Models, Rules, and Deductive Reasoning

We formulate a simple theory of deductive reasoning based on mental models. One prediction of the theory is experimentally tested and found to be incorrect. The bearing of our results on contemporary theories of mental models is discussed. We then consider a potential objection to current rule-theories of deduction. Such theories picture deductive reasoning as the successive application of inference-schemata from rst-order logic. Relying on a theorem due to George Boolos, we show that under weak hypotheses rst-order schemata cannot account for many people's ability to verify the validity of rst-order arguments. The hypothesis that deductive reasoning is mediated by the construction of mental models has enjoyed predictive success across several studies. It has also proven to be a fertile source of ideas about other kinds of judgment, for example, temporal, spatial, and probabilistic. At the same time, the theory has su ered from persistent criticism for ambiguity about the details of model construction and assignment. A defect of this character, however, is to be expected in such an original and dynamic thesis; it should not discourage attempts at clari cation and extension. In view of assisting the latter process, the present paper de nes an elementary theory of deductive reasoning that embodies a clear version of the mental models hypothesis. The new theory applies to a class of arguments that seem not yet to have been examined within the mental models framework. For this reason we do not claim that our theory is strictly implied by the more general thesis illustrated in (Johnson-Laird, 1983) or (Johnson-Laird and Byrne, 1991). To avoid confusion, we denote the theory de ned in the latter articles by MMT, and the theory stated below by EST. Although EST is not a formal corollary of MMT, it preserves some important features of the latter. It will be seen that these common features lead EST to an incorrect experimental prediction. The question thus arises whether MMT is committed to the same mistake. Subsequent to examining MMT we consider its principal rival, namely, rule-based theories. A theorem of proof-theory reported in (Boolos, 1987) is exploited for the purpose of raising a potential objection to a large class of theories of this kind. Our discussion proceeds as follows. Section 1 presents EST. Two empirical consequences of EST are derived in Section 2. Experimental data inconsistent with the consequences are reported in Section 3. In Section 4 we describe a follow-up experiment designed to isolate the defect in EST. Section 5 discusses the bearing of our ndings on MMT. Remarks about rule-theories begin in Section 6. We conclude in Section 9.