Modeling biconditionals: Equivalence in an uncertain world

Abstract

For almost a half century, it has been known that participants consider the truth value of “if p then q,” in a “defective” way, as true when p and q are both true, false when p is true but q is false, but uncertain whenever p is false. Recently, researchers has given this truth table a new normative status, under the theory of subjective probability by de Finetti, as of conditional event, q|p. On the basis of ample evidence that P(if p then q)=P(q|p), we study biconditionals, “if p then q, and if q then p.” Here we show the psychological priority of biconditional event to material equivalence. Additionally, we discuss the logical background of (bi-)conditional event and three types of uncertainty. Two are ones in the domain and codomain of the truth-function, and the other is connected to the indefiniteness of a world or the frame problem.


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