"If Oswald had not killed Kennedy" – Spohn on Counterfactuals

Wolfgang Spohn's theory of ranking functions is an elegant and powerful theory of the structure and dynamics of doxastic states. In two recent papers, Spohn has applied it to the analysis of conditionals, claiming to have presented a unified account of indicative and subjunctive (counterfactual) conditionals. I argue that his analysis fails to account for counterfactuals that refer to indirect causes. The strategy of taking the transitive closure that Spohn employs in the theory of causation is not available for counterfactuals. I have a close look at Spohn's treatment of the famous Oswald-Kennedy case in order to illustrate my points. I sketch an alternative view that seems to avoid the problems

From probabilities to categorical beliefs: Going beyond toy models

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of

Two-Dimensional Belief Change

The idea of two-dimensional belief change operators is that a belief state is transformed by an input sentence $A$ in such a way that $A$ gets accepted with at least the strength or certainty of a sentence $B$ (the reference sentence). The input of such a transformation may alternatively be conceived as `$B leq A$\u27 [`$B$ less-than-or-equal-to $A$\u27]. This notation makes explicit that the process induced is basically one of doxastic preference change. The principal case of two-dimensional belief change obtains when $B$ is a prior belief which is more strongly accepted than both $A$ and $eg A$, but the non-principal cases are interesting in their own right. Various two-dimensional revision operators were studied by Cantwell (1997, `raising\u27 and `lowering\u27), Fermé and Rott (2003, `revision by comparison\u27), and Rott (2007, `bounded revision\u27). Special choices of a fixed input sentence $A$ or a fixed reference sentence $B$ lead to some well-known unary oparators of belief change: `irrevocable\u27 (aka `radical\u27) revision, `severe withdrawal\u27 (aka `mild contraction\u27), `natural\u27 (aka `conservative\u27) and `lexicographic\u27 (aka `moderate\u27) revision. The talk gives a survey of several variants of two-dimensional belief change and their representations. I argue that two-dimensional belief change operators offer an interesting qualitative model with an expressive power between (all too poor) unary operators and (all too demanding) quantitative models of belief change

On the Logical Form of Evidential Conditionals

The dominant analyses of the logical form of natural-language conditionals take them to be “suppositional conditionals”. The latter are true or accepted if the consequent is true/accepted on the supposition of the antecedent. But this can happen although the antecedent is completely irrelevant (or even somewhat adverse) to the consequent. In natural-language conditionals, however, the antecedent is typically meant to support or be evidence for the consequent. The logical form of conditionals will thus be more complex than the suppositional theory would have it. Recently some suggestions as to what this logical form might look like have been made. In this paper, I critically discuss Vincenzo Crupi and Andrea Iacona’s account of “evidential conditionals”, including its recent amendments

Notes on contraposing conditionals

The contraposing conditional 'If A then C' is defined by the conjunction of A > C and ~C > ~A, where > is a conditional of the kind studied by Stalnaker, Lewis and others. This idea has recently been explored, under the name 'evidential conditional', in a sequence of papers by Crupi and Iacona and Raidl, and it has been found of independent interest by Booth and Chandler. I discuss various properties of these conditionals and compare them to the 'difference-making conditionals' studied by Rott, which are defined by the conjunction of A > C and not ~A > C. I raise some doubts about Crupi and Iacona's claim that contraposition captures the idea of evidence or support

Notes on contraposing conditionals

The contraposing conditional 'If A then C' is defined by the conjunction of A > C and ~C > ~A, where > is a conditional of the kind studied by Stalnaker, Lewis and others. This idea has recently been explored, under the name 'evidential conditional', in a sequence of papers by Crupi and Iacona and Raidl, and it has been found of independent interest by Booth and Chandler. I discuss various properties of these conditionals and compare them to the 'difference-making conditionals' studied by Rott, which are defined by the conjunction of A > C and not ~A > C. I raise some doubts about Crupi and Iacona's claim that contraposition captures the idea of evidence or support