Week 3: Discussion 1 and 2

Week 3 - Instructor Guidance

This week’s guidance will cover the following topics:

1. The Nature of Inductive Reasoning

2. Appeals to Authority

3. Inductive Generalizations

4. Statistical Syllogisms

5. Arguments from Analogy

6. Inferences to the Best Explanation

7. Causal Reasoning

8. Things to Do This Week

Will the sun rise tomorrow morning? Of course it will, but how do you know? The reasoning seems to go as follows:

Premise 1: The sun has risen every morning throughout known history

Conclusion: Therefore, the sun will rise tomorrow

Deductively, this argument is invalid, for it is logically possible that the earth could stop spinning tonight. Does that mean that the argument is no good? Of course not. In fact, its premise makes the conclusion is virtually certain. This is an example of a very good argument that is not intended to be deductively valid. That is because it is actually an inductive argument.

An argument is inductive if it does not attempt to be valid, but intends to give strong evidence for the truth of its conclusion.

Many might see inductive reasoning as inferior to deductive reasoning, but that is not generally the case. In fact, inductive arguments often provide much better arguments for the truths of their conclusions than deductive ones. The deductively valid version of our argument about the sun, for example, goes:

Premise 1: The sun will always rise in the morning

Conclusion: Therefore the sun will rise tomorrow morning

This second argument, while valid, actually gives less evidence for the conclusion because its second premise is false (the sun will eventually expand to engulf the earth and then collapse). Therefore the deductive argument is unsound and so offers little evidence for the conclusion, whereas the original inductive argument made the conclusion virtually certain. In other words, inductive reasoning in general can be even better than deductive reasoning in many cases; the trick is to determine which inductive arguments are good and which ones are not so good.

Just as it is the goal of deductive reasoning to be valid, it is the goal of a inductive reasoning to be

strong

. An inductive argument is strong in case its premises, if true, would make the conclusion very likely to be true as well. The above argument about the sun rising is very strong. Most inductive arguments are less strong, all the way along a spectrum between strength and weakness. Here are three with varying degrees of inductive strength:

Note that the degree of strength of an inductive argument is independent of whether the premises are actually true. Inductive strength is solely a matter of the strength of the connection between the premises and the conclusion (the parallel of deductive validity). We have another word for an inductive argument that is both strong and has all true premises (the parallel of deductive soundness): An inductive argument is cogent if it is strong and has all true premises.

This guidance will cover five main categories of inductive arguments. Each type is capable of presenting very strong evidence for the truth of the conclusion. However, each type also has common errors that can make arguments weak or even fallacious. Each of these forms, therefore, is good, but should be applied with caution and with an eye to a critical evaluation of its strength.

Our book covers the same types of inductive inference: Appeals to authority, Arguments from Analogy, Inductive Generalizations, Inferences to the Best Explanations, and Statistical Syllogisms.

It would be nearly impossible to discover all truth for ourselves; therefore it is necessary frequently to learn from others. To do so we have to learn which sources to trust. Appealing to Authority is saying something is true because an authority says so.

Despite the fact that many make fun of appeals to authority (by asking if you would jump off a bridge if the authority told you so), they actually can actually supply very good arguments. They are also necessary in real life, as it would be nearly impossible to learn almost anything without them. Even in the hard sciences, one could not learn without trusting the claims from the textbook, the instructors, or of researchers in the field. The trick is being able to tell which appeals to authority are worth trusting. Here are some good questions to ask:

1. Is this the kind of question that can be settled by an appeal to authority (e.g. an objective matter that is testable)?

2. Is the person sited a genuine authority on the topic?

3. Do experts on the topic tend to agree about this question?

4. Can the authority be trusted to be honest in this context? (There will be a discussion of ulterior motives and interested parties later on in this guidance.

5. Has the authority been interpreted correctly? (Sometimes, especially when it comes to sources like the bible or the constitution, this is the most important question.)

An appeal to authority that violates some of the above can commit the fallacy of appeal to inadequate authority.

Here are two strong ones:

1. My physics textbook teaches that e = mc2, so it probably is correct.

2. The civil war started in 1861; my history professor said so.

Here are two weak ones:

1. That toothpaste is the best; the commercial said that 9 out of 10 dentists surveyed recommended it

2. The president is evil; I read all about it on some guy’s blog.

Here are some more examples of appeals to authority. How strong would you classify each of them as (and why)?

Often we draw conclusions about groups based upon polls or studies of sub-groups from within those populations. Inductive Generalizations are arguments that draw conclusions about a general population from results about a sample population. Here are some examples:

1. “Nine out of ten students surveyed preferred the earlier start schedule; so most of our students must prefer to start earlier.”

