inductive. Fran/Cartoonstock Sometimes a simple deductive argument needs to be combined with a persuasive inductive argument to convince others to accept it. A similar thing happens when we combine inductive arguments of different strength. In general, an argum ent is only as strong as its weakest part. You can think of each inference in an argument as being like a link in a c hain. A chain is only as strong as its weakest link. Practice Problem 6.3 Click here (https://ne.edgecastcdn.net/0004BA/constellation/PD Fs/PHI103_2e/Answers_PracticeProblems6.3.pdf) to check your answers.

1. When an argument contains both inductive and deductive ele ments, the entire argument is considered deductive. a. true b. false 6.4 Reasoning About Science: The Hypothetico–Deductive Method Science is one of the most successful endeavors of the modern world, and arguments play a central role in it. Science uses both deductive and inductive reaso ning extensively. Scientific reasoning is a broad field in itself—and this chapter will only touch on th e basics—but discussing scientific reasoning will provide good examples of how to apply what we have learned abou t inductive and deductive arguments.

At some point, you may have learned or heard of the scientific method, which often refers to how scientists systematically form, test, and modify hypothese s. It turns out that there is not a single method that is universally used by all scientists.

In a sense, science is the ultimate critical thinking e xperiment. Scientists use a wide variety of reasoning techniques and are constantly examining those techniqu es to make sure that the conclusions drawn are justified by the premises—that is exactly what a good cr itical thinker should do in any subject. The next two sections will explore two such methods—the hypothet ico–deductive method and inferences to the best explanation—and discover ways that they can improv e our understanding of the types of reasoning used in much of science.

The hypothetico–deductive method consists of four steps:

1. Formulate a hypothesis.

2. Deduce a consequence from the hypothesis.

3. Test whether the consequence occurs.

4. Reject the hypothesis if the consequence does not occur.

Although these four steps are not sufficient to explain all scientific reasoning, they still remain a core part of much discussion of how science works. You may rec ognize them as part of the scientific method that you likely learned about in school. Let us take a look at eac h step in turn.

Step 1: Formulate a Hypothesis A hypothesis is a conjecture about how some part of the world wor ks. Although the phrase “educated guess” is often used, it can give the impression that a h ypothesis is simply guessed without much effort. In reality, scientific hypotheses are formulated on t he basis of a background of quite a bit of knowledge and experience; a good scientific hypothesis often com es after years of prior investigation, thought, and research about the issue at hand.

You may have heard the expression “necessity is the moth er of invention.” Often, hypotheses are formulated in response to a problem that needs to be so lved. Suppose you are unsatisfied with the performance of your car and would like better fuel econom y. Rather than buy a new car, you try to figure out how to improve the one you have. You guess that yo u might be able to improve your car’s fuel economy by using a higher grade of gas. Your guess is not just random; it is based on what you already know or believe about how cars work. Your hypothesis is that higher grade gas will improve your fuel economy.

Of course, science is not really concerned with your c ar all by itself. Science is concerned with general principles. A scientist would reword your hypothesis in terms of a general rule, something like, “Increasing fuel octane increases fuel economy in aut omobiles.” The hypothetico–deductive method can work with either kind of hypothesis, but the general hypothesis i s more interesting scientifically. Step 2: Deduce a Consequence From the Hypothesis Your hypothesis from step 1 should have predictive value: Things should be different in some noticeable way, depending on whether the hypothesis is true or fa lse. Our hypothesis is that increasing fuel octane improves fuel economy. If this general fact is true, then it is true for your car. So from our general hypothesis we can deduce the consequence that your car will get more miles per gallon if it is running on higher octane fuel.

It is often but not always the case that the predictio n is a more specific case of the hypothesis. In such cases it is possible to infer the prediction deductively fro m the general hypothesis. The argument may go as follows:

Hypothesis: All things of type A have characteristic B.

Consequence (the prediction): Therefore, this specific thing of type A will have characteristic B.

Since the argument is deductively valid, there is a st rong connection between the hypothesis and the prediction. However, not all predictions can be deductively inferred. In such cases we can get close to the hypothetico–deductive method by using a strong inducti ve inference instead. For example, suppose the argument went as follows:

Hypothesis: 95% of things of type A have characteristic B.

Consequence: Therefore, a specific thing of type A will probab ly have characteristic B.

In such cases the connection between the hypothesis and the prediction is less strong. The stronger the connection that can be established, the better for the reliabi lity of the test. Essentially, you are making an argument for the conditional statement “If H, then C,” w here H is your hypothesis and C is a consequence of the hypothesis. The more solid the connection is bet ween H and C, the stronger the overall argument will be.

In this specific case, “If H, then C” translates to “If increasing fuel octane increases fuel economy in all cars, then using higher octane fuel in your car will increase its fuel economy.” The truth of this conditional is deductively certain.

We can now test the truth of the hypothesis by testing the truth of t he consequence.

