Figure 161

The percentage of subjects endorsing the various conditional inferences from Marcus and Rips (1979, Experiment 2).

Making valid and invalid inferences

The literature on conditional reasoning in cognitive science is vast, as are the range of findings on how people reason with conditionals (see Evans et al., 1993b; Johnson-Laird & Byrne, 1991; Manktelow, 1999). We consider just some of these findings; the patterns of valid and invalid inferences made by subjects, the effects of context, and testing a conditional rule (i.e., the selection task). Later, during our review of the various theories we introduce further empirical tests that are based on the predictions made by specific theories.

As we hinted earlier, it is not the case that people automatically make the valid modus ponens and modus tollens inferences and resist the invalid denial of the antecedent and affirmation of the consequence inferences. Sometimes people fail to make valid inferences and consider invalid inferences to be acceptable. These results have been found in experiments where subjects are presented with a conditional statement (e.g., "if she gets up early, she will go for a run") and a premise (e.g., "she gets up early") and are asked to either evaluate a conclusion, draw a conclusion, or choose from a list of possible conclusions.

Figure 16.1 charts the characteristic pattern of inferences for each of the four forms (from Experiment 2 by Marcus & Rips, 1979). Typically, nearly 100% of subjects make the valid modus ponens inference, but most people find the modus tollens inference much harder, about 50% or so of subjects do not make this inference. On the other hand, many subjects accept the invalid inferences; the rates for making the denial of the antecedent and affirmation of the consequent inferences can increase to around 70%. In the Marcus and Rips' (1979) study 21% of subjects make the denial of the antecedent inference and 33% make the affirmation of the consequent inference (although the difference is not always in this direction; see Evans, 1993a, and Evans et al., 1993b, p. 36, for a composite table showing the results from several different experiments). As we will see, this pattern of inferences should be explained by any adequate theory of deductive reasoning.

Context effects on inference with "if..."

In some contexts people do not make the inferences outlined earlier, what are called context effects. The rates of invalid or fallacious inferences can be modified by contexts in which further information is given (Rumain, Connell, & Braine, 1983). For example, if alternative antecedents to the conditional are provided then people avoid making the fallacious inferences (Markovits, 1984, 1985; Rumain et al., 1983). For example, the following argument explicitly indicates alternative antecedents to the consequent:

If it is raining then she will get wet, If P then Q,

If it is snowing then she will get wet, If R then Q,

Therefore, ? Therefore, ?

The data show that people are more likely to produce the correct answer (i.e., no conclusion can be made) than the fallacious P conclusion they usually make in the affirmation of the consequent. So, when people are told about an explicit alternative to the consequent (the woman getting wet), they can use this extra information to generate the logically appropriate inference. On the face of it this suggests that extra information can help people to improve their logical reasoning.

However, Byrne (1989a) has found, using a similar paradigm to Rumain et al., that the provision of extra information can suppress the valid inferences as well as the invalid inferences. Byrne replicated the alternative-antecedents effect but also showed that additional antecedents reduced the frequency of valid modus ponens and modus tollens inferences (see Figure 16.2).

So, when subjects were given:

If she has an essay to write then she will study late in the library. If P then Q,

If the library stays open then she will study late in the library, If R then Q,

She has an essay to write P,

Therefore, ? Therefore, ?

which contained the additional requirement of the "library staying open", people typically did not make the modus ponens inference to conclude that "she will study late in the library" (i.e., Q). This result has become important in the debate between different theoretical positions (Bach, 1993; Byrne, 1991, 1997; Fillenbaum, 1993; Politzer & Braine, 1991; Savion, 1993). Byrne, Espino, and Santamaria (1999) have explored the effects further to rule out a number of possible alternative explanations raised in these discussions (see later section on mental models).

There have also been several extensions of the work examining a group of related factors like causality, saliency, and uncertainty. Cummins, Lubart, Alksnis, and Rist (1991; Cummins, 1995) have examined causality effects on suppression by getting subjects to generate disabling conditions or alternative causal conditions:

Premise: If a student gets under 40% the exam is failed.

Disabling Condition: The student was sick.

Alternative Cause: The student did no coursework.

In general, the more disabling and alternative causes that are present the greater the implicit suppression of the valid inferences. Indeed, it seems that the more additional conditions people can think of, the greater the

Modus Modus Affirmation Denial ponem tollens of the of the consequent antecedent

Modus Modus Affirmation Denial ponem tollens of the of the consequent antecedent

Inference type

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