2. “The pre-election poll showed that candidate A leads by 60%, so he will probably win.”

Here are some questions to ask about whether this is a strong pattern of reasoning:

1. Was the sample large enough? If not many are surveyed then this is called a hasty generalization, and it does not supply very good evidence for the conclusion.

2. Was the sampling method biased in any way? If the sampling method has a tendency (even a subtle one) to favor some results over others then this is called a biased sample.

Chapter five of our textbook discusses the science of inductive generalizations in much more detail; it can be a very tricky thing to make inductive generalizations correctly. One thing, however, that it is essential to avoid it the harmful use of inductive generalizations known as stereotyping.

One phenomenon that logicians have noted with pain throughout human history is the habit of stereotyping, or holding general, especially negative, views about all members of a group independent of individual merit. This is what is meant by the term “prejudice,” or judging in advance.

For some reason, humans seem quite prone to holding general attitudes about people based upon the group they are in, especially based upon visible and unchangeable traits like race and gender. Studies have repeatedly found that these sorts of stereotypes to be based upon faulty generalizations. Hasty generalizations are especially rife, as people sometimes only need one example or two before they will conclude something negative about a whole group. The samples are often biased as well, since people seem only to remember the negative examples from a group. They may notice one or two people driving poorly, and for some reason blame a whole group to which that person belongs. Therefore, stereotyping generalizations are prone to both common errors of generalizations.

Research shows that Stereotypes can cause great amounts of harm

Stereotyping Has Lasting Negative Impact.

A rational person seeks to live without prejudice either for or against groups but to judge cases on their merits based upon careful, critical, and impartial reasoning.

Statistical syllogisms reason from a statistical claim about a group to a claim about a specific member of that group. Here is the general form:

Premise 1: X % of F’s are G’s

Premise 2: Individual A is an F

Conclusion: Therefore, A is a G (or, if X is a low percentage we can conclude that A is not a G).

Here is an example:

Premise 1: 97% of Americans eat pizza

Premise 2: He is an American

Conclusion: So he probably eats pizza.

Some of these can be quite strong and quite essential. How can we know how people will behave, for example, unless we know how the typically behave? How do we know that someone with whom we have lunch won't poison our food unless we have a clue about the likelihood of such an event? We only get to know people because we (implicitly) judge that such adverse events are rare. Whether we realize it or not, we are using statistical syllogisms all of the time. When we decide to drive to the store we are making an implicit statistical inference that the chances of getting into an accident are low enough to justify the risk.

Without using this type of reasoning it would be extremely difficult to function in society! We just have to make sure that our reasoning is strong and based on good evidence. Can you think of areas of life in which our statistical syllogisms are not so good?

We often make inferences about new situations based upon our experiences in similar situations. Arguments from Analogy allow us to make these types of inferences. Here is the general form:

Premise 1: I have experienced things of this type in the past, and they have all had attribute G

Conclusion: Therefore the next thing of this type will have attribute G

A simple example would be:

Premise 1: Every time I have eaten at that restaurant in the past I’ve really enjoyed it

Conclusion: Therefore I will enjoy it tonight as well

Arguments from analogy are very similar to statistical syllogisms; the difference is that a statistical syllogism makes an inference about an individual within the reference class, while arguments from analogy make inference to a new individual not in but having something in common with the reference class. The reference class above is “times I’ve eaten at that restaurant in the past.” We are making an inference to a new individual based on an analogy with the previous experiences.

Here are some questions to ask in relation to the strength of an argument from analogy:

1. How many individuals have you experienced before? As with inductive generalizations, a small sample size can make for a weak inference.

2. How relevant is the characteristic in question to the possession of the attribute in question? One can probably make a strong inference about whether a nickel will conduct electricity based on only one or two past cases, since nickels are very likely to act the same in relation to conducting electricity. Other cases, for example in which one infers that someone is nice because past tall people he or she has known have been nice, are likely to be much weaker.

Like statistical syllogisms, we use arguments from analogy implicitly to make decisions all day long. I figure that my Aunt Bea has been happy to see me when I went to visit her before, so she probably will be again today. My Ketchup has never been poisoned before, so I can probably pour it on my fries now. We expect, that when we reach out to shake someone’s hand that he or she will not punch us in the face based on the fact that people have not done so in the past.

(whoops ... not this time)

We draw conclusions about which shows to watch based on what we have liked in the past, and that is typically how we live our lives. Can you think of any arguments from analogy that we typically make that are faulty? How could we improve them?