Step 3: Test Whether the Consequence Occurs Your prediction (the consequence) is that your car will get better fuel economy if you use a higher grade of fuel. How will you test this? You may think this is o bvious: Just put better gas in the car and record your fuel economy for a period before and after cha nging the type of gas you use. However, there are many other factors to consider. How long should the pe riod of time be? Fuel economy varies depending on the kind of driving you do and many other factor s. You need to choose a length of time for which you can be reasonably confident the driving conditions ar e similar on average. You also need to account for the fact that the first tank of better gas you put in will be mixed with some of the lower grade gas that is still in your tank. The more you can address these and other issues, the more certain you can be that your conclusion is correct. IPGGutenbergUKLtd/iStock/Thinkstock At best, the fuel economy hypothesis will be a strong inductive argument because there is a chance that something other than higher octane gas is improving fuel economy. The more you can address relevant issues that may impact your test results, the stronger your conclusions will be. In this step, you are constructing an inductive argum ent from the outcome of your test as to whether your car actually did get better fuel economy. The arguments in this step are inductive because there is always some possibility that you have not adequately ad dressed all of the relevant issues. If you do notice better fuel economy, it is always possible that the increase in economy is due to some factor other than the one you are tracking. The possibility may be very small, but it is enough to make this kind of argument inductive rather than deductive.

Step 4: Reject the Hypothesis If the Consequence Does Not Occu r We now compare the results to the prediction and find out if the prediction came true. If your test finds that your car’s fuel economy does not improve when yo u use higher octane fuel, then you know your prediction was wrong.

Does this mean that your hypothesis, H, was wrong? That depends on the strength of the connection between H and C. If the inference from H to C is ded uctively certain, then we know for sure that, if H is true, then C must be true also. Therefore, if C is false, it follows l ogically that H must be false as well.

In our specific case, if your car does not get better fuel economy by switching to higher octane fuel, the n we know for sure that it is not true that all cars get better fuel economy by doing so. However, i f the inference from H to C is inductive, then the connect ion between H and C is less than totally certain. So i f we find that C is false, we are not absolutely sure that the hypothe sis, H, is false.

For example, suppose that the hypothesis is that cars tha t use higher octane fuel will have a higher tendency to get better fuel mileage. In that case if your car does not get higher gas mileage, then you st ill cannot infer for certain that the hypothesis is false. To test that hypothesis adequately, you would have to do a large study with many cars. Such a study would be much more complicated, but it could provide very strong evidence that the hypothesis is false.

It is important to note that although the falsity of the prediction can demonstrate that the hypothesis is false, the truth of the prediction does not prove that the hypo thesis is true. If you find that your car does get better fuel economy when you switch gas, you cannot conclude that your hypothesis is true.

Why? There may be other factors at play for which yo u have not adequately accounted. Suppose that at the same ti me you switch fuel grade, you also get a tune­up and new tires and start driving a completely different route to wo rk. Any one of these things might be the cause of the improved gas mileage; you cannot conclude that it is due to the c hange in fuel (for this reason, when conducting experiments it is best to change only one variable at a time and carefully control the rest). In other words, in the hypothetico–deductiv e method, failed tests can show that a hypothesis is wrong, but tests that succeed do not show that the hypothesis wa s correct. Keystone/Getty Images Karl Popper, a 20th­ century philosopher of science, put forth This logic is known as falsification; it can be demonstrated clearly by looking at the st ructure of the argument. When a test yields a negative result, the hy pothetico–deductive method sets up the following argument:

If H, then C.

Not C.

Therefore, not H.

You may recognize this argument form as modus tollens, or denying the consequent , which was discussed in the chapter on propositional logic (Chapter 4). T his argument form is a valid, deductive form. Therefore, if both of these premises are true, then we can be certain that the conclusion is true as well; namely, that our hypothesis, H, is not true. In the sp ecific case at hand, if your test shows that higher octane fuel does not increase your mileage, then we c an be sure that it is not true that it improves mileage in all vehicles (though it may improve it in some).

Contrast this with the argument form that results when your fuel e conomy yields a positive result:

If H, then C.

C.

Therefore, H.

This argument is not valid. In fact, you may recogniz e this argument form as the invalid deductive form called affirming the consequent (see Chapter 4). It is possible that the two premises ar e true, but the conclusion false. Perhaps, for example, the improvement in fuel economy was caused by a change in tires or different driving conditions instead. So the hypot hetico –deductive method can be used only to reject a hypothesis, not to confirm it. This fact has led many to see the primary role of science to be the falsification of hypotheses. Philosopher Karl Popper is a central source for this view (see A Closer Look: Karl Popper and Falsification in Science ). A Closer Look: Karl Popper and Falsification in Science Karl Popper, one of the most influential philosophers of science to emerge from the early 20th century, is perhaps best kn own for rejecting the idea that scientific theories could be proved by simply finding confirming evidence—the prevailing philosophy at the time. Instead, Popper emphasized that claims must be testable and falsifiable in order to be considered scientific.

A claim is testable if we can devise a way of seeing if it is true or not . We can test, for instance, that pure water will freez e at 0°C at sea level; we cannot currently test the claim that the oceans in another galaxy taste like root beer. We have no realistic way to det ermine the truth or falsity of the second claim.

A claim is said to be falsifiable if we know how one could show it to be false. For instance, “there are no wild kangaroos in G eorgia” is a falsifiable claim; if one went to Georgia and found some wild the idea that unfalsifiable claims are unscientific. Learn more about Karl Popper's criterion of falsifiability in this video. Karl Popper and Falsification Critical Thinking Questions 1. Karl Popper argues that only hypotheses that can be tested and falsified are scientific. Do you agree? 2. In addition to being unscientific, Popper states that unfalsifiable claims tell us nothing and do not allow us to learn from our mistakes. Can you make an argument against Popper's? kangaroos, then it would have been shown to be false. But what if someone claimed that there are ghosts in Georgia but that they are imperceptible (unseeable, unfeelable, unhearable, et c.)? Could one ever show that this claim is false? Since such a claim c ould not conceivably be shown to be false, it is said to be unfa lsifiable. While being unfalsifiable might sound like a good thing, according to Popper it is no t, because it means that the claim is unscientific.

