Conditionals and inferential connections: A hypothetical inferential theory.

Intuition suggests that for a conditional to be evaluated as true, there must be some kind of connection between its component clauses. In this paper, we formulate and test a new psychological theory to account for this intuition. We combined previous semantic and psychological theorizing to propose that the key to the intuition is a relevance-driven, satisficing-bounded inferential connection between antecedent and consequent. To test our theory, we created a novel experimental paradigm in which participants were presented with a soritical series of objects, notably colored patches (Experiments 1 and 4) and spheres (Experiment 2), or both (Experiment 3), and were asked to evaluate related conditionals embodying non-causal inferential connections (such as "If patch number 5 is blue, then so is patch number 4"). All four experiments displayed a unique response pattern, in which (largely determinate) responses were sensitive to parameters determining inference strength, as well as to consequent position in the series, in a way analogous to belief bias. Experiment 3 showed that this guaranteed relevance can be suppressed, with participants reverting to the defective conditional. Experiment 4 showed that this pattern can be partly explained by a measure of inference strength. This pattern supports our theory's "principle of relevant inference" and "principle of bounded inference," highlighting the dual processing characteristics of the inferential connection.

The probability of iterated conditionals.

Iterated conditionals of the form If p, then if q, r are an important topic in philosophical logic. In recent years, psychologists have gained much knowledge about how people understand simple conditionals, but there are virtually no published psychological studies of iterated conditionals. This paper presents experimental evidence from a study comparing the iterated form, If p, then if q, r with the "imported," noniterated form, If p and q, then r, using a probability evaluation task and a truth-table task, and taking into account qualitative individual differences. This allows us to critically contrast philosophical and psychological approaches that make diverging predictions regarding the interpretation of these forms. The results strongly support the probabilistic Adams conditional and the "new paradigm" that takes this conditional as a starting point.