We analyze three interesting arguments from the literature, where ascribing a probability of 1 to a certain right-nested conditional A→(B→C) leads to strong theses concerning conditionals: they serve as counterexamples to important general claims. The first is the classic and much discussed McGee’s counterexample to Modus Ponens from McGee [“A Counterexample to Modus Ponens.” The Journal of Philosophy 82 (9): 462–471]. The second example was given by Santorio [“Trivializing Informational Consequence.” Philosophy and Phenomenological Research 104:297–320] and is intended to undermine (...) the probabilistic version of Modus Ponens. The third example was presented in Cantwell [“Revisiting McGee’s Probabilistic Analysis of Conditionals.” Journal of Philosophical Logic 51 (5): 973–1017] in order to reject the general version of the Ramsey Test (i.e. PCCP) and Modus Ponens. These examples are based on a specific interpretation of right-nested conditional which is not the only possible one. We provide examples demonstrating that alternative interpretations are feasible. As a result, the arguments presented in the three cited works possess limited efficacy, as they are confined solely to the particular interpretation of the conditional. (shrink)

In the paper, we provide a general formalism for computing probabilities of indicative conditionals. Our model is based on the idea of constructing a (labeled) Markov graph G(α), which models the sentence α, containing an arbitrarily complex conditional (exhibiting in particular its structure). The formalism makes computing these probabilities an easy task—it consists of solving simple systems of linear equations. The graph G(α) generates a canonical probability space S(α) = (Ωα, Σα, Pα), where α is given an interpretation as an (...) event so that the probability can be computed mathematically. We present a general inductive definition of the graph G(α) for a sentence α of arbitrary complexity. It is based on the idea of defining graph-building operations which correspond to the negation and conjunction and the non-Boolean conditional connective →. The definition enables the construction of graphs and the corresponding systems of equations for arbitrarily complex conditionals in an algorithmic and efficient manner. (shrink)