Uncertainty and the de Finetti tables
Résumé
The new paradigm in the psychology of reasoning adopts a Bayesian, or prob-abilistic, model for studying human reasoning. Contrary to the traditional binary approach based on truth functional logic, with its binary values of truth and falsity, a third value that represents uncertainty can be introduced in the new paradigm. A variety of three-valued truth table systems are available in the formal literature, including one proposed by de Finetti. We examine the descriptive adequacy of these systems for natural language indicative condi-tionals and bets on conditionals. Within our framework the so-called " defective " truth table, in which participants choose a third value when the antecedent of the indicative conditional is false, becomes a coherent response. We show that only de Finetti's system has a good descriptive fit when uncertainty is the third value. The new Bayesian, or probabilistic, paradigm in the psychology of reasoning (Oaksford & Chater, 2007, 2009; Over, 2009; Pfeifer & Kleiter, 2010) implies a close parallel relationship between assertions of the indicative conditional of natural language, if A then C, and other uses of conditionals, particularly bets on conditionals, I bet that if A then B. Politzer, Over, and Baratgin (2010) explain how this predicted relation goes back to Ramsey (1926/1990, 1929/1990) and de Finetti (1936/1995, 1937/1964) and provide experimental evidence that this parallel relation exists (see also Baratgin, Over, & Politzer, in press). Financial support for this work was provided by the French ANR agency under grant ANR Chorus 2011 (project BTAFDOC). We would like to thank Paul Egr e, Jean-Louis Stilgenbauer, and Tatsuji Takahashi for much discussion and other help in our research. We also thank Shira Elqayam, Jean-François Bonnefon, and two anonymous reviewers.
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