New Psychological Paradigm for Conditionals and General de Finetti Tables

Abstract

Abstract: The new Bayesian paradigm in the psychology of reasoning aims tointegrate the study of human reasoning, decision making, and rationality. It is supportedby two findings. One, most people judge the probability of the indicative conditional,P(if A then B), to be the conditional probability, P(B|A), as implied by the Ramsey test.Two, they judge if A then B to be void when A is false. Their three-valued responsetable used to be called ‘defective’, but should be termed the de Finetti table. We showhow to study general de Finetti truth tables for negations, conjunctions, disjunctions, andconditionals. 1. Introduction Bayesian models of cognition have become increasingly prominent in thepsychology of reasoning in recent years, and this trend has resulted in thedevelopment of a new Bayesian paradigm (Manktelow, Over and Elqayam, 2011;Oaksford and Chater, 2007, 2009; Over, 2009; Pfeifer and Kleiter, 2010). Theolder binary paradigm in the psychology of reasoning focused on deduction fromassumptions. Propositions were classified as either true or false, or consistent orinconsistent with each other. Conclusions either followed necessarily or not atall. If the participants in a reasoning experiment did not assume the premises, butrelied on their subjectively relevant beliefs, or they inferred conclusions that didnot necessarily follow, they were deemed to be biased and to commit fallacies. Thisolder paradigm inspired many theoretical models (mental rules, mental models,rules or schemas, and others) but limited the field of research to the study of thehuman deduction ability (Evans, 2012). The new paradigm recognizes that mostinferences in everyday affairs and science, whether logically valid or not, are fromuncertain beliefs or hypotheses and not assumptions, and that reasoning must takeaccount of this uncertainty if it is to be useful for acquiring rational beliefs andmaking rational decisions. The basic goal of the new paradigm is to integrate thepsychology of reasoning and the psychology of judgment and decision making andprovide a full account of human reasoning, decision making, and rationality.