Journal of Philosophical Logic 50 (2):187-213 (2021)

Authors
Jan Sprenger
University of Turin
Lorenzo Rossi
University of Salzburg
Abstract
This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of the predicament: one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties.
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DOI 10.1007/s10992-020-09549-6
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References found in this work BETA

Counterfactuals.David Lewis - 1973 - Blackwell.
Truth and Probability.F. Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
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