Counterfactuals without Possible Worlds? A Difficulty for Fine’s Exact Semantics for Counterfactuals

In this paper I argue that there is a difficulty for Fine's exact semantics for counterfactuals. The difficulty undermines Fine's reasons for preferring exact semantics to possible worlds semantics

On the Substitution of Identicals in Counterfactual Reasoning

It is widely held that counterfactuals, unlike attitude ascriptions, preserve the referential transparency of their constituents, i.e., that counterfactuals validate the substitution of identicals when their constituents do. The only putative counterexamples in the literature come from counterpossibles, i.e., counterfactuals with impossible antecedents. Advocates of counterpossibilism, i.e., the view that counterpossibles are not all vacuous, argue that counterpossibles can generate referential opacity. But in order to explain why most substitution inferences into counterfactuals seem valid, counterpossibilists also often maintain that counterfactuals with possible antecedents are transparency‐preserving. I argue that if counterpossibles can generate opacity, then so can ordinary counterfactuals with possible antecedents. Utilizing an analogy between counterfactuals and attitude ascriptions, I provide a counterpossibilist‐friendly explanation for the apparent validity of substitution inferences into counterfactuals. I conclude by suggesting that the debate over counterpossibles is closely tied to questions concerning the extent to which counterfactuals are more like attitude ascriptions and epistemic operators than previously recognized

Backtracking Counterfactuals Revisited

I discuss three observations about backtracking counterfactuals not predicted by existing theories, and then motivate a theory of counterfactuals that does predict them. On my theory, counterfactuals quantify over a suitably restricted set of historical possibilities from some contextually relevant past time. I motivate each feature of the theory relevant to predicting our three observations about backtracking counterfactuals. The paper concludes with replies to three potential objections

Frontiers of Conditional Logic

Conditional logics were originally developed for the purpose of modeling intuitively correct modes of reasoning involving conditional—especially counterfactual—expressions in natural language. While the debate over the logic of conditionals is as old as propositional logic, it was the development of worlds semantics for modal logic in the past century that catalyzed the rapid maturation of the field. Moreover, like modal logic, conditional logic has subsequently found a wide array of uses, from the traditional (e.g. counterfactuals) to the exotic (e.g. conditional obligation). Despite the close connections between conditional and modal logic, both the technical development and philosophical exploitation of the latter has outstripped that of the former, with the result that noticeable lacunae exist in the literature on conditional logic. My dissertation addresses a number of these underdeveloped frontiers, producing new technical insights and philosophical applications. I contribute to the solution of a problem posed by Priest of finding sound and complete labeled tableaux for systems of conditional logic from Lewis\u27 V-family. To develop these tableaux, I draw on previous work on labeled tableaux for modal and conditional logic; errors and shortcomings in recent work on this problem are identified and corrected. While modal logic has by now been thoroughly studied in non-classical contexts, e.g. intuitionistic and relevant logic, the literature on conditional logic is still overwhelmingly classical. Another contribution of my dissertation is a thorough analysis of intuitionistic conditional logic, in which I utilize both algebraic and worlds semantics, and investigate how several novel embedding results might shed light on the philosophical interpretation of both intuitionistic logic and conditional logic extensions thereof. My dissertation examines deontic and connexive conditional logic as well as the underappreciated history of connexive notions in the analysis of conditional obligation. The possibility of interpreting deontic modal logics in such systems (via embedding results) serves as an important theoretical guide. A philosophically motivated proscription on impossible obligations is shown to correspond to, and justify, certain (weak) connexive theses. Finally, I contribute to the intensifying debate over counterpossibles, counterfactuals with impossible antecedents, and take—in contrast to Lewis and Williamson—a non-vacuous line. Thus, in my view, a counterpossible like If there had been a counterexample to the law of the excluded middle, Brouwer would not have been vindicated is false, not (vacuously) true, although it has an impossible antecedent. I exploit impossible (non-normal) worlds—originally developed to model non-normal modal logics—to provide non-vacuous semantics for counterpossibles. I buttress the case for non-vacuous semantics by making recourse to both novel technical results and theoretical considerations

Metaphysical Dependence and Set Theory

In this dissertation, I articulate and defend a counterfactual analysis of metaphysical dependence. It is natural to think that one thing x depends on another thing y if had y not existed, then x wouldn\u27t have existed either. But counterfactual analyses of metaphysical dependence are often rejected in the current literature. They are rejected because straightforward counterfactual analyses fail to accurately capture dependence relations between objects that exist necessarily, like mathematical objects. For example, it is taken as given that sets metaphysically depend on their members, while members do not metaphysically depend on the sets they belong to. The set {0} metaphysically depends on 0, while 0 does not metaphysically depend on {0}. The dependence is asymmetric. But if counterfactuals are given a possible worlds analysis, as is standard, then the counterfactual approach to dependence will yield a symmetric dependence relation between these two sets. Because the counterfactual analysis fails to accurately capture dependence relations between sets and their members, most reject this approach to metaphysical dependence. To generate the desired asymmetry, I argue that we should introduce impossible worlds into the framework for evaluating counterfactuals. I review independent reasons for admitting impossible worlds alongside possible worlds. Once we have impossible worlds at our disposal, we can consider worlds where, e.g., the empty set does not exist. I argue that in the worlds that are ceteris paribus like the actual world, where 0 does not exist, {0} does not exist either. And so, according to the counterfactual analysis of dependence, {0} metaphysically depends on 0, as desired. Conversely, however, there is no reason to think that every world that is ceteris paribus like the actual world, where {0} does not exist, is such that 0 does not exist either. And so 0 does not metaphysically depend on {0}. After applying this extended counterfactual analysis to several set-theoretic cases, I show that it can be applied to account for dependence relations between other mathematical objects as well. I conclude by defending the counterfactual analysis, extended with impossible worlds, against several objections