Following Popper, most scientists today operate with th e assumption that any scientific hypothesis must be testable and must be the kind of clai m that one could possibly show to be false. So if a claim turns out not to be conceivably fal sifiable, the claim is not really scientific—and some philosophers have gone so far as to regard such claims as meaningl ess (Thornton, 2014).

As an example, suppose a friend claims that “everything works out for the best.” Then suppose that you have the worst month of your life, and you go back to your friend and say that the claim is false: Not everything is for the best. Your friend might then reply that in fact it was for the best because you learned from the experience. Such a statement may make you feel better, but it runs afoul of Popper’s rule. Can you imagine any circumstance that your friend would not claim is for the best? Since your friend would probably say that it was for the best no matter what happens, your friend’s claim is unfalsifiable and therefore unscientific.

In logic, claims that are interpreted so that they come out true no matter what happens are called self­sealing propositions . They are understood as being internally protected against any objections. People who state such claims may feel that they are saying something deeply meaningful, but according to Popper’s rule, since the claim could never be falsified no matter what, it does not really tell us anything at all.

Other examples of self­sealing propositions occur within philosophy itself. There is a philosophical theory known as psychological egoism, for example, which teaches that everything everyone does is completely selfish. Most people respond to this claim by coming up with examples of unselfish acts: giving to the needy, spending time helping others, and even dying to save so meone’s life. The psychological egoist predictably responds to all such examples by stating that pe ople who do such things really just do them in order to feel better about themselves. It appear s that the word selfish is being interpreted so that everything everyone does will automatically b e considered selfish by definition. It is therefore a self­sealing claim (Rachels, 1999). Accord ing to Popper’s method, since this claim will always come out true no matter what, it is unfalsifiab le and unscientific. Such claims are always true but are actually empty because they tell us nothing a bout the world. They can even be said to be “too true to be good.” Popper’s explorations of scientific hypotheses and what it means to confirm or disconfirm such hypotheses have been very influential among both scien tists and philosophers of scientists. Scientists do their best to avoid making claims that are not falsif iable.

If the hypothetico­deductive method cannot be used t o confirm a hypothesis, how can this test give evidence for the truth of the claim? By failing to falsify the claim. Though the hypothetico–deductive method does not ever specifically prove the hypothesi s true, if researchers try their hardest to refute a claim but it keeps passing the test (not being refuted) , then there can grow a substantial amount of inductive evidence for the truth of the claim. If y ou repeatedly test many cars and control for other variables, and if every time cars are filled with hig her octane gas their fuel economy increases, you may have strong inductive evidence that the hypothesis mig ht be true (in which case you may make an inference to the best explanation , which will be discussed in Section 6.5).

Experiments that would have the highest chance of ref uting the claim if it were false thus provide the strongest inductive evidence that it may be true. For example, suppose we want to test the claim that all swans are white. If we only look for swans at places in which they are known to be white, then we are not providing a strong test for the claim. The best th ing to do (short of observing every swan in the whole world) is to try as hard as we can to refute the claim, to find a swan that is not white. If our best methods of looking for nonwhite swans still fail to ref ute the claim, then there is a growing likelihood that perhaps all swans are indeed white.

Similarly, if we want to test to see if a certain type of medicine cures a certain type of disease, we test the product by giving the medicine to a wide variety of patients with the disease, including those with the least likelihood of being cured by the medicine. Onl y by trying as hard as we can to refute the claim can we get the strongest evidence about whether all instan ces of the disease are treatable with the medicine in question.

Notice that the hypothetico–deductive method involve s a combination of inductive and deductive reasoning. Step 1 typically involves inductive reasoni ng as we formulate a hypothesis against the background of our current beliefs and knowledge. Step 2 ty pically provides a deductive argument for the premise “If H, then C.” Step 3 provides an inductive argument for whether C is or is not true. Finally, if the prediction is falsified, then the conclusion—that H is false—is derived by a deductive inference (using the deductively valid modus tollens form). If, on the other hand, the best attempts to prove C to be false fail to do so, then there is growing evidence that H might be true. Therefore, our overall argument has both inductive and deductive elements. It is valuable to know that, although the methodology of science involves research and experimentation that goes well beyond the scope of pure logic, we can use logic to understand and clarify th e basic principles of scientific reasoning. Practice Problems 6.4 Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.4.pdf) to check your answers.

