On the Evaluation of If p then q Conditionals

On the Evaluation of If p then q Conditionals Constantinos Hadjichristidis (constantinos.hadjichristidis@durham.ac.uk) Department of Psychology, University of Durham Durham, DH1 3LE, UK Rosemary J. Stevenson (rosemary.stevenson@durham.ac.uk) Department of Psychology, University of Durham Durham, DH1 3LE, UK David E. Over (david.over@sunderland.ac.uk) School of Social Sciences, University of Sunderland Sunderland, SR1 3SD, UK Steven A. Sloman (steven_sloman@brown.edu) Department of Cognitive & Linguistic Sciences, Brown University Box 1978, Providence, RI 02912, USA Jonathan St. B. T. Evans (j.evans@plymouth.ac.uk) Centre for Thinking and Language, Department of Psychology University of Plymouth, Plymouth PL4 8AA, UK. Aidan Feeney (aidan.feeney@durham.ac.uk) Department of Psychology, University of Durham Durham, DH1 3LE, UK Abstract We propose that when evaluating conditionals, people construct an imaginary world that contains the antecedent, and then evaluate the plausibility of the consequent being true in the same world. Thus, when asked for an estimate of the probability of the conditional, people should produce the conditional probability of its consequent given its antecedent. We contrast this view with a view based on the theory of mental models, in which the judged probability of a conditional is derived from the proportion of models in which the premises are true. Study 1 examined this hypothesis by comparing probability estimates for (i) category-based conditional arguments (e.g. If robins have ulnar arteries then sparrows have ulnar arteries ), (ii) corresponding conditional probabilities in the form of suppositions (e.g. Suppose you knew that robins have ulnar arteries. How likely would you think it was that sparrows have ulnar arteries? ) and (iii) the argument strength of corresponding inductive arguments (e.g. Fact: Robins have ulnar arteries. Therefore: Sparrows have ulnar arteries. How convincing do you find this argument? ) All three estimates were highly correlated, a finding that supports our hypothesis. The similarity between the two categories (e.g. robins and sparrows) was also manipulated. Similarity affected all three estimates equally, similar items being given higher estimates than dissimilar items. This finding indicates that similarity is one basis for the plausibility judgements. Study 2 tested our hypothesis using conditional statements with known probabilities. The results favoured our hypothesis. We discuss these results in terms of philosophical and psychological views of conditionals, and suggest that they bring together kinds of reasoning that are traditionally studied separately, such as conditional reasoning, induction, and judgements of probability. Introduction Psychological research on inductive and deductive reasoning has traditionally examined reasoning based on premises classified as true. Such research ignores most everyday reasoning, which is based on uncertain premises. Premise uncertainty, in turn, rightly influences the degree of certainty in the conclusion of an inference (e.g. Stevenson & Over, 1995). Understanding everyday reasoning, therefore, involves understanding subjective premise uncertainty, and the way in which such uncertainty gets translated into uncertainty about the conclusion of an inference. The present article investigates subjective uncertainty about conditional premises of the form If p then q. The article focuses on the way in which people evaluate conditional arguments and how they arrive at judgements of the probability of a conditional. We propose that people evaluate conditionals with reference to imaginary situations that they mentally