Psychological experiments have found much evidence that people generally judge the probability of a natural language if A then C, P(if A then C), to be the conditional probability of C given A, P(C|A). These findings support suppositional analyses of the conditional and the new Bayesian paradigm in the psychology of reasoning. In the new paradigm, rational inferences are mainly from degrees of belief, and not arbitrary assumptions, and often support rational decision making. A central goal of this paradigm is to integrate the study of reasoning and decision making. Its fundamental normative system is what de Finetti called the logic of probability, probability logic for short. In this talk, I will introduce the suppositional conditional, the new paradigm, and probability logic, using the dilemma inference as my primary example. This inference goes from premises if A then C and if not-A then C to the conclusion C. It is closely related to the sure-thing principle in decision making, which allows to infer what we should do from conditionals if A then C and if not-A then C. Dilemma inferences are valid in probability logic but cannot be rational for inferentialist theories of the so-called "normal" or "standard" conditional. The conditional in these theories is supposedly only acceptable, or true, when the antecedent raises the probability of the consequent by giving a reason for it. I will critique inferentialism and argue that the suppositional conditional, if A then C, has the advantage that it can express the independence of A and C in some contexts as well as the dependence of C on A in others. This flexibility is of great value, as knowledge of independence can be as important for rationality as knowledge of dependence.  

References 

Over, D. E., & Evans, J. St. B. T. (2024). Human reasoning, especially Chapter 5. (Cambridge: Cambridge University Press). https://www.researchgate.net/profile/David-Over-2

Cruz, N., & Over, D.E. (2026). From de Finetti’s three values to conditional probabilities in the psychology of reasoning. In P. Egré and L. Rossi (Eds.), Handbook of Trivalent Logics. Cambridge: MIT Press. https://www.researchgate.net/profile/David-Over-2

De Finetti, B. (1937). Foresight: its logical laws, its subjective sources. In H. E. Kyburg & H. E. Smokier (Eds.), Studies in subjective probability (55-118). New York, US: Wiley.

Over, D.E., Gilio, A., Pfeifer, N., Sanfilippo, G. (2026). Probability logic, inferentialism, and rationality. In Proceedings of the 4th International Conference on Human and Artificial Rationalities (HAR 2025). Lecture Notes in Computer Science, Springer, Cham, 21. https://www.researchgate.net/profile/David-Over-2

Pearl, J. (2016). The sure-thing principle. Journal of Causal Inference, 4 (1), 81-86.