1. A hypothesis is __________. a. something that is a mere guess b. something that is often arrived at after a lot of research c. an unnecessary component of the scientific method d. something that is already solved 2. In a scientific experiment, __________. a. the truth of the prediction guarantees that the hypothesis wa s correct b. the truth of the prediction negates the possibility of the hyp othesis being correct c. the truth of the prediction can have different levels of pr obability in relation to the hypothesis being correct d. the truth of the prediction is of little importance 3. The argument form that is set up when a test yields negative re sults is __________. a. disjunctive syllogism b. modus ponens c. hypothetical syllogism d. modus tollens 4. A claim is testable if __________. a. we know how one could show it to be false b. we know how one could show it to be true c. we cannot determine a way to prove it false d. we can determine a way to see if it is true or false 5. Which of the following claims is not falsifiable? a. The moon is made of cheese.

b. There is an invisible alien in my garage. c. Octane ratings in gasoline influence fuel economy.

d. The Willis Tower is the tallest building in the world. Image Asset Management/SuperStock Sherlock Holmes often used abductive reasoning, not deductive reasoning, to solve his mysteries. 6.5 Inference to the Best Explanation You may feel that if you were very careful about test ing your fuel economy, you would be entitled to conclude that the change in fuel grade really did h ave an effect. Unfortunately, as we have seen, the hypothetico–deductive method does not support this infe rence. The best you can say is that changing fuel might have an effect; that you have not been able to show that it does not have an effect. The method does, however, lend inductive support to whichever hy pothesis withstands the falsification test better than any other. One way of articulating this type of support is with an inference pattern known as inference to the best explanation .

As the name suggests, inference to the best explanation draws a conclusion based on what would best explain one’s observations. It is an extremely importan t form of inference that we use every day of our lives. This type of inference is often called abductive reasoning, a term pioneered by American logician Charles Sanders Peirce (Douven, 2011).

Suppose that you are in your backyard gazing at the stars. Suddenly, you see some flashing lights hovering above you in the sky. You do not hear any sou nd, so it does not appear that the lights are coming from a helicopter. What do you think it is? What ha ppens next is abductive reasoning: Your brain searches among all kinds of possibilities to attempt to come up wit h the most likely explanation.

One possibility is that it is an alien spacecraft coming to get you (one could joke that this is why it is called abductive reasoning). Another possibility is that it is some kind of military vessel or a weather balloon. A more extreme hypothesis is that you are actually drea ming the whole thing.

Notice that what you are inclined to believe depend s on your existing beliefs. If you already think that alien spaceships come to Earth all the time, then you may arrive at that conclusion with a high degree of certainty (you may even shout, “Take me with you!”). However, if you are somewhat skeptical of those kinds of theories, then you will try hard to find any other explanation. Therefore, the strength of a particular inference to the best explanation can be measured only in relation to the rest of the things that we already believe.

This type of inference does not occur only in unusual circumstances like the one described. In fact, we mak e inferences to the best explanation all the time. Retu rning to our fuel economy example from the previous section, suppose that you test a higher octane fuel and notice that your car gets better gas mileage. It is possible that th e mileage change is due to the change in fuel. Howeve r, as noted there, it is possible that there is another expla nation. Perhaps you are not driving in stop­and­go traffic as much. Perhaps you are driving with less weight in the car. T he careful use of inference to the best explanation can help us to discern what is the most likely among many possibilit ies (for more examples, see A Closer Look: Is Abductive Reasoning Everywhere? ).

If you look at the range of possible explanations and find one of them is more likely than any of the others, i nference to the best explanation allows you to conclude that t his explanation is likely to be the correct one. If you are driving the same way, to the same places, and with the same weight in your car as before, it seems fairly likely that it was the change in fuel that caused the improvement in fuel economy (if you have studied Mil l’s methods in Chapter 5, you should recognize this as the method of difference ). Inference to the best explanation is the engine th at powers many inductive techniques.

The great fictional detective Sherlock Holmes, for e xample, is fond of claiming that he uses deductive reasoning. Chapter 2 suggested that Holmes instead uses i nductive reasoning. However, since Holmes comes up with the most reasonable explanation of observ ed phenomena, like blood on a coat, for example, he is actually doing abductive reasoning. There is some dispute about whether inferen ce to the best explanation is inductive or whether it is an enti rely different kind of argument that is neither inductive nor deductive. For our purposes, it is treated as induc tive. A Closer Look: Is Abductive Reasoning Everywhere?

Some see inference to the best explanation as the most common type of inductive inference. A few of the inferences we have discussed in this book, fo r example, can potentially be cast as examples of inferences to the best explanation.

For example, appeals to authority (discussed in Chapter 5) can be seen as implicitly using inference to the best explanation (Harman, 1965). If you accept something as true because someone said it was, then you can be described as seeing the truth of the claim as the best explanation for why he or she said it. If we have good reason to thi nk that the person was deluded or lying, then we are less certain of this conclusion b ecause there are other likely explanations of why the person said it.

Furthermore, it is possible to see what we do when we i nterpret people’s words as a kind of inference to the best explanation of what they proba bly mean (Hobbs, 2004). If your neighbor says, “You are so funny,” for instance, we might use the context and tone to decide what he means by “funny” and why he is saying it (and whether he i s being sarcastic). His comment can be seen as either rude or flattering, depending on what expl anation we give for why he said it and what he meant.

Even the classic inductive inference pattern of induc tive generalization can possibly be seen as implicitly involving a kind of inference to the best explanation: The best explanation of why our sample population showed that 90% of students have lapto ps is probably that 90% of all students have laptops. If there is good evidence that o ur sample was biased, then there would be a good competing explanation of our data.

Finally, much of scientific inference may be seen as t rying to provide the best explanation for our observations (McMullin, 1992). Many hypotheses are atte mpts to explain observed phenomena. Testing them in such cases could then be seen as being do ne in the service of seeking the best explanation of why certain things are the way they are.

