Argumenta – Journal of Analytic Philosophy

The trivalent and functional theory of the truth of conditionals developed by Bruno de Finetti has recently gathered renewed interests, particularly from philosophical logic, psychology and linguistics. It is generally accepted that de Finetti introduced his theory in 1935. However, a reading of his first publications indicates an earlier conception of almost all his theory. We bring to light a manuscript and unknown writings, dating back to 1928 and 1932, detailing de Finetti’s theory. The two concepts of thesis and hypothesis are presented as a cornerstone on which logical connectives are established in a 2-to-3 valued logic. The proposed generalisation of the bivalent material implication to the trivalent framework, based on the bivalent entailment is however different from the one that will be introduced in 1935. In these early writings de Finetti presents original results that will later be independently rediscovered by other researchers. In particular, the ‘suppositional logic’ developed by Theodore Hailperin in 1996 presents numerous similarities. Conversely, we consider the notion of validity proposed by Hailperin in line with de Finetti’s approach. Overall we attribute the primacy of the trivalent theory to de Finetti; this early conception enabled him to take an original position and argue with Hans Reichenbach.

For 20 years the trivalent theory of the truth of conditionals, proposed by Bruno de Finetti (1906-1985), has gathered numerous interests in various fields such as Philosophical Logic (e.g. Milne 1997; Mura 2009; Vidal 2014; Égré, Rossi and Sprenger 2020a, 2020b), Linguistics (e.g. Rothschild 2014; Douven 2016; Lassiter 2020; Lassiter and Baratgin 2021), Artificial Intelligence (e.g. Dubois and Prade 1994; Coletti and Scozzafava 2002), Psychology (e.g. Baratgin, Over and Politzer …


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