Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. (...) Another justification derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time (...) would have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

Several themes of David Lewis's theory of counterfactuals, especially their sensitivity to context, pave the way for a viable theory of non-trivial counterpossibles. If Lewis was successful in defending his account against the early objections, a semantics of counterpossibles can be defended from similar objections in the same way. The resulting theory will be extended to address 'might' counterfactuals and questions about the relative "nearness" of impossible worlds.

I develop a theory of counterfactuals about relative computability, i.e. counterfactuals such as 'If the validity problem were algorithmically decidable, then the halting problem would also be algorithmically decidable,' which is true, and 'If the validity problem were algorithmically decidable, then arithmetical truth would also be algorithmically decidable,' which is false. These counterfactuals are counterpossibles, i.e. they have metaphysically impossible antecedents. They thus pose a challenge to the orthodoxy about counterfactuals, which would treat them as uniformly true. What’s more, (...) I argue that these counterpossibles don’t just appear in the periphery of relative computability theory but instead they play an ineliminable role in the development of the theory. Finally, I present and discuss a model theory for these counterfactuals that is a straightforward extension of the familiar comparative similarity models. (shrink)

Dispositionalists try to provide an account of modality—possibility, necessity, and the counterfactual conditional—in terms of dispositions. But there may be a tension between dispositionalist accounts of possibility on the one hand, and of counterfactuals on the other. Dispositionalists about possibility must hold that there are no impossible dispositions, i.e., dispositions with metaphysically impossible stimulus and/or manifestation conditions; dispositionalist accounts of counterfactuals, if they allow for non-vacuous counterpossibles, require that there are such impossible dispositions. I argue, first, that there are (...) in fact no impossible dispositions; and second, that the dispositionalist can nevertheless acknowledge the non-vacuity of some counterpossibles. The strategy in the second part is one of ‘divide and conquer’ that is not confined to the dispositionalist: it consists in arguing that counterpossibles, when non-vacuous, are read epistemically and are therefore outside the purview of a dispositional account. (shrink)

Several theorists have been attracted to the idea that in order to account for counterpossibles, i.e. counterfactuals with impossible antecedents, we must appeal to impossible worlds. However, few have attempted to provide a detailed impossible worlds account of counterpossibles. Berit Brogaard and Joe Salerno’s ‘Remarks on Counterpossibles’ is one of the few attempts to fill in this theoretical gap. In this article, I critically examine their account. I prove a number of unanticipated implications of their account that (...) end up implying a counterintuitive result. I then examine a suggested revision and point out a surprising implication of the revision. (shrink)

Several theists, including Linda Zagzebski, have claimed that theism is somehow committed to nonvacuism about counterpossibles. Even though Zagzebski herself has rejected vacuism, she has offered an argument in favour of it, which Edward Wierenga has defended as providing strong support for vacuism that is independent of the orthodox semantics for counterfactuals, mainly developed by David Lewis and Robert Stalnaker. In this paper I show that argument to be sound only relative to the orthodox semantics, which entails vacuism, and (...) give an example of a semantics for counterfactuals countenancing impossible worlds for which it fails. (shrink)

In a series of articles, Wes Morriston has launched what can only be considered a full-scale assault on the divine command theory (DCT) of morality. According to Morriston, proponents of this theory are committed to an alarming counterpossible: that if God did command an annual human sacrifice, it would be morally obligatory. Since only a ‘terrible’ deity would do such a ‘terrible’ thing, we should reject DCT. Indeed, if there were such a deity, the world would be a terrible place—certainly (...) far worse than it is. We argue that Morriston’s non-standard method for assessing counterpossibles of this sort is flawed. Not only is the savvy DCT-ist at liberty to reject it, but Morriston’s method badly misfires in the face of theistic activism—a metaphysical platform available to DCT-ists, according to which if God didn’t exist, neither would anything else. (shrink)

Guy Kahane asks an axiological question: what value would (or does) God’s existence bestow on the world? Supposing God’s existence is a matter of necessity, this axiological question faces a problem because answering it will require assessing the truth-value of counterpossibles. I argue that Kahane, Paul Moser, and Richard Davis and Paul Franks fail in their attempts to render the axiological question substantive. I then offer my own solution by bringing work in cognitive psychology and philosophy of mind to (...) bear on the possibility of assessing counterpossibles. I argue that humans can engage in counterpossible reasoning by “accepting” or “supposing” that the antecedent is true and “screening out” those beliefs that would result in contradictions when combined in inferences with the acceptance or supposition. These screened out propositions are not treated as false, but are ignored. I offer a three-valued logic for counterpossible reasoning. I conclude by outlining some implications for the axiological question. (shrink)

