Deductive Reasoning

Sherlock Holmes and his ever-affable yet slow-witted sidekick Dr. Watson go camping. They pitch their tent and go to sleep, but Holmes awakens in the middle of the night. He nudges his companion and says, “Watson, look at the sky. What do you see?”

“Millions and millions of stars,” replies Watson.

“And what’s that tell you?”

“If only a few of those stars have planets, it’s possible that some of those planets are like Earth. If some of those planets are like Earth, there must be life out there.” Watson turns his head. “And what does it tell you?”

Holmes replies, “Watson, you idiot. Somebody stole our tent.”

If you enjoyed this joke, you’re not alone. In one survey it was voted the funniest out of 50,000 entries (see Radford, 2001). Many people think of Sherlock Holmes as the personification of deductive reasoning. But is deduction really Holmes’ modus operands At times, the great detective did employ deduction. More often than not, however, Holmes relied on inductive reasoning (Kincaid, 2015). That is, he gathered facts to arrive at a probable inference rather than a certain conclusion. Others have suggested that he used abductive reasoning, which entails reasoning from the available data to the best hypothesis possible (Lyne, 2005; Walton 2005). With deductive reasoning, however, a person seeks to reach a certain, inescapable conclusion. The conclusion isn’t merely probable, it is indisputable. When using deduction, the conclusion necessarily follows from the premises.

In this chapter we examine such reasoning. After exploring deduction’s applicability to everyday life, you will learn about its role in a variety of fields and contexts. Next, we will look at rules for testing the validity of syllogisms, which are one of the most common types of deductive reasoning. But first, let’s take a closer look at the difference between inductive and deductive reasoning.

Deductive Versus Inductive Reasoning: A Whole Different Animal

As we learned in previous chapters, inductive reasoning deals with probabilities. Returning to a Sherlock Holmes example, in The Hound of the Baskervilles (Doyle, 1902), Holmes inferred that whoever mailed a letter made of cut and pasted letters must be well educated because:

the utmost pains have been taken to remove all clues. The address, you observe, is printed in rough characters. But The Times is a paper which is seldom found in any hands but those of the highly educated. We may take it, therefore, that the letter was composed by an educated man who wished to pose as an uneducated one. (p. 32)

However, the conclusion doesn’t necessarily follow from the assumptions as it would if deductive reasoning were being used. A less-educated person could have found a copy of the newspaper

“Well, by that logic no one would ever shave a clock onto a monkey. ”

Figure 11.1 Caught up in a logical quandary. Paul Noth, cartoonbank.com, 2010-09-13, TCB-34912. © Paul Noth/The New Yorker Collection/www.cartoonbank.com.

lying about on a bus, or a train, or in a pub. Deductive reasoning deals with certainties. To see why, let’s examine a common type of deductive argument, known as a categorical syllogism, which looks like this:

Premise # 1 : All tortoises are vegetarians.

Premise #2: Bessie is a tortoise.

Conclusion: Therefore, Bessie is a vegetarian.

As you can see, a categorical syllogism has two premises followed by a conclusion. If both premises are true, the conclusion is a sure thing. In this case, Bessie is a vegetarian, no doubt about it.

What Is Formal Logic?

The word logic often conjures up images of cold calculation. For example, Mr. Spock from the Star Trek series is ultra-logical, perhaps because he’s only half human. That said, formal logic and deduction are not as perplexing as they sometimes seem. Simply stated, formal logic is the science of correct reasoning, which leads to valid, rather than invalid, conclusions. Deduction is a method of logical reasoning.

Formal logic has rules, which, if followed correctly, lead to valid conclusions. These rules have to do with the form of arguments. In other words, it is the arrangement of the premises and conclusion that determine whether a deductive argument is valid or invalid. In addition, the specific wording of premises and conclusions matters too. Ordinary language is often vague or ambiguous. As such, when fashioning logical statements, you must be careful to make the wording clear and precise (see Box 11.1).

Box I 1.1 Wording Counts: Casting Ordinary Language into Syllogistic Form

Because the form of a syllogism determines its validity, language must be precise. This may seem like nitpicking, but ambiguous language can render an otherwise valid syllogism invalid. The following are key considerations when wording syllogisms.

