AbstractThis thesis studies Judea Pearl’s logic of counterfactuals derived from the causal modeling framework, in comparison to the influential Stanlnaker-Lewis counterfactual logics.
My study focuses on a characteristic principle in Pearl’s logic, named reversibility. The principle, as Pearl pointed out, goes beyond Lewis’s logic. Indeed, it also goes beyond the stronger logic of Stanlnaker, which is more analogous to Pearl’s logic. The first result of this thesis is an extension of Stanlnaker’s logic incorporating reversibility. It will be observed that the translation of reversibility from Pearl’s language to the standard language for conditional logic deserves some attention. In particular, a straightforward translation following Pearl’s suggestion would render reversibility incompatible with Stanlnaker’s logic. A new translation of reversibility will be proposed, and an extension of Stanlnaker’s logic with the inclusion of the translated reversibility will be investigated. More importantly, it will be shown that the extended Stanlnaker’s logic is sound and complete with respect to a modified Stanlnaker’s semantics.
The extension of Stanlnaker’s logic has an interesting implication. Zhang, Lam, and de Clercq (2012) have shown that special case of reversibility, despite its name, actually states an important kind of irreversibility: counterfactual dependence (as defined by David Lewis) between distinct events is irreversible. In other words, reversibility entails that there is no cycle of counterfactual dependence altogether generalizations of reversibility. However, as shown in Zhang et al. (2012), Pearls’ logic does not rule out cycles of counterfactual dependence altogether. It in fact allows cycles that involve three or more distinct events. This is peculiar because the status of cyclic counterfactual dependence seems no more metaphysically secure than that of mutual counterfactual dependence. This consideration leads to an exploration of logics that rule out all cycles of counterfactual dependence. A surprising result is that the extension of Stanlnaker’s logic is precisely a logic of this sort.
|Date of Award||2012|
|Supervisor||Jiji ZHANG (Supervisor)|