Counterpossibles are counterfactuals with necessarily false antecedents. The problem of counterpossibles is easiest to state within the "nearest possible world" framework for counterfactuals: on this approach, a counterfactual is true when the consequent is true in the "nearest" possible world where the antecedent is true. Since counterpossibles have necessarily false antecedents, there is no possible world where the antecedent is true. On the approach favored by Lewis, Stalnaker, Williamson, and others, counterpossibles are all trivially true. I (...) introduce several arguments against the trivial approach. First, it is counter-intuitive to think that all counterpossibles are true. Second, if all counterpossibles were true, then we could not make sense of their use in logical, philosophical, or mathematical arguments. Making sense of the role of sentences like these requires that they not have vacuous truth conditions. The account of counterpossibles I ultimately favor is an extension of the "nearest possible world" semantics discussed above. The Lewis/Stalnaker account is supplemented with the addition of impossible worlds, and the nearness metric is extended to range over these impossible worlds as well as possible worlds. Thus, a counterfactual is true when its consequent is true in the nearest world where the antecedent is true; if the counterfactual's antecedent is impossible, then the nearest world in question will be an impossible world. Once the framework of impossible worlds and similarity is in place, we can put it to use in the analysis of other philosophical phenomena. I examine one proposal that makes use of a theory of counterpossibles to develop an analysis of the notion of metaphysical dependence. (shrink)

To solve the problem of counterpossibles, many philosophers have been arguing that one needs to invoke impossible worlds. This extension of the ontology of modality should save the analysis of counterfactuals from being insensitive to the problem of counterpossibles. Since theories of impossible worlds are extensions of original accounts of modalities, it is worth stressing that proper analyses of counterpossibles should not weaken the latter.In this paper I argue that these theories of impossible wolrds, which are based (...) on D. Lewis' modal realism - Extended Modal Realism and Hybrid Modal Realism - might be consider as either an unattractive for modal realists or insufficient for analyzing counterpossibles. (shrink)

The aim of this paper is to show why the theories of impossible worlds do not fully solve the problem of counterpossibles, but merely shift it. Moreover, by making a distinction between two types of languages, we will show that some expectations about proper theory of counterfactuals might be too great.

Wright (In Gendler and Hawthorne (Eds.), Conceivability and possibility, 2002) rejects some dominant responses to Kripke’s modal argument against the mind-body identity theory, and instead he proposes a new response that draws on a certain understanding of counterpossibles. This paper offers some defensive remarks on behalf of Lewis’ objection to that argument, and it argues that Wright’s proposal fails to fully accommodate the conceivability intuitions, and that it is dialectically ineffective.

One well-known objection to the traditional Lewis-Stalnaker semantics of counterfactuals is that it delivers counterintuitive semantic verdicts for many counterpossibles (counterfactuals with necessarily false antecedents). To remedy this problem, several authors have proposed extending the set of possible worlds by impossible worlds at which necessary falsehoods may be true. Linguistic ersatz theorists often construe impossible worlds as maximal, inconsistent sets of sentences in some sufficiently expressive language. However, in a recent paper, Bjerring (2014) argues that the “extended” Lewis-Stalnaker semantics (...) delivers the wrong truth-values for many counterpossibles if impossible worlds are required to be maximal. To make room for non-maximal or partial impossible worlds, Bjerring considers two alternative world-ontologies: either (i) we construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences, or (ii) we construe them as (maximal or partial) inconsistent sets of sentences that are closed and consistent with respect to some non-classical logic. Bjerring raises an objection against (i), and suggests that we opt for (ii). In this paper, I argue, first, that Bjerring’s objection against (i) conflates two different conceptions of what it means for a logic to be true at a world. Second, I argue that (ii) imposes too strong constraints on what counts as an impossible world. I conclude that linguistic ersatzists should construe impossible worlds as arbitrary (maximal or partial) inconsistent sets of sentences. (shrink)

According to the most popular theories, counterfactuals with impossible antecedents are vacuously true. Critiques of this view argue that contrary to this, we tend to consider only some of them true and others to be false. In his recent paper Timothy Williamson has ingeniously explained the motivations for the orthodox view and argued that although there are some heuristic reasons that may suggest the plausibility of the unorthodox view, they are fallible. The most important of Williamson’s arguments is that the (...) unorthodox interpretation is inconsistent with the heuristic assumption that supposedly motivates this very view. The aim of this paper is to consider Williamson’s critique and to support the unorthodox approach towards counterpossibles. In order to do so, we argue in favor of the modified version of the heuristic assumption. (shrink)

This dissertation explores various attempts to solve the Dependence Problem problem posed by the following question: How can necessary truths stand to God in a one-way relation of dependence, given that neither they nor God could have failed to exist?

