In this thesis I present an account of the formal semantics of counterfactuals that systematically deals with impossible antecedents. This, in turn, allows us to gain a richer understanding of what makes certain thought experiments informative in spite of the impossibility of the situations they consider. In Chapter II, I argue that there are major shortcomings in the leading theories of counterfactuals. The leading theories of counterfactuals (based on classical two-valued logic) are unable to account for counterfactuals with impossible antecedents. In such accounts, everything and anything follows from an impossible antecedent. In Chapter III, I examine some crucial notions such as conceivability, imaginability, and possibility. Herein I argue that there is a distinction to be made between the notions of conceiving and imagining. Conceivability, it turns out, is a sufficient condition for being a case. Recent literature on the semantics for relevance logic have made some use of the notion of a “state”, which differs from a world in that contradictions are true in some states; what is not done in that literature is to clarify how the notion of a state differs from an arbitrary collection of claims. I use the notion of a case as a (modal) tool to analyze counterfactuals with impossible antecedents, one for which, unlike the notion of states, it is clear why arbitrary collections of claims do not count. In Chapter IV, I propose a new account of counterfactuals. This involves modifying existing possible worlds accounts of counterfactuals by replacing possible worlds by the “cases” identified in Chapter III. This theory discerns counterfactuals such as: “If Dave squared the circle, he would be more famous than Gödel” which seems true, from others like: “If Dave squared the circle, the sun would explode”, which seems false. In Chapter V I discuss one of the main pay offs of having an account of counterfactuals that deals systematically with counterfactuals with impossible antecedents. To apply the new account of counterfactual to thought experiments, first we have to transform the thought experiment in question into a series of counterfactuals. I show how this is to be done, in Chapter V. There are two advantages of such an account when we apply it to thought experiments: First, for thought experiments with impossible scenarios, our new account can explain how such thought experiments can still be informative. Secondly, for thought experiments like the Chinese Room, where it is not clear whether there is a subtle impossibility in the scenario or not, this new account with its continuous treatment of possible and impossible cases makes clear why the debate about such thought experiments looks the way it does. The crucial question is not whether there is such an impossibility, but what is the "nearest" situation in which there is a Chinese Room (whether it is impossible or not) and what we would say there (about the intentionality of the room). On traditional accounts, it becomes paramount to deal with the possibility question, because if it is an impossible scenario the lessons we learn are very different from the ones we learn if it is possible. There are no available theories of thought experiments that account for thought experiments with impossible/incomplete scenarios. With the new account of counterfactual and by applying it to thought experiments we over come this difficulty.

In this thesis I present an account of the formal semantics of counterfactuals that systematically deals with impossible antecedents. This, in turn, allows us to gain a richer understanding of what makes certain thought experiments informative in spite of the impossibility of the situations they consider. In Chapter II, I argue that there are major shortcomings in the leading theories of counterfactuals. The leading theories of counterfactuals (based on classical two-valued logic) are unable to account for counterfactuals with impossible antecedents. In such accounts, everything and anything follows from an impossible antecedent. In Chapter III, I examine some crucial notions such as conceivability, imaginability, and possibility. Herein I argue that there is a distinction to be made between the notions of conceiving and imagining. Conceivability, it turns out, is a sufficient condition for being a case. Recent literature on the semantics for relevance logic have made some use of the notion of a “state”, which differs from a world in that contradictions are true in some states; what is not done in that literature is to clarify how the notion of a state differs from an arbitrary collection of claims. I use the notion of a case as a (modal) tool to analyze counterfactuals with impossible antecedents, one for which, unlike the notion of states, it is clear why arbitrary collections of claims do not count. In Chapter IV, I propose a new account of counterfactuals. This involves modifying existing possible worlds accounts of counterfactuals by replacing possible worlds by the “cases” identified in Chapter III. This theory discerns counterfactuals such as: “If Dave squared the circle, he would be more famous than Gödel” which seems true, from others like: “If Dave squared the circle, the sun would explode”, which seems false. In Chapter V I discuss one of the main pay offs of having an account of counterfactuals that deals systematically with counterfactuals with impossible antecedents. To apply the new account of counterfactual to thought experiments, first we have to transform the thought experiment in question into a series of counterfactuals. I show how this is to be done, in Chapter V. There are two advantages of such an account when we apply it to thought experiments: First, for thought experiments with impossible scenarios, our new account can explain how such thought experiments can still be informative. Secondly, for thought experiments like the Chinese Room, where it is not clear whether there is a subtle impossibility in the scenario or not, this new account with its continuous treatment of possible and impossible cases makes clear why the debate about such thought experiments looks the way it does. The crucial question is not whether there is such an impossibility, but what is the "nearest" situation in which there is a Chinese Room (whether it is impossible or not) and what we would say there (about the intentionality of the room). On traditional accounts, it becomes paramount to deal with the possibility question, because if it is an impossible scenario the lessons we learn are very different from the ones we learn if it is possible. There are no available theories of thought experiments that account for thought experiments with impossible/incomplete scenarios. With the new account of counterfactual and by applying it to thought experiments we over come this difficulty.

Lewisian Genuine Realism (GR) about possible worlds is often deemed unable to accommodate impossible worlds and reap the benefits that these bestow to rival theories. This thesis explores two alternative extensions of GR into the terrain of impossible worlds. It is divided in six chapters. Chapter I outlines Lewis’ theory, the motivations for impossible worlds, and the central problem that such worlds present for GR: How can GR even understand the notion of an impossible world, given Lewis’ reductive theoretical framework? Since the desideratum is to incorporate impossible worlds into GR without compromising Lewis’ reductive analysis of modality, Chapter II defends that analysis against (old and new) objections. The rest of the thesis is devoted to incorporating impossible worlds into GR. Chapter III explores GR-friendly impossible worlds in the form of set-theoretic constructions out of genuine possibilia. Then, Chapters IV-VI venture into concrete impossible worlds. Chapter IV addresses Lewis’ objection against such worlds, to the effect that contradictions true at impossible worlds amount to true contradictions tout court. I argue that even if so, the relevant contradictions are only ever about the non-actual, and that Lewis’ argument relies on a premise that cannot be nonquestion- beggingly upheld in the face of genuine impossible worlds in any case. Chapter V proposes that Lewis’ reductive analysis can be preserved, even in the face of genuine impossibilia, if we differentiate the impossible from the possible by means of accessibility relations, understood non-modally in terms of similarity. Finally, Chapter VI counters objections to the effect that there are certain impossibilities, formulated in Lewis’ theoretical language, which genuine impossibilia should, but cannot, represent. I conclude that Genuine Realism is still very much in the running when the discussion turns to impossible worlds.