Capturing the relationship between conditionals and conditional probability with a trivalent semantics

Assigning truth-conditions to conditional statements leads to problems in assigning probabilities to those statements (Lewis, 1976). This note presents and assesses a trivalent semantics of conditional sentence, arguing that this semantics does well at capturing the probabilities of conditional statements. The major problems and prospects for this view are reviewed

Conditionals and Propositions in Semantics

The project of giving an account of meaning in natural languages goes largely by assigning truth-conditional content to sentences. I will call the view that sentences have truth-conditional content propositionalism as it is common to identify the truth-conditional content of a sentence with the proposition it expresses. This content plays an important role in our explanations of the speech-acts, attitude ascriptions, and the meaning of sentences when they appear as parts of longer sentences. Much work in philosophy of language and linguistics semantics over the last halfcentury has aimed to characterize the truth-conditional content of different aspects of language

A note on conditionals and restrictors

Within linguistic semantics, it is near orthodoxy that the function of the word ‘if’ (in most cases) is to mark restrictions on quantification. Despite its linguistic prominence, this view of the word ‘if’ has played little role in the philosophical discussion of conditionals. This paper tries to fill in this gap by systematically discussing the impact of the restrictor view on the competing philosophical views of conditionals. I argue that most philosophical views can and should be understood in a way that is compatible with the restrictor view, but that accepting the restrictor allows for new responses to some prominent arguments for non-truth-conditional account of conditionals

De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity

This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti (1936) and Reichenbach (1935, 1944). 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 (DF) with validity as the preservation of non-false values (TT-validity), 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 (CC) proposed by Cooper (Inquiry 11, 295–320, 1968) and Cantwell (Notre Dame Journal of Formal Logic 49, 245–260, 2008). 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