The paper clarifies and defends the orthodox view that counterfactual conditionals with impossible antecedents are vacuously true against recent criticisms. It argues that apparent counterexamples to orthodoxy result from uncritical reliance on a fallible heuristic used in the processing of conditionals. A comparison is developed between such counterpossibles and vacuously true universal generalizations.

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time (...) would have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

Closest-possible-world analyses of counterfactuals suffer from what has been called the ‘problem of counterpossibles’: some counterfactuals with metaphysically impossible antecedents seem plainly false, but the proposed analyses imply that they are all (vacuously) true. One alleged solution to this problem is the addition of impossible worlds. In this paper, I argue that the closest possible or impossible world analyses that have recently been suggested suffer from the ‘new problem of counterpossibles’: the proposed analyses imply that some plainly true (...) counterpossibles (viz., ‘counterlogicals’) are false. After motivating and presenting the ‘new problem’, I give reasons to think that the most plausible objection to my argument is not compelling. (shrink)

I. Non-Trivial Counterpossibles On Lewis’ account, a subjunctive of the form ‘if it were the case that p, it would be the case that q’ (represented as ‘p → q’) is to be given the following rough meta-linguistic truth-conditions1.

The object of this paper is to examine two approaches to giving non-vacuous truth conditions for counterpossibles, counterfactuals with impossible antecedents. I first develop modifications of a Lewis-style sphere semantics with impossible worlds. I argue that this approach sanctions intuitively invalid inferences and is supported by philosophically problematic foundations. I then develop modifications of certain ceteris paribus conditional logics with impossible worlds. Tableaux are given for each of these in an appendix and soundness and completeness results are proved. While (...) certain of the latter systems are shown to have similar problems to logics from the first approach, at least one relatively weak system appears to offer an adequate uniform semantics for counterpossibles and counterfactuals. (shrink)

Nina Emery and Christopher Hill proposed a pragmatic approach toward the debate about counterpossibles—i.e., counterfactuals with impossible antecedents. The core of this approach is to move the burden of the problem from the notion of truth value into the notion of assertion. This is meant to explain our pre-theoretical intuitions about counterpossibles while claiming that each and every counterpossible is vacuously true. The aim of this paper is to indicate a problematic aspect of this view.

Lewis/Stalnaker semantics has it that all counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are vacuously true. Non-vacuism, by contrast, says the truth-values of counterpossibles are affected by the truth-values of the consequents. Some counterpossibles are true, some false. Williamson objects to non-vacuism. He asks us to consider someone who answered ‘11’ to ‘What is 5 + 7?’ but who mistakenly believes that he answered ‘13’. For the non-vacuist, (1) is false, (2) true: (1) If 5 + 7 (...) were 13, x would have got that sum right (2) If 5 + 7 were 13, x would have got that sum wrong Williamson is not persuaded by the initial intuitiveness of such examples: ... they tend to fall apart when thought through. For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1. (2006) That’s the whole argument—much of it implicit. Alan Baker’s critique (2007) of Brogaard and Salerno (2007) prompts us to say something less abbreviated about a less abbreviated form of Wiliamson’s argument. Then we further develop our (2007) counterfactual analysis of essense. (shrink)

In this paper I critically examine Brian Leftow's attempt to construct a theistic semantics for counterpossibles, one that can be used to make sense of the fact that propositions, which exist necessarily, nevertheless depend on God as their cause. I argue that the impressive theoretical framework erected by Leftow cannot guarantee an asymmetrical dependence of propositions on God, and ultimately leads to a semantic collapse in which every counterpossible comes out false. I end by defending an alternative account of (...) God and propositions -- what I call 'theistic existentialism'. It is shown how this account underwrites a semantics for counterpossibles that conveniently avoids the problems attending Leftow's theory. (shrink)

