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)

A counterpossible is a counterfactual whose antecedent is impossible. The vacuity thesis says all counterpossibles are true solely because their antecedents are impossible. Recently, some have rejected the vacuity thesis by citing purported non-vacuous counterpossibles in science. One limitation of this work, however, is that it is not grounded in experimental data. Do scientists actually reason non-vacuously about counterpossibles? If so, what is their basis for doing so? We presented biologists (N = 86) with two counterfactual formulations of a well-known (...) model in biology, the antecedents of which contain what many philosophers would characterize as a metaphysical impossibility. Participants consistently judged one counterfactual to be true, the other to be false, and they explained that they formed these judgments based on what they perceived to be the mathematical relationship between the antecedent and consequent. Moreover, we found no relationship between participants’ judgments about the (im)possibility of the antecedent and whether they judged a counterfactual to be true or false. These are the first experimental results on counterpossibles in science with which we are familiar. We present a modal semantics that can capture these judgments, and we deal with a host of potential objections that a defender of the vacuity thesis might make. (shrink)

Frege puzzles exploit cognitive differences between co-referential terms. Traditionally, they were handled by some version of Frege’s distinction between sense and reference, which avoided disruptive consequences for epistemology. However, the Fregean programme did not live up to its original promise, and was undermined by the development of theories of direct reference; for semantic purposes, its prospects now look dim. In particular, well-known analogues of Frege puzzles concern pairs of uncontentious synonyms; attempts to deal with them by distinguishing idiolects or postulating (...) ‘narrow contents’ or elaborate forms of context-sensitivity are inadequate or semantically implausible. Although ascriptions of knowledge, belief, and other attitudes are ubiquitous in epistemology, epistemologists have not properly come to terms with the surprising consequences of anti-Fregean semantic accounts of attitude ascriptions. In ‘A Puzzle about Belief ’, Saul Kripke shows that natural-seeming disquotational principles for ascribing belief lead to apparently unacceptable consequences, including outright contradictions, in problem cases. Such disquotation principles, I argue, are best regarded not as conceptual connections but just as heuristics in the psychological sense, quick and easy ways of assessing belief ascriptions, usually accurate under normal conditions but far from 100% reliable. I discuss similar heuristics for ascribing knowledge and other attitudes. That the principles have a merely heuristic status need not be pre-theoretically manifest to their users. This view vindicates Kripke’s conclusion that it would be wrong-headed to draw semantic conclusions from Frege puzzles. I discuss the epistemological consequences of an anti-Fregean approach to Frege puzzles, including for Kripke’s cases of the contingent a priori and the necessary a posteriori, but also for evidence, for epistemic modalities, and for epistemic and subjective conceptions of probability. Anna Mahtani’s recent identification of Frege puzzles for the ex ante Pareto Principle as used in welfare economics provides an interesting example. I suggest a model-building methodology as the most promising way of handling at least some of the difficulties. A final issue is the choice between different anti-Fregean approaches to semantics, from very coarse-grained intensional approaches on which sentences express functions from possible worlds to truth-values to more fine-grained hyperintensional approaches on which sentences express functions from possible or impossible worlds to truth-values or else Russellian structured propositions. Some of the hyperintensional theories violate semantic compositionality. More generally, since our attitude ascriptions rely on heuristics, they should be expected to exhibit some level of error; although hyperintensional approaches may be able slightly to reduce the level of postulated error, they do so at the cost of vastly increased theoretical complexity, and so have weak explanatory power. Methodologically, a simple intensional approach does better. (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 (roughly) 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)

The epistemology of modality is gradually coming to play a central role in general discussions about modality. This paper is a contribution in this direction, in particular I draw a comparison between Lewis’s Modal realism and Timothy Williamson’s recent account of modality in terms of counterfactual thinking. In order to have criteria of evaluation, I also formulate four requirements which are supposed to be met by any theory of modality to be epistemologically adequate.