Take a look at the following examples of everyday in ferences and see if they seem to involve arriving at the conclusion because it seems to offer th e most likely explanation of the truth of the premise: • “John is smiling; he must be happy.” • “My phone says that Julie is calling, so it is probably Julie.” • “I see a brown Labrador across the street; my neighbor’s dog must have gotten out.” • “This movie has great reviews; it must be good.” • “The sky is getting brighter; it must be morning.” • “I see shoes that look like mine by the door; I apparently left my shoes there.” • “She still hasn’t called back yet; she probably doesn’t like me. ” • “It smells good; someone is cooking a nice dinner.” • “My congressperson voted against this bill I support; she must have been afraid of offending her wealthy donors.” • “The test showed that the isotopes in the rock surrounding newly e xcavated bones had decayed X amount; therefore, the animals from which the bones c ame must have been here about 150 million years ago.” These examples, and many others, suggest to some that inf erence to the explanation may be the most common form of reasoning that we use (Douven, 201 1). Do you agree? Whether you agree with these expanded views on the role of inference or not, it clearly makes an enormous contribution to how we understand the world around us. Form Inferences to the best explanation generally involve the fol lowing pattern of reasoning:

X has been observed to be true.

Y would provide an explanation of why X is true.

No other explanation for X is as likely as Y.

Therefore, Y is probably true.

One strange thing about inferences to the best explanat ion is that they are often expressed in the form of a common fallacy, as follows:

If P is the case, then Q would also be true.

Q is true.

Therefore, P is probably true.

This pattern is the logical form of a deductive falla cy known as affirming the consequent (discussed in Chapter 4). Therefore, we sometimes have to use the pr inciple of charity to determine whether the person is attempting to provide an inference to the b est explanation or making a simple deductive error. The principle of charity will be discussed in detail i n Chapter 9; however, for our purposes here, you can think of it as giving your opponent and his or her argument the be nefit of the doubt.

For example, the ancient Greek philosopher Aristotle reasoned as follows: “The world must be spherical, for the night sky looks different in the northern and southern regions, and that would be the case if the earth were spherical” (as cited in Wolf, 2004). His argument app ears to have this structure:

If the earth is spherical, then the night sky would lo ok different in the northern and southern regions. The night sky does look different in the northern and southern regions.

Therefore, the earth is spherical.

It is not likely that Aristotle, the founding father of formal logic, would have made a mistake as silly as to affirm the consequent. It is far more likely that he was using inference to the best explanation. It is logically possible that there are other explanations f or southern stars moving higher in the sky as one moves south, but it seems far more likely that it is due to the shape of the earth. Aristotle was just practicing strong abductive reasoning thousands of year s before Columbus sailed the ocean blue (even Columbus would have had to use this type of reasoning, for he would have had to infer why he did not sail off the edge).

In more recent times, astronomers are still using infere nce to the best explanation to learn about the heavens. Let us consider the case of discovering planets outside our solar system, known as “exoplanets.” There are many methods employed to disco ver planets orbiting other stars. One of them, the radial velocity method, uses small changes in the f requency of light a star emits. A star with a large planet orbiting it will wobble a little bit as the p lanet pulls on the star. That wobble will result in a pattern of changes in the frequency of light coming from the star. When astronomers see this pattern, they conclude that there is a planet orbiting the sta r. We can more fully explicate this reasoning in the following way:

That star’s light changes in a specific pattern.

Something must explain the changes.

A large planet orbiting the star would explain the changes.

No other explanation is as likely as the explanation provided by the large planet.

Therefore, that star probably has a large planet orbiting it.

The basic idea is that if there must be an explanation, an d one of the available explanations is better than all the others, then that explanation is the one that i s most likely to be true. The key issue here is that the explanation inferred in the conclusion has to be the best explanation available. If another explanation is as good—or better—then the inference is not nearly as strong. Virtue of Simplicity Another way to think about inferences to the best exp lanation is that they choose the simplest explanation from among otherwise equal explanations. In other words, if two theories make the same prediction, the one that gives the simplest explanati on is usually the best one. This standard for comparing scientific theories is known as Occam’s razor, because it was originally posited by William of Ockham in the 14th century (Gibbs & Hiroshi, 1997).

A great example of this principle is Galileo’s demonst ration that the sun, not the earth, is at the center of the solar system. Galileo’s theory provided the simplest explanation of observations about the planets. His heliocentric model, for example, provides a simpl er explanation for the phases of Venus and why some of the planets appear to move backward (retrogra de motion) than does the geocentric model. Geocentric astronomers tried to explain both of these with the idea that the planets sometimes make little loops (called epicycles) within their orbits (G ronwall, 2006). While it is certainly conceivable that they do make little loops, it seems to make the theor y unnecessarily complex, because it requires a type of motion with no independent explanation of why it occurs, whereas Galileo’s theory does not require such extra assumptions. ©Warner Bros./Courtesy Everett Collection In The Matrix , we learn that our world is simulated by machines, and although we can see X, hear X, and feel X, X does not exist. Therefore, putting the sun at the center allows one t o explain observed phenomena in the most simple manner possible, without making ad hoc assumptions (like epicycles) that today seem absurd. Galileo’s theory was ultimately correct, and he demonstrated it with strong inductive (more specifically, abductive) reasoning. (For another example of Occam’ s razor at work, see A Closer Look: Abductive Reasoning and the Matrix .) A Closer Look: Abductive Reasoning and the Matrix One of the great questions from the history of philosop hy is, “How do we know that the world exists outside of us as we perceive it?” We see a tree an d we infer that it exists, but do we actually know for sure that it exists? The argument seems to go as follows:

I see a tree.