Counterpossibles are counterfactuals that involve some metaphysical impossibility. Modal normativism is a non-descriptivist account of metaphysical necessity and possibility according to which modal claims, e.g. ‘necessarily, all bachelors are unmarried’, do not function as descriptive claims about the modal nature of reality but function as normative illustrations of constitutive rules and permissions that govern the use of ordinary non-modal vocabulary, e.g. ‘bachelor’. In this paper, I assume modal normativism and develop a novel account of counterpossibles and claims about (...) metaphysical similarity between possible and impossible worlds. I argue that considerations of metaphysical similarity between various impossible worlds and the actual world only require us to tacitly consider how the actual constitutive rules that govern the use of our terms change in order to accommodate the description of some hypothetical impossible scenario. I then argue for my account by raising worries for alternative epistemic and realist accounts of counterpossibles and showing how my account avoids those worries. (shrink)

A counterpossible conditional is a counterfactual with an impossible antecedent. Common sense delivers the view that some such conditionals are true, and some are false. In recent publications, Timothy Williamson has defended the view that all are true. In this paper we defend the common sense view against Williamson’s objections.

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (shrink)

A counterpossible conditional, or counterpossible for short, is a conditional proposition whose antecedent is impossible. The filioque doctrine is a dogma of western Christian Trinitarian theology according to which the Holy Spirit proceeds from the Father and the Son. The filioque doctrine was the principal theological reason for the Great Schism, the split between Eastern Orthodoxy and western Christianity, which continues today. In the paper, I review one of the earliest medieval defenses of the doctrine in Anselm of Canterbury, and (...) I show that Anselm’s treatment of counterpossible conditionals concerning the procession of the spirit from the son in Trinitarian theology represent an early foray into default logic. Thus, the mutual estrangement of eastern and western positions on the matter may not lie fundamentally in a change in dogma, but rather in a change in logic. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) (...) causal counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (shrink)

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. (shrink)

A counteridentical is a counterfactual with an identity statement in the antecedent. While counteridenticals generally seem non-trivial, most semantic theories for counterfactuals, when combined with the necessity of identity and distinctness, attribute vacuous truth conditions to such counterfactuals. In light of this, one could try to save the orthodox theories either by appealing to pragmatics or by denying that the antecedents of alleged counteridenticals really contain identity claims. Or one could reject the orthodox theory of counterfactuals in favor of a (...) hyperintensional semantics that accommodates non-trivial counterpossibles. In this paper, I argue that none of these approaches can account for all the peculiar features of counteridenticals. Instead, I propose a modified version of Lewis’s counterpart theory, which rejects the necessity of identity, and show that it can explain all the peculiar features of counteridenticals in a satisfactory way. I conclude by defending the plausibility of contingent identity from objections. (shrink)

Modal knowledge accounts that are based on standards possible-worlds semantics face well-known problems when it comes to knowledge of necessities. Beliefs in necessities are trivially sensitive and safe and, therefore, trivially constitute knowledge according to these accounts. In this paper, I will first argue that existing solutions to this necessity problem, which accept standard possible-worlds semantics, are unsatisfactory. In order to solve the necessity problem, I will utilize an unorthodox account of counterfactuals, as proposed by Nolan, on which we also (...) consider impossible worlds. Nolan’s account for counterpossibles delivers the intuitively correct result for sensitivity i.e. S’s belief is sensitive in intuitive cases of knowledge of necessities and insensitive in intuitive cases of knowledge failure. However, we acquire the same plausible result for safety only if we reject his strangeness of impossibility condition and accept the modal closeness of impossible worlds. In this case, the necessity problem can be analogously solved for sensitivity and safety. For some, such non-moderate accounts might come at too high a cost. In this respect, sensitivity is better off than safety when it comes to knowing necessities. (shrink)

A great deal has been written about 'would' counterfactuals of causal dependence. Comparatively little has been said regarding 'would' counterfactuals of ontological dependence. The standard Lewis-Stalnaker semantics is inadequate for handling such counterfactuals. That's because some of these counterfactuals are counterpossibles, and the standard Lewis-Stalnaker semantics trivializes for counterpossibles. Fortunately, there is a straightforward extension of the Lewis-Stalnaker semantics available that handles counterpossibles: simply take Lewis's closeness relation that orders possible worlds and unleash it across impossible worlds. (...) To apply the extended semantics, an account of the closeness relation for counterpossibles is needed. In this paper I offer a strategy for evaluating 'would' counterfactuals of ontological dependence that understands closeness between worlds in terms of the metaphysical concept of grounding. (shrink)

We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...) to rely on counterpossibles. We conclude that the CTE is a promising candidate for a monist account of explanation in both science and mathematics. (shrink)