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are known. (...) Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence. (shrink)

Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts (...) do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal. (shrink)

In this paper we discuss how Causal Decision Theory should be modified to handle a class of problematic cases involving deterministic laws. Causal Decision Theory, as it stands, is problematically biased against your endorsing deterministic propositions (for example it tells you to deny Newtonian physics, regardless of how confident you are of its truth). Our response is that this is not a problem for Causal Decision Theory per se, but arises because of the standard method for assessing the truth of (...) certain counterfactuals. The truth of deterministic laws is `modally fragile' on the standard semantics for counterfactuals: if determinism is true and you were to do otherwise, the laws would be different. We provide two ways of avoiding this problem: 1) supplement the standard semantics for counterfactuals with impossible worlds, or 2) introduce rigid designators into the description of problematic decision situations. We argue that both of these approaches are well-motivated and can be readily incorporated into Lewisian Causal Decision Theory. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, (...) it is emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

It is known that indicative and subjunctive conditionals interact differently with a rigidifying "actually" operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing "actually" instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they (...) preserve material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed. (shrink)

Writers such as Stalnaker and Dummett have argued that specific features of subjunctive conditional statements undermine the principle of bivalence. This, paper is concerned with rebutting such claims. 1. It is shown how subjective conditionals pose a prima facie threat to bivalence, and how this threat can be dissolved by a distinction between the results of negating a subjective conditional and of negating its consequent. To make this distinction is to side with Lewis against Stalnaker in a dispute about (...) class='Hi'>possible worlds semantics for such conditionals, and reasons are given for doing so. 2. These arguments are extended to answer Dummett''s claim that behaviourist and phenomenalist analyses in terms of subjunctive conditions violate bivalence. This answer is shown to be compatible with the principle that hypothetical statements are true only in virtue of categorical facts. (shrink)

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.

The standard semantics for counterfactuals ensures that any counterfactual with a true antecedent and true consequent is itself true. There have been many recent attempts to amend the standard semantics to avoid this result. I show that these proposals invalidate a number of further principles of the standard logic of counterfactuals. The case against the automatic truth of counterfactuals with true components does not extend to these further principles, however, so it is not clear that rejecting the latter should be (...) a consequence of rejecting the former. Instead I consider how one might defuse putative counterexamples to the truth of true-true counterfactuals. (shrink)

Stephen Barker argues that a possible worlds semantics for the counterfactual conditional of the sort proposed by Stalnaker and Lewis cannot accommodate certain examples in which determinism is true and a counterfactual Q > R is false, but where, for some P, the compound counterfactual P > (Q > R) is true. I argue that the completeness theorem for Lewis’s system VC of counterfactual logic shows that Stalnaker–Lewis semantics does accommodate Barker’s example, and I argue that its doing (...) so should be understood as showing that the example is an exception to Lewis’s Time’s Arrow requirements. (shrink)

Timothy Williamson has defended the claim that any philosophically satisfying conception of modality that encompasses possible worlds semantics (PWS) commits us to the Barcan Formula. His argument depends on the assumption that the domain of what there is (the domain of the actual world) has to be identified with the domain D(@), where @ is the index or possible world that in PWS represents , or stands for , the actual world. I work out an (...) interpretation of the relation between PWS and possible worlds terminology that makes it plausible to reject that assumption. (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.

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals.

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)

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)

Necessitists hold that, necessarily, everything is such that, necessarily, something is identical to it. Timothy Williamson has posed a number of challenges to contingentism, the negation of necessitism. One such challenge is an argument that necessitists can more wholeheartedly embrace possible worlds semantics than can contingentists. If this charge is correct, then necessitists, but not contingentists, can unproblematically exploit the technical successes of possible worlds semantics. I will argue, however, that the charge is incorrect: (...) contingentists can embrace possible worlds semantics as wholeheartedly as necessitists. Williamson offers a criterion for a class of models of quantified modal logic to be intended, and argues on its basis that contingentists must deny that there is an intended class of models. I argue that Williamson’s criterion is objectionable, supply an alternative that does not support Williamson’s argument, and adapt Williamson’s construction of an intended model structure to the needs of contingentist metaphysics. (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)

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)

Speakers differ from one another in philosophically problematic ways. Two speakers can vary not simply with respect to what they believe, but also in the ways they speak, the concepts they employ, and the standards they bring to bear. The fact of imperfect convergence gives rise to a wide range of philosophical puzzles, largely via a single generalization: If two speakers disagree with each other, then at least one of them says something false. The generalization is plausible, but mistaken. Counterexamples (...) are common, diverse, and thoroughly entrenched in ordinary talk, scientific discourse, and philosophical inquiry. I focus on a particular family of counterexamples, disagreements about the proper application of linguistic items, or what I call metalinguistic disagreements. Coming to grips with the widespread existence of metalinguistic disagreement requires a nuanced account of the ways in which information can be transmitted via an utterance, and it suggests a substantial rethinking of conventional philosophical wisdom about the nature of meaning. I begin with a philosophical case study in metalinguistic disagreement—disagreements about aesthetics. I go on to explore the more general linguistic properties of metalinguistic disagreements, focusing on their striking failure to license so-called metalinguistic negation. I conclude with a consideration of semantic methodology, arguing that, despite widely held assumptions to the contrary, metalinguistic disagreements can be adjudicated with reference to objective, non-linguistic features of the world. It is possible therefore to roundly reject a pernicious relativism about scientific discourse while simultaneously allowing for widespread, interpersonal variation in meaning. (shrink)

Possible world semantics considers not only what an expression actually refers to but also what it might have referred to in counterfactual circumstances. This has proven exceptionally useful both inside and outside philosophy. The way this is achieved is by using intensions. An intension of an expression is a function that assigns to each possible world the reference of the expression in that world. However, the specific intension of terms has been subject to frequent disputes. How is one (...) to determine the intension of a term? Carnap has shown how the intension of a term depends on the type of that term. Two-dimensional semantics has shown how intensions also depend on the actual state of affairs. I will show how, in addition, intensions are no less dependent on metaphysical criteria of identity. Furthermore, I will reveal how these three factors interact to fix the exact intension of a term. In other words, I propose an outline of the overall mechanism by which intensions are being fixed. (shrink)

The canonical version of possible worlds semantics for story prefixes is due to David Lewis. This paper reassesses Lewis's theory and draws attention to some novel problems for his account.

Possible world semantics has been gradually fine-grained over the years. First, simple extensional semantics was fine-grained by relativizing it to worlds considered as counterfactual, thus generating standard possible-world semantics, which was later further fine-grained by relativizing it to worlds considered as actual, thus generating two-dimensional semantics. However, worlds considered as actual were only considered with respect to the empirical facts obtaining in such worlds. This paper shows that no less of an important role is (...) played by another feature of actual worlds, namely, the criteria of identity that obtain in such worlds. (shrink)

This chapter discusses four packages, including Ludovician, Aristotelian, Fortibracchian, and Quietist. There are two quite coherent packages of answers to the some issues: a neo‐Humeist or Ludovician package, and a neo‐Aristotelian package. Ludovicians put little weight on common sense beliefs, especially when they are embedded in ethical and legal practices, and they do not rely heavily on the "manifest image of the world". Aristotelians rely more heavily on the semantic intuition about what could possibly be the truthmakers for familiar kinds (...) of claims, including those involving tense and modality. This chapter lists the Aristotelian package as including Meinongianism, ontological vagueness, and Tensism on the passage of time. Fortibracchians are very similar in methodology to Ludovicains. In practice, Fortibracchians give more weight to a kind of naive realism with respect to scientific theory than do Ludovicians. (shrink)

Saul Kripke did more than anyone else to bring possible worlds into the contemporary philosophical discourse, first with his more formal work on the model theory for modal logic in the 1960s, and then with his more philosophical lectures on reference and modality, delivered in January 1970, that used the possible worlds apparatus informally to clarify the relations between semantic issues about names and metaphysical issues about individuals and kinds. Possible worlds semantics have been (...) widely applied since then, both in philosophy and in other fields such as linguistic semantics and pragmatics, theoretical computer science, and game theory. Kripke’s work, along with that of David Lewis, stimulated an ongoing debate about the nature and metaphysical status of possible worlds. Kripke himself has had little to say about the issues raised in this debate, in print, beyond what he said in Naming and Necessity and in brief remarks in a preface to a later edition of the lectures, published in 1980. But there is a clear view of the nature of possible worlds, and of the status of an explanation of modality in terms of possible worlds, implicit in the lectures and the preface. -/- The central focus of the post–Naming and Necessity debate about possible worlds has been a contrast between David Lewis’s modal realism and various versions of actualism. On this general issue, it is clear enough where Kripke stands: His criticisms of what he describes as the “other countries” picture of possible worlds are an explicit rejection of Lewis’s realism about possible worlds. But the rejection of modal realism raises a range of further questions: What exactly are possible worlds (or possible states of the world, which Kripke suggests would be less misleading terminology)? What contribution do they make to the explanation of modal discourse, and of the distinctive facts that modal discourse is used to state? Does the slogan “necessity is truth in all possible worlds” provide, or point to, a reductive analysis of necessity? Are possible worlds, in some sense, prior to modal operators and modal auxiliaries? If not, in what sense are they explanatory? How are possible worlds, or counterfactual situations, specified? How do they contribute to our understanding of specific meta- physical questions about the relations between particular individuals and their qualitative characteristics, the kinds to which they belong, and the matter of which they are constituted? How are we to understand the possible existence of individuals that do not actually exist? What is the status of the domains of individuals in merely possible worlds? -/- My aim in this