Therefore, a tree exists.

This inference, however, is invalid; it is possible for the premise to be true and the con clusion false. For example, we could be dreaming. Perhaps we think that the testimony of our other senses will make the argument valid:

I see a tree, I hear a tree, I feel a tree, and I smell a tree.

Therefore, a tree exists.

However, this argument is still invalid; it is possible that we could be dreaming all of those things as well. Some people state that senses like smell do not exist within dreams, but how do we know t hat is true? Perhaps we only dreamed that someone said that! In any case, even that would not rescue our argument, for there is an e ven stronger way to make the premise true and the conclusion false: Wha t if your brain is actually in a vat somewhere attached to a computer , and a scientist is directly controlling all of your perceptions? (Or think of the 1999 movie The Matrix , in which humans are living in a simulated reality created by machines.) One individual who struggled with these types of quest ions (though there were no computers back then) was a French philo sopher named René Descartes. He sought a deductive proof that the world outside of us is real, despite these types of disturbing possibilities (Descartes, 1641/1993). He eventually came up with one of philoso phy’s most famous arguments, “I think, therefore, I am” (or, mor e precisely, “I am thinking, therefore, I exist”), and from there attempted to prove that the world must e xist outside of him.

Many philosophers feel that Descartes did a great job o f raising difficult questions, but most feel that he failed in his attempt to find deductive proo f of the world outside of our minds. Other philosophers, including David Hume, despaired of the p ossibility of a proof that we know that there is a world outside of us and became skeptics: The y decided that absolute knowledge of a world outside of us is impossible (Hume, 1902). However, perhaps the problem is not the failure of the particular arguments but the type of reasoning employed. Perhaps the solution is not deducti ve at all but rather abductive. It is not that it is logically impossible that tables and chairs a nd trees (and even other people) do not really exist; it is just that their actual existence pr ovides the best explanation of our experiences. Consider these competing explanations of our experiences:

• We are dreaming this whole thing.

• We are hallucinating all of this.

• Our brains are in a vat being controlled by a scientist.

• Light waves are bouncing off the molecules on the surface of the tree and entering our eyeballs, where they are turned into electrical impulses that t ravel along neurons into our brains, somehow causing us to have the perception of a tree.

It may seem at first glance that the final option is t he most complex and so should be rejected. However, let us take a closer look. The first two opti ons do not offer much of an explanation for the details of our experience. They do not tell us why we are seeing a tree rather than something else or nothing at all. The third option seems to assume that there is a real world somewhere from which these experiences are generated (that is, the lab with the scientist in it). The full explanation of how things work in that world presumab ly must involve some complex laws of physics as well. There is no obvious reason to think that such an account would require fewer assumptions than an account of the world as we see it. H ence, all things considered, if our goal is to create a full explanation of reality, the final option seems to give the best account of why we are seeing the tree. It explains our observations without needle ss extra assumptions.

Therefore, if knowledge is assumed only to be deductiv e, then perhaps we do not know (with absolute deductive certainty) that there is a world o utside of us. However, when we consider abductive knowledge, our evidence for the existence of the world as we see it may be rather strong. How to Assess an Explanation There are many factors that influence the strength of an inference to the best explanation. However, when testing inferences to the best explanation for strength, th ese questions are good to keep in mind:

• Does it agree well with the rest of human knowledge? Suggesting that your roommate’s car is gone because it floated away, for example, is not a very credibl e story because it would violate the laws of physics.

• Does it provide the simplest explanation of the observed phen omena? According to Occam’s razor, we want to explain why things happen without unnecessary compl exity.

• Does it explain all relevant observations? We cannot simply ignore contradicting data because it contradicts our theory; we have to be able to explain why we see what we see.

• Is it noncircular? Some explanations merely lead us in a circle. Stating that it is r aining because water is falling from the sky, for example, does not give us any new information about what causes the water to fall.

• Is it testable? Suggesting that invisible elves stole the car does not allow for em pirical confirmation. An explanation is stronger if its elements are pot entially observable. •Does it help us explain other phenomena as well? The best scientific theories do not just explain one thing but allow us to understand a whole range of related ph enomena. This principle is called fecundity. Galileo’s explanation of the orbits of the planets is an example o f a fecund theory because it explains several things all at once.

An explanation that has all of these virtues is likely to be better than one that does not. A Limitation One limitation of inference to the best explanation is that it depends on our coming up with the correct explanation as one of the candidates. If we do not th ink of the correct explanation when trying to imagine possible explanation, then inference to the b est explanation can steer us wrong. This can happen with any inductive argument, of course; induc tive arguments always carry some possibility that the conclusion may be false even if the premises are tr ue. However, this limitation is a particular danger with inference to the best explanation because it rel ies on our being able to imagine the true explanation.

This is one reason that it is essential to always keep an open mind when using this technique. Further information may introduce new explanations or change which explanation is best. Being open to further information is important for all inductive inference s, but especially so for those involving inference to the best explanation. Practice Problems 6.5 Click here (https://ne.edgecastcdn.net/0004BA/constellation/PD Fs/PHI103_2e/Answers_PracticeProblems6.5.pdf) to check your answers.

