Deductive reasoning from uncertain conditionals

Abstract

This paper begins with a review of the literature on plausible reasoning with deductive arguments containing a conditional premise. There is concurring evidence that people presented with valid conditional arguments such as Modus Ponens and Modus Tollens generally do not endorse the conclusion, but rather find it uncertain, in case (i) the plausibility of the major conditional premise is debatable, (ii) the major conditional premise is formulated in frequentist or probabilistic terms, or (iii) an additional premise introduces uncertainty about the major conditional premise. This third situation gives rise to non monotonic effects by a mechanism that can be characterised as follows: the reasoner is invited to doubt the major conditional premise by doubting the satisfaction of a tacit condition which is necessary for the consequent to occur. Three experiments are presented. The first two aim to generalise the latter result using various types of conditionals and the last shows that performance in conditional reasoning is significantly affected by the representation of the task. This latter point is discussed along with various other issues: we propose a pragmatic account of how the tacit conditions mentioned earlier are treated in plausible reasoning; the relationship of this account with the conditional probability view on conditional sentences is examined; an application of the same account to the Suppression Effect (Byrne, 1989) is proposed and compared with the counterexample availability explanation; and finally some suggestions on how uncertainty could be implemented in a mental logic system are presented. Uncertain Conditionals 2People may have more or less confidence in the truth of the propositions that originate from their sources of information: communication, perception, memory, and inference. A person was told that P, saw that Q, recalls that R, infers that S; but was her informant dependable, her senses reliable, her memory faithful, her conclusion valid ? People face such questions constantly (this is made possible by their metacognitive skills): they are more or less confident in the truth of the propositions they entertain. We take this fact as a psychologically primitive phenomenon and call degree of belief the subjective degree of confidence that people experience in such situations.Belief comes by degrees: having full belief in a proposition is to consider it as true (hence full belief in not-P is to consider not-P as true, i. e. , P as false, which is full disbelief in P). One can have less than full belief in P, in which case one is uncertain (or doubts) about the truth of P; in particular, one can have slightly less than full belief, in which case one is slightly uncertain about P (and at the same time nearly certain about not-P): uncertainty about P is the extent to which one disbelieves P (within the limits where belief in P is greater than belief in not-P). When degree of belief decreases from full belief in P, a point of indeterminacy is reached where belief in P equals belief in not-P: ...

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