THE WASON TASK(S) AND THE PARADOX OF CONFIRMATION

Abstract

The (recent, Bayesian) cognitive science literature on the Wason Task (WT) has been modeled largely after the (not-so-recent, Bayesian) philosophy of science literature on the Paradox of Confirmation (POC). In this paper, we apply some insights from more recent Bayesian approaches to the (POC) to analogous models of (WT). This involves, first, retracing the history of the (POC), and, then, re-examining the (WT) with these historico-philosophical insights in mind. 1. The Paradox of Confirmation Before getting into the recent (Bayesian) cognitive science literature on the Wason Task, we will re-trace the historical (and philosophical) background of the Paradox of Confirmation. In this section, we will tell a revised and extended version of a story about (the history and philosophy of) The Paradox that that we have (partially) told elsewhere [6, 8, 7]. In section two, we move on to the Wason Task(s). 1.1. Hempel and Goodman on the Paradox of Confirmation. Not surprisingly, the Paradox of Confirmation involves a relation called the confirmation relation. For Hempel and Goodman (and also for Carnap, who’ll enter our story shortly), the confirmation relation was a logical relation, akin to deductive entailment. Thus, in the heady early days of confirmation theory, [E confirms was meant to express a logical relation between propositions (or, better still, sentences) E and H. The precise nature of this logical relation will, of course, vary, depending on one’s favorite explication of said logical confirmation concept. But, the basic idea (common to all such explications) is that “confirms” is supposed to be a weaker relation than “entails”, and there are supposed to be substantive and non-trivial true instances of [E confirms H\, where [E entails is false. So, on this traditional view, confirmation is a generalization of (classical) entailment. In the beginning, there was Hempel’s confirmation relation [16], which is purely syntactical (defined over a first-order language L), and which fully supervenes on classical deductive entailment relations (of L). The full details of Hempel’s confirmation theory won’t be crucial for present purposes. We’ll only need to know a few of the formal consequences of Hempel’s theory — mainly, the following two: (NC) For all names and for all (classically) logically independent predicate expressions and : [ & x confirms [„8y „ y y \. (EQC) For all statements, E, H, and H0: if E confirms H and H is (classically) logically equivalent to H0, then E also confirms H0. Date: 08/01/10. Draft: Final version to appear in Philosophical Perspectives, J. Hawthorne (ed.).