An inference to the best explanation is an argument in which the conclusion is supposed to supply the best or most likely explanation for why the premises are true. Here are some examples:

1. Brad is smiling; he must have gotten the job.

2. The truck won’t start; the battery must be dead.

3. The dog is yelping; he is probably hungry.

The general form of such arguments looks like this:

Premise 1: If P were true then Q would be observed

Premise 2: Q has been observed

Premise 3: P appears to be the most likely explanation of why Q has occurred

Conclusion: Therefore P is probably true

You may notice that this argument form appears similar to the invalid argument form known as affirming the consequent. However, the fact that it is invalid is not a problem here, because this is not intended to be a deductive inference. As an inductive inference, inferences to the best explanation can be quite strong. Here is a very strong one:

There is snow everywhere outside; it must have snowed last night.

Much of what we believe in life is based on inferences to the best explanation. Do you believe that trees exist? How do you know? Is it because you see them? Well, the deductive argument:

Premise 1: I see trees

Conclusion: Therefore, trees exist

Is actually invalid, and the suppressed premise "Everything I see exists" is not true. You could be sleeping, or hallucinating.

It is possible that how we are actually reasoning as more like this:

Premise 1: I see trees

Premise 2: While it is logically possible that I am dreaming them up, that I am hallucinating, or that an evil scientist has my brain in a vat somewhere (programming me to see trees), those explanations seem very unlikely given everything else I have experienced

Premise 3: The most likely explanation of why I am seeing trees is that they exist (and that light is bouncing off of them into my eyes)

Conclusion: Therefore, trees exist

Science also works frequently by inference to the best explanation.

Our basic interpretations of reality come from forming complex explanations of our experiences. For example, the fact that we believe in things like trees, planets, and stars, is based upon an attempt to explain why we observe the things that we do. In fact, science works largely by inference to the best explanation. Here are some examples:

1. Gregor Mendel observed certain patterns among the generations of cross-bred pea plants, and from this he inferred a series of things about recessive and dominant traits. His theory formed the foundations of our understanding of genetics.

2. Gailieo observed certain patterns in the motions of the planets and concluded that the only way to explain it was to put the sun at the center of the solar system.

3. Charles Darwin observed certain patterns in variations of living species and concluded that species diversified through a process of natural selection.

4. Scientists today discover fossils and draw all kinds of inferences about what life on earth must have been long ago to yield the kinds of fossils that we see today.

5. Doctors diagnose diseases by observing symptoms and inferring the most likely cause. Sometimes distinguishing between two causal explanations requires further tests, yielding results that would only be true under one but not the other interpretation.

Since these inferences form the foundations of our theories of our reality, it is very important, then, that we get them right. However, with inferences to the best explanation, we may never arrive at just one correct final answer. Instead, science works by creating ever more sophisticated and more accurate explanations of reality. When scientists find cases in which the data does not match the theory, they seek to find still better explanations to explain all anomalies. This does not mean that the process is in error; it means that the process is an ongoing one, characterized by periods of refinement to better and better create a unified and accurate explanations of what we observe.

Chapter 6 or our book has a substantial discussion of causal reasoning. Part of that reasoning utilized Mill’s Methods. A full discussion of these matters is way beyond the present scope, here is a brief example of how to apply these methods to reason about causes.

As noted in the book, Mill’s methods use the method of agreement and the method of difference to look for necessary and sufficient conditions for a phenomenon. There is also the joint method of agreement and difference in which one looks for both at the same time. As Aristotle put it, one learns by doing, so here is an interesting puzzle:

Suppose that twelve people attend a conference in a remote village (the village has no unusual history of disease). Of the twelve people, four suddenly experience the same terrible symptoms soon after dinner. The symptoms are so unusual and similar that it seems to be more than a coincidence. Your assistant interviews all those present and compiles the following data:

See if you can figure out the most likely cause of the sudden illness (keeping in mind that it could be a combination of factors).

I hope you enjoyed this foray into inductive reasoning. For more on each of these categories of inductive inference and how to evaluate their strength take a look at the handout: Inductive Argument Forms.

1. Read the required materials for the week, including this guidance and chapters 5 & 6 from the textbook.

2. Watch the weekly intro video and all of the videos under the “Lectures” tab for this week of the course and view all other required materials.

3. Post a timely (initial post by day 3) and thorough response to both discussion forums as well as substantive replies to peers. Note that both discussion prompts are up to your instructor. The instructor will post the prompt as the first response within the forum.

4. Take the Quiz for the week (by day 7). It covers the central concepts of the course as covered in the textbook, this guidance, and the lecture videos for this week.

5. Post your Counterargument Paper (by day 7). Make sure to follow all instructions for the assignment very carefully.

If you have any questions, make sure to let your instructor know, either via email or in the Ask Your Instructor forum.

Hardy, J., Foster, C., & Zúñiga y Postigo, G. (2015). With good reason: A guide to critical thinking [Electronic version]. Retrieved from https://content.ashford.edu