de Finetti's trivalent system and partitioning sentences

Jean BARATGIN, Professor, Université Paris 8, CHArt Laboratory, France

The trivalent and functional theory of the truth of conditionals, proposed by de Finetti in 1928, has received particular echoes in the philosophical, linguistic and psychological literature. This theory justifies the equation between the probabilities of conditionals and the conditional probabilities. It also provides a faithful representation of the human understanding of connectors in ordinary language. However, it gives never true the partitioning sentence "if A, C and if not A, D" whereas in natural language such sentences are used and accepted. We present how such sentences have been analyzed in logic, linguistics and psychology of reasoning. We argue that such sentences refer from a linguistic perspective to an uncertainty about the realization of either A or not A. In this interpretation, de Finetti's system can represent such sentences. First experimental data supporting this hypothesis are presented.