How People Reason With Conditionals

Before giving an overview of the various theories of reasoning, we saw how truth tables are used to define the meaning of if. Using these truth tables it is possible to define what inferences are valid (or correct) and invalid (incorrect) according to logic. This definition of valid and invalid inferences is critical to the empirical treatment of reasoning because it defines the dependent measures used in most experiments. In this section, we show how the validity of inferences is determined and then review some of the standard evidence on conditional inference found in the literature. Our review focuses on inference tasks using conditional premises and on tasks about testing conditional rules (i.e., Wason's selection task).

Conditional inferences: Valid and invalid forms

Earlier, we saw how propositions, like P and Q, were acted upon by logical operators. When a number of propositions are related together by a given logical operator we have a premise (e.g., If P then Q). Logics define a variety of rules of inference that can be used to make logically valid conclusions from premises. Consider the inference rules used on premises involving the conditional. Two valid inferences that can be made using conditionals are: modus ponens and modus tollens. An argument of the modus ponens form is as follows (it may help to keep the truth table in Table 16.1 close by, to understand the following discussion):

Valid: Modus ponens

Premises

If it is raining, then Alicia gets wet It is raining.

Conclusion

Therefore, Alicia gets wet.

Therefore, Q

So, if you are given the conditional about it raining and Alicia getting wet, and are then told that it is raining, you can validly conclude that "Alicia gets wet". To understand this conclusion, note that there is only one line in the truth table where P is true and if P then Q is true, and this is the one where Q is also true (see Table 16.1).

It is important to remember that logical validity is not about the actual truth or falsehood of statements but about possibilities; that is, for a valid argument there is no possibility, as represented by lines on a truth table, in which all the premises are true and the conclusion false. So, even premises and conclusions we know to be patently ridiculous can be logically valid:

Valid: Modus ponens

The modus ponens form is obvious and most people readily make it when the content is sensible. However, the other valid inference made from the conditional—modus tollens—is not as intuitively obvious. This rule states that, if we are given the proposition If P then Q and that Q is false, then we can infer that P is false. Thus, the following argument is valid:

Valid: Modus tollens

Again, this inference is consistent with the truth table (in Table 16.1). The line where If P then Q is true and Q is false, is that one in which P is false.

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