Social pragmatic factors in reasoning from disjunctions of numerical estimations

Social pragmatic factors in reasoning from disjunctions of numerical estimations Robert Mackiewicz (rmackiew@swps.edu.pl) University of Social Sciences and Humanities Chodakowska 19/31, 03-815 Warsaw, Poland Pawel Koniak (pkoniak@swps.edu.pl) University of Social Sciences and Humanities Chodakowska 19/31, 03-815 Warsaw, Poland statement of politician B is false leads to a contradiction, i.e. the average holiday time is both lower than 19 days and higher than 32 days. Abstract The paper presents two studies that investigated how individuals reason from disjunctive statements that use numerical estimations. In the experiments two types of such statements were used. In the first type both constituents of a disjunction could be a logically correct answer. That is, if “The average life time of a fruit fly is either 9 or 27 days”, any of those numbers is logically possible. In the second type that truth of one constituent excluded the truth of the other, e.g. “The average time of holidays in the EU is either higher than 9 days or else higher than 27 days”. A simple repetition of any of those figures is an illusory inference as it renders both constituents true. The results of Experiment 1 proved that although the participants showed a tendency to repeat one of the disjuncts as their answer, this tendency was smaller when the content of the statements referred to politics and social life in comparison with the general knowledge questions. The results of Experiment 2 showed that individuals reveal the tendency to repeat opinions coming from speakers who are more likeable, even if such opinions are incorrect illusory inferences. The results of both studies show that illusory inferences appear also in the domain of numerical cognition but they may be reduced by pragmatic factors such as the content of the message and the knowledge about its source. Mental models and the principle of truth When two statements are presented in the form of a disjunction, one has to represent the fact that if one of them is true, then the other must be false. But naive individuals seldom do this, as they typically represent only what is true at the expense of what is false. Forgetting about false possibilities is one of the principles of the theory of mental models (the model theory for short, Johnson–Laird, 2007). The basic assumption of the model theory is that mental representations are iconic and they represent different possibilities as different mental models. Specifically, models represent what is common in all “possible worlds” when a certain type of relation holds. Therefore, the structure of models corresponds to the structure of what they represent (Johnson-Laird, 2006). The same objects may be represented by different types of mental models depending on the relation that was made salient in a given context. For example, if one is informed that the average life of a common fruit fly is three times longer than 9 days, he or she will understand this expression as a multiplication problem and will know that the correct answer is 27, even though an experimenter has not yet started to ask any questions. On the other hand, if a participant of a psychological study was informed that: The average life of a fruit fly is either shorter than 9 days or else it is shorter than 27 days. he or she might see this expression as a disjunction of two possibilities, and represent them as two separate mental models: shorter than 9 days shorter than 27 days As none of those mental models represent false cases (i.e. not shorter than 27 days in the first model and not shorter than 9 days in the second model), the model theory predicts that individuals without training in logic should see both possibilities as equally probable. But choosing any of them as the correct answer is a so-called illusory inference as shorter than 9 means also shorter than 27 and shorter than 27 does not exclude it being shorter than 9. Keywords: reasoning, mental models, persuasion, illusory inferences, social pragmatics Introduction Imagine that you heard the following statements from two different politicians: Politician A: The average number of holiday days in The European Union is lower than 19 days. Politician B: The average number of holiday days in The European Union is lower than 32 days. How would you answer a question about the average number of holiday days in the EU, if you were informed that one of the above statements is definitely true and the other is definitely false? If both politicians are equally likely to be speaking the truth, it seems quite reasonable to expect one of their statements to be the correct answer. However, assuming that both options are equally possible would be a logical mistake as the truth of one of them excludes the truth of the other. Therefore, the correct estimate of the number of holiday days in the EU must lie between 19 and 32 days, which comes from the fact that the statement of politician A is false and the statement of politician B is true. This is the only possible answer because an assumption that the