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' 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. (shrink)

In this book, Richard Brian Davis explores various attempts to solve the Dependence Problem – the problem posed by the following question: How can necessary truths stand to God in a one-way relation of dependence when neither they nor God could have failed to exist? Critics charge that this problem is insoluble. Davis argues at length that the most powerful and promising contemporary solutions to this problem – those offered by Linda Zagzebski, Brian Leftow, Thomas V. Morris, and William Mann (...) – are all fatally flawed. In making his case, Davis treats the reader to helpful and interesting discussions of counterpossibles, broadly logical necessity, identity statements, as well as the divine attributes of sovereignty, aseity, and simplicity. He concludes with what is perhaps the most forceful and sustained defense of the claim that necessary truths can stand to God in an asymmetrical relation of causal dependence. (shrink)

The theory of possible worlds has permeated analytic philosophy in recent decades, and its best versions have a consequence which has gone largely unnoticed: in addition to the panoply of possible worlds, there are a great many impossible worlds. A uniform ontological method alone should bring the friends of possible worlds to adopt impossible worlds, I argue, but the theory's applications also provide strong incentives. In particular, the theory facilitates an account of counterfactuals which avoids several of the implausible results (...) of David Lewis's account, and it paves the way for the analogues of Kripkean semantics for epistemic and relevant logics. On the theories of possible worlds as abstract objects, worlds bear a strong resemblance to propositions. I contend that if there are distinct necessarily false propositions, then there are likewise distinct impossible worlds. However, one who regards possible worlds as concrete objects must not recognize impossible worlds, in part because concrete worlds cannot misrepresent certain features of reality, as some impossible worlds must. Accordingly, I defend and develop a theory of impossible worlds as maximal impossible states of affairs. Impossible worlds perform admirably in the analysis of counterfactuals with impossible antecedents. I argue that, contrary to standard accounts, not all counterpossibles are trivially true, and I develop a Lewis-style semantics which allows this result. The point is crucial, since many views presuppose that some counterpossibles are substantive philosophical truths. Finally, I show that impossible worlds hold great promise for doxastic and relevant logics. Epistemic logic needs a domain of propositions which is not closed under strict implication to avoid the problem of logical omniscience, and relevant logic needs such a domain to avoid the famous paradoxes of implication. In sum, impossible world theory promises natural, elegant solutions to philosophical problems in numerous areas where possible worlds alone flounder. These solutions come to most possible world theorists at no cost, since the existence of impossible worlds is entailed by theses they already hold. (shrink)

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel (...) way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic. (shrink)

We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

Sentences about logic are often used to show that certain embedding expressions, including attitude verbs, conditionals, and epistemic modals, are hyperintensional. Yet it not clear how to regiment “logic talk” in the object language so that it can be compositionally embedded under such expressions. This paper does two things. First, it argues against a standard account of logic talk, viz., the impossible worlds semantics. It is shown that this semantics does not easily extend to a language with propositional quantifiers, which (...) are necessary for regimenting some logic talk. Second, it develops an alternative framework based on logical expressivism, which explains logic talk using shifting conventions. When combined with the standard S5π+ semantics for propositional quantifiers, this framework results in a well-behaved system that does not face the problems of the impossible worlds semantics. It can also be naturally extended with hybrid operators to regiment a broader range of logic talk, e.g., claims about what laws hold according to other logics. The resulting system, called hyperlogic, is therefore a better framework for modeling logic talk than previous accounts. (shrink)

If moral properties lacked causal powers, would moral skepticism be true? I argue that it would. Along the way I respond to various arguments that it would not.

Brogaard and Salerno (2005, Nous, 39, 123–139) have argued that antirealism resting on a counterfactual analysis of truth is flawed because it commits a conditional fallacy by entailing the absurdity that there is necessarily an epistemic agent. Brogaard and Salerno's argument relies on a formal proof built upon the criticism of two parallel proofs given by Plantinga (1982, "Proceedings and Addresses of the American Philosophical Association", 56, 47–70) and Rea (2000, "Nous," 34, 291–301). If this argument were conclusive, antirealism resting (...) on a counterfactual analysis of truth should probably be abandoned. I argue however that the antirealist is not committed to a controversial reading of counterfactuals presupposed in Brogaard and Salerno's proof, and that the antirealist can in principle adopt an alternative reading that makes this proof invalid. My conclusion is that no reductio of antirealism resting on a counterfactual analysis of truth has yet been provided. (shrink)