1. This philosopher coined the term abductive reasoning. a. Karl Popper b. Charles Sanders Peirce c. Aristotle d. G. W. F. Hegel 2. Sherlock Holmes is often said to be engaging in this form of rea soning, even though from a logical perspective he wasn’t. a. deductive b. inductive c. abductive d. productive 3. In a specific city that happens to be a popular tourist destinat ion, the number of residents going to the emergency rooms for asthma attacks increases in the su mmer. When the winter comes and tourism decreases, the number of asthma attacks go es down. What is the most probable inference to be drawn in this situation? a. The locals are allergic to tourists. b. Summer is the time that most people generally have asthma attacks.

c. The increased tourism leads to higher levels of air pollution d ue to traffic.

d. The tourists pollute the ocean with trash that then causes the lo cals to get sick.

4. A couple goes to dinner and shares an appetizer, entrée, and de ssert. Only one of the two gets sick. She drank a glass of wine, and her husband drank a beer. Wh at is the most probable inference to be drawn in this situation? a. The wine was the cause of the sickness.

b. The beer protected the man from the sickness. c. The appetizer affected the woman but not the man.

d. The wine was rotten.

5. You are watching a magic performance, and there is a woman who appears to be floating in space. The magician passes a ring over her to give the impression t hat she is floating. What explanation fits best with Occam’s razor? a. The woman is actually floating off the ground.

b. The magician is a great magician. c. There is some sort of unseen physical object holding the woman.

6. You get a stomachache after eating out at a restaurant. What ex planation fits best with Occam’s razor? a. You contracted Ebola and are in the beginning phases of symptom s.

b. Someone poisoned the food that you ate. c. Something was wrong with the food you ate.

7. In order to determine how a disease was spread in humans, research ers placed two groups of people into two rooms. Both rooms were exactly alike, a nd no people touched each other while in the rooms. However, researchers placed someo ne who was infected with the disease in one room. They found that those who were in the room with the infected person got sick, whereas those who were not with an infec ted person remained well. What explanation fits best with Occam’s razor? a. The disease is spread through direct physical contact.

b. The disease is spread by airborne transmission. c. The people in the first room were already sick as well.

8. There is a dent in your car door when you come out of the grocer y store. What explanation fits best with Occam’s razor? a. Some other patron of the store hit your car with their car.

b. A child kicked your door when walking into the store. c. Bad things tend to happen only to you in these types of situation s.

9. A student submits a paper that has an 80% matching rate when submit ted to Turnitin. There are multiple sites that align exactly with the content of the paper. What explanation fits best with Occam’s razor? a. The student didn’t know it was wrong to copy things word for wo rd without citing.

b. The student knowingly took material that he did not write an d used it as his own.

c. Someone else copied the student’s work. 10. You are a man, and you jokingly take a pregnancy test. The test comes up positive. What explanation fits best with Occam’s razor? a. You are pregnant.

b. The test is correct. c. The test is defective.

11. A bomb goes off in a supermarket in London. A terrorist group t akes credit for the bombing. What explanation fits best with Occam’s razor? a. The British government is trying to cover up the bombing by b laming a terrorist group.

b. The terrorist group is the cause of the bombing. c. The U.S. government actually bombed the market to get the B ritish to help them fight terrorist groups.

12. You have friends and extended family over for Thanksgiving d inner. There are kids running through the house. You check the turkey and find that it is overcooked because the temperature on the oven is too high. What explanation fits b est with Occam’s razor? a. The oven increased the temperature on its own.

b. Someone turned up the heat to sabotage your turkey. c. You bumped the knob when you were putting something into the oven.

13. Researchers recently mapped the genome of a human skeleton t hat was 45,000 years old. They found long fragments of Neanderthal DNA integrated into this human genome. What explanation fits best with Occam’s razor? a. Humans and Neanderthals interbred at some point prior to the l ife of this human.

b. The scientists used a faulty method in establishing the genetic se quence.

c. This was actually a Neanderthal skeleton.

14. There is a recent downturn in employment and the economy. A politically far­leaning radio host claims that the downturn in the economy is the direct r esult of the president’s actions. What explanation fits best with Occam’s razor? a. The downturn in employment is due to many factors, and more r esearch is in order.

b. The downturn in employment is due to the president’s actions. c. The downturn in employment is really no one’s fault.

15. In order for an explanation to be adequate, one should reme mber that __________. a. it should agree with other human knowledge b. it should include the highest level of complexity c. it should assume the thing it is trying to prove d. there are outlying situations that contradict the explanat ion 16. The fecundity of an explanation refers to its __________. a. breadth of explanatory power b. inability to provide an understanding of a phenomenon c. lack of connection to what is being examined d. ability to bear children 17. Why might one choose to use an inductive argument rather tha n a deductive argument? a. One possible explanation must be the correct one.

b. The argument relates to something that is probabilistic rath er than absolute.

c. An inductive argument makes the argument valid.

d. One should always use inductive arguments when possible.