1 Unless otherwise stated, the subject term (first term) in a premise is presumed to be universal. Thus, the premise “Donuts have holes” is synonymous with saying “All donuts have holes.” Proper nouns are also treated as universal. It sounds odd, but the premise “Socrates is a man” means all Socrates, implying that there is a class or category of persons named Socrates with only one member.

“Lonnie has a short temper” means “[all of the person we refer to as] Lonnie has a short temper.”

“Toyota is the world’s biggest car maker” means “[all of the company known as] Toyota is the world’s biggest car maker.”

  • 2 Importantly, the predicate term (second term) is not presumed to be universal, unless the premise is negative. The statement “all bowtie wearers are dapper dressers” should be interpreted as “all bowtie wearers are [among those who are] dapper dressers,” not “all bowtie wearers are the only ones who are dapper dressers.” With a negative statement, however, both terms are universal. Saying “No French fries are healthy foods” is equivalent to saying “no healthy foods are French fries.”
  • 3 Quantifiers are limited to “all,” “none,” or “some.” Quantifiers such as “many,” “most,” or “several” are not allowed.

Allowed: Some CEOs of Fortune 500 companies are women.

Not allowed: Few CEOs of Fortune 500 companies are women.

  • 4 The quantifier “some” means “at least one.” Thus, saying “Some people with disabilities are athletes” is synonymous with saying “At least one person with a disability is an athlete.” Saying “Some hockey players are missing front teeth” really means “At least one hockey player is missing front teeth.”
  • 5 Technically speaking, the major term and minor term should be nouns or noun phrases. Rather than saying “Some cab drivers are smelly,” one should say “Some cab drivers are smelly people.” Rather than saying “Weevils are annoying,” one could say “Weevils are annoying varmints.” This requirement is often ignored with no serious consequences, as long as everyone understands what is meant. Most people can easily make sense of both premises below, even though one is technically incorrect.

Technically correct: Some two year olds are [children who are] incorrigible.

Technically incorrect: Some two year olds are incorrigible.

6 The copula, which is the verb connecting the major, minor, and middle terms, must be some form of the verb to be, such as “is,” “are,” or “are not.” This may require some rewording. On the other hand, people often understand the copula just fine even though it is not technically correct.

The premise “Some baboons have red butts,” should be reworded to “Some baboons [are monkeys] with red butts.”

The premise “All stoners love Cheetos,” should be rephrased as “All stoners are [people who love] Cheetos.”

Also, the copula cannot be qualified, as in “is probably is . . .” “are mostly . . .” “often are . . . .”

Are People Naturally Logical?

Early on, scholars subscribed to the doctrine that “logic provides the basis for rational human thought” (Evans, 2002, p. 979). According to this view’, human beings are naturally logical and deductive thinking is hard-wired into our brains. There is some merit to this point of view. For example, some evidence suggests that people intuitively prefer valid over invalid arguments (Morsanyi & Handley, 2012). What’s more, logical thinking is correlated with intelligence

(Newstead, Handley, Harley, Wright & Farrelly, 2004; Stanovich, 1999). Nonetheless, as we saw in previous chapters, people are often anything but logical in their thinking.1 Among other things, they allow subjective biases to get in the way (Evans, Newstead & Byrne, 1993; Khemlani & Johnson-Laird, 2012). Studies reveal, for example, that ordinary people can accurately distinguish valid from invalid syllogisms only 37—55 percent of the time (Jacobs, Allen, Jackson & Petrel, 1985; Johnson-Laird & Bara, 1984; Johnson-Laird & Steedman, 1978). Worse yet, and somewhat surprisingly, did you know that being in a positive mood hinders your ability to assess syllogisms (Melton, 1995)? Our advice; try stubbing your toe before taking the LSAT, MCAT, or GRE.

Cognitive Fitness: Don Your Thinking Cap

The good news is that, with training and practice, you can improve your powers of deduction (Neilens, Handley & Newstead, 2009), especially on more difficult reasoning tasks (Leighton, 2006). Better yet, scholars have come to view deductive reasoning as a useful mental exercise, sort of like calisthenics for your brain. In fact, regularly engaging in mental exercise, or what has been dubbed neurobics, can help you stave off cognitive decline (Katz & Rubin, 1999). In the same way that playing Sudoku, crossword puzzles, and other “brain teasers” can sharpen your mind, analyzing syllogisms can hone your reasoning skills.

 
Source
< Prev   CONTENTS   Source   Next >