What to Think About Machines

INFORMAL WRITING ASSIGNMENT FIVE

Your task: Please read the article What to Think About Machines That Think (Canvas Modules).  Pages 318 and 319 are accidentally switched around in that article. Write a 200- word summary in your own words.

 Two Valid Rules of Inference

A particularly central rule of inference in the logic of conditional statements is known as modus ponens (which loosely translates from Latin as “method of affirming”). It allows us to infer that the consequent of a conditional statement is true if both the statement itself and the antecedent are true. Thus, given that both the conditional statement If A, then B and its antecedent A are true, we can infer that its consequent B is true. This rule of inference is illustrated by the following example in which the two premises are the conditional statement and its antecedent, and the conclusion is the consequent:

• Modus Ponens
• If Joan understands this book, then she will get a good grade.
• Joan understands this book.
• Therefore:Joan will get a good grade.

Although this example illustrates a valid deduction, it also illustrates the artificiality of applying logic to real-world situations. How is one to really know whether Joan understands the book? One can only assign a certain probability to her understanding. Also, even if Joan does understand the book, at best it is only likely—not certain—that she will get a good grade. However, in research investigating how people reason, participants are asked to suspend their real-world knowledge about such matters and treat these types of statements as if they were certainly true. Or, more precisely, they are asked to reason about what would follow for certain if these statements were true. Participants do not find these instructions particularly strange, but as we will see, they are not always able to make logically correct inferences.

Another valid rule of inference is known in logic as modus tollens (which loosely translates as “method of denying”). It allows us to infer that the antecedent of a conditional statement is false if the statement itself is true and the consequent is false. Thus, given that the conditional statement If A, then B is true and given that its consequent B is false, we can infer that its antecedent A is false. This rule of inference is illustrated by the following example:

• Modus Tollens
• If Joan understands this book, then she will get a good grade.
• Joan will not get a good grade.
• Therefore:Joan does not understand this book.

This conclusion might strike the reader as less than totally compelling because, again, in the real world such statements are not typically treated as certain.

If a conditional statement is true, modus ponens allows us to infer the consequent from the antecedent, and modus tollens allows us to infer that the antecedent is false if the consequent is false.

Two Invalid Patterns of Inference

People sometimes accept two patterns of inference that are invalid—that is, they are fallacies because the conclusion does not logically follow from the premises. The first, called affirmation of the consequent, asserts that, if a conditional statement is true and if the consequent is true, then the antecedent must also be true, as illustrated by the following example:

• Fallacy: Affirmation of the Consequent
• If Joan understands this book, then she will get a good grade.
• Joan will get a good grade.
• Therefore:Joan understands this book.

The other invalid pattern, called denial of the antecedent, asserts that, if a conditional statement is true and if the antecedent is false, then the consequent must also be false, as illustrated by this example:

• Fallacy: Denial of the Antecedent
• If Joan understands this book, then she will get a good grade.
• Joan does not understand this book.
• Therefore:Joan will not get a good grade.

In both of these cases, the inference is invalid because there might be other ways in which Joan could get a good grade.

Evans (1993) reviewed a large number of studies that compared the frequency with which people accept the valid modus ponens and modus tollens inferences to the frequency with which they accept these two types of invalid inferences (see Figure 10.2). As can be seen, people rarely fail to accept a modus ponens inference, but the frequency with which they accept the valid modus tollens is only slightly greater than the frequencies with which they accept the invalid inferences.