18. This is the method by which one can make a valid argument inva lid. a. adding false supporting premises b. demonstrating that the argument is valid c. adding true supporting premises d. valid arguments cannot be made invalid 19. This form of inductive argument moves from the general to th e specific. a. generalizations b. statistical syllogisms c. hypothetical syllogism d. modus tollens Questions 20–24 relate to the following passage:

If I had gone to the theater, then I would have seen the new film a bout aliens. I didn’t go to the theater though, so I didn’t see the movie. I think that films abou t aliens and supernatural events are able to teach people a lot about what the future might hold in the realm of technology. Things like cell phones and space travel were only dreams in old movies, a nd now they actually exist. Science fiction can also demonstrate new futures in which peop le are more accepting of those that are different from them. The different species of charact ers in these films all working together and interacting with one another in harmony display s the unity of different people without explicitly making race or ethnicity an issue, thereby bringing people into these forms of thought without turning those away who do not want to explicit ly confront these issues.

20. How many arguments are in this passage? a. 0 b. 1 c. 2 d. 3 21. How many deductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3 22. How many inductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3 23. Which of the following are conclusions in the passage? Selec t all that apply. a. If I had gone to the theater, then I would have seen the new fil m about aliens. b. I didn’t go to the theater.c. Films about aliens and supernatural events are able to teach pe ople a lot about what the future might hold in the realm of technology.

d. The different species of characters in these films all working t ogether and interacting with one another in harmony displays the unity of d ifferent people without explicitly making race or ethnicity an issue.

24. Which change to the deductive argument would make it vali d? Select all that apply. a. Changing the first sentence to “If I would have gone to the the ater, I would not have seen the new film about aliens.” b. Changing the second sentence to “I didn’t see the new film abo ut aliens.” c. Changing the conclusion to “Alien movies are at the theater. ” d. Changing the second sentence to “I didn’t see the movie, so I did n’t go to the theater.” Summary and Resources Chapter Summary Although induction and deduction are treated differently in the field of logic, they are frequently combined in arguments. Arguments with both deductive and inductive components are generally considered to be inductive as a whole, but the import ant thing is to recognize when deduction and induction are being used within the argument. Argum ents that combine inductive and deductive elements can take advantage of the strengths of each. They can retain the robustness and persuasiveness of inductive arguments while using the stronger connec tions of deductive arguments where these are available.

Science is one discipline in which we can see inductiv e and deductive arguments play out in this fashion. The hypothetico–deductive method is one of the centra l logical tools of science. It uses a deductive form to draw a conclusion from inductively supported premi ses. The hypothetico–deductive method excels at disconfirming or falsifying hypotheses but cannot be used to con firm hypotheses directly.

Inference to the best explanation, however, does provide ev idence supporting the truth of a hypothesis if it provides the best explanation of our observations an d withstands our best attempts at refutation. A key limitation of this method is that it depends on ou r being able to come up with the correct explanation as a possibility in the first place. Nevert heless, it is a powerful form of inference that is used all the time, not only in science but in our daily lives. Critical Thinking Questions 1. You have probably encountered numerous conspiracy theories on the Internet and in popular media. One such theory is that 9/11 was actually plotted and orche strated by the U.S. government. What is the relationship between conspiracy theor ies and inference to the best possible explanation? In this example, do you think that this is a b etter explanation than the most popular one? Why or why not?

2. What are some methods you can use to determine whether or not in formation represents the best possible explanation of events? How can you evaluate sources o f information to determine whether or not they should be trusted?

3. Descartes claimed that it might be the case that humans are tota lly deceived about all aspects of their existence. He went so far as to claim that God could be evil a nd could be making it so that human perception is completely wrong about everything. However, he also claimed that there is one thing that cannot be doubted: So long as he is thinking, it is i mpossible for him to doubt that it is he who is thinking. Hence, so long as he thinks, he exists. Do you t hink that this argument establishes the inherent existence of the thinking being? Why or why not?

4. Have you ever been persuaded by an argument that ended up le ading you to a false conclusion? If so, what happened, and what could you have done differently to prevent yourself from believing a false conclusion?

5. How can you incorporate elements of the hypothetico–deduct ive method into your own problem solving? Are there methods here that can be used to analy ze situations in your personal and professional life? What can we learn about the search for tr uth from the methods that scientists use to enhance knowledge? Web Resources https://www.youtube.com/watch?v=RauTW8F­PMM (https://www.youtube.com/watch?v=RauTW8F­ PMM) Watch Ashford professor Justin Harrison lecture on the d ifference between inductive and deductive arguments.

https://www.youtube.com/watch?v=VXW5mLE5Y2g (https://www.youtube.com/watch? v=VXW5mLE5Y2g) Shmoop offers an animated video on the difference between ind uction and deduction.

http://www.ac4d.com/2012/06/03/abductive­reasoning­in­ airport­security­and­profiling (http://www.ac4d.com/2012/06/03/abductive­reasoning­in­airport­security­and­profiling) >Design expert Jon Kolko applies abductive reasoning to airpor t security in this blog post.

Key Terms abductive reasoning See inference to the best explanation . falsifiable Describes a claim that is conceivably possible to prove false. That does not mean that it is false; only that prior to testing, it is possible that it could have been. falsification The effort to disprove a claim (typically by finding a counter example to it). hypothesis A conjecture about how some part of the world works. hypothetico–deductive method The method of creating a hypothesis and then attempting to falsi fy it through experimentation. inference to the best explanation The process of inferring something to be true because it is the most l ikely explanation of some observations. Also known as abductive reasoning. Occam’s razor The principle that, when seeking an explanation for some phenomena, the simpler the explanation the better. self-sealing propositions Claims that cannot be proved false because they are interpreted in a way that protects them against any possible counterexample. Choose a Study Mode 