In recent years, Bayesian models of cognition have been used - with considerable success - to explain human reasoning in a variety of inferential tasks (Chater, Tenenbaum, & Yuille, 2006). These models represent a "probabilistic approach" that seeks to derive the optimal solutions to inferential problems, and the success of these models is often interpreted as evidence that intuitive reasoning is fundamentally rational. Other successful research traditions, however, adopt a starkly different view of human rationality. Researchers interested in judgment and decision making, for example, often assume that intuitive inference is heuristic, error-prone, and subject to biases (Kahneman & Tversky, 1982; Gilovich, Griffin, & Kahneman, 2002).
How is it possible that the probabilistic and heuristic-and-biases approaches have both been successful while adopting fundamentally incompatible views of rationality? I suspect that many psychologists have thought about this question, but so far as I can tell, these approaches have only been directly compared on a few inferential tasks, and there are still fewer (published) attempts to derive any general answers to this question.
Chater, N., Tenenbaum, J.B., & Yuille, A. (2006) Probabilistic models of cognition: Conceptual foundations. Trends in Cognitive Sciences 10(7): 287-291. [pdf]
Gilovich, T., Griffin, D., & Kahneman, D. (Eds.) (2002) Heuristics and biases: The psychology of intuitive judgement. Cambridge Univ. Press.
Kahneman, D. & Tversky, A. (1982) The psychology of preferences. Scientific American 246(1): 160-173.