P.N. Johnson-Laird, Sangeet S. Khemlani, Geoffrey P. Goodwin, Logic, probability, and human reasoning, Trends in Cognitive Sciences, Volume 19, Issue 4, April 2015, Pages 201-214, ISSN 1364-6613, DOI: 10.1016/j.tics.2015.02.006.
This review addresses the long-standing puzzle of how logic and probability fit together in human reasoning. Many cognitive scientists argue that conventional logic cannot underlie deductions, because it never requires valid conclusions to be withdrawn – not even if they are false; it treats conditional assertions implausibly; and it yields many vapid, although valid, conclusions. A new paradigm of probability logic allows conclusions to be withdrawn and treats conditionals more plausibly, although it does not address the problem of vapidity. The theory of mental models solves all of these problems. It explains how people reason about probabilities and postulates that the machinery for reasoning is itself probabilistic. Recent investigations accordingly suggest a way to integrate probability and deduction.