Contradictions and Counterfactuals: Generating Belief Revisions in Conditional Inference

Contradictions and Counterfactuals: Generating Belief Revisions in Conditional Inference Ruth M.J. Byrne (rmbyrne@tcd.ie) Psychology Department, University of Dublin, Trinity College, Dublin, Ireland Clare R. Walsh (cwalsh@tcd.ie) Psychology Department, University of Dublin, Trinity College, Dublin, Ireland Abstract Reasoners revise their beliefs in the premises when an inference they have made is contradicted. We describe the results of an experiment that shows that the belief they revise depends on the inference they have made. They revise their belief in a conditional (if A then B) when they make a modus tollens inference (from not-B to not-A) that is subsequently contradicted (A). But when they make a modus ponens inference (from A to B) that is contradicted (not-B) they revise their belief in the categorical assertion (A). The experiment shows that this inference contradiction effect occurs not only for factual conditionals but also for counterfactual conditionals. However, reasoners revise their beliefs in factual conditionals more than counterfactuals. Belief Revision Suppose you know the following well-established set of knowledge to be true: If the car was out of petrol then it stalled. The car was out of petrol. What, if anything, follows? You may conclude: The car stalled. But suppose additional knowledge comes to light at a later time and you discover the following is true: The car did not stall. What do you think you should believe to be true at this point? New information can contradict previously held beliefs and inferences about the world. The ability to recognise inconsistency is a necessary step in revising beliefs (e.g., Legrenzi, Girotto, & Johnson-Laird, 2002). Once inconsistencies and contradictions are detected, they must be resolved (e.g., Elio & Pelletier, 1997). For example, you may decide to revise your belief in the conditional, and believe instead that the car being out of petrol does not necessarily mean that it stalled (it may be a diesel engine). Or you may revise your belief in the categorical, and believe instead that the car was not entirely out of petrol. Dealing with contradictions is common not only in scientific discovery but also in everyday ‘non- monotonic’ inference. Which beliefs do people revise most readily? Conditionals can convey explanations, regularities or hypotheses about the world; categoricals can convey facts, data or observations (Elio, 1997). Revising the conditional or categorical is equally acceptable logically (Revlin, Cate, & Rouss, 2002). Yet most studies show that reasoners revise their belief in the conditional (Dieussaert, Schaeken, De Neys, & d’Ydewalle, 2000; Elio, 1997; Elio & Pelletier, 1997 Politzer & Carles, 2001; Revlin, et al, 2002). Reasoners may prefer to revise some sorts of beliefs more than others because they accommodate new information by changing little of their existing beliefs (Harman, 1986). Minimal changes can be accomplished by altering beliefs that have the least explanatory power or informational content (Gardenfors, 1988). Categoricals convey more semantic information (they rule out more states of affairs as false) than conditionals (Johnson-Laird & Byrne, 1991); but conditionals and categoricals may differ in how entrenched they are in a belief system. Intriguingly, some studies suggest that the belief reasoners revise depends on the inference contradicted. Consider a second problem: If the car was out of petrol then it stalled. The car did not stall. You may conclude: The car was not out of petrol.. But suppose the additional knowledge comes to light: The car was out of petrol. What do you think you should believe to be true? Once again you may decide to revise your belief in the conditional; or you may revise your belief in the categorical, and believe instead that the car did stall. The first example illustrates a modus ponens inference and the second illustrates a modus tollens inference, and Table 1 summarizes the structure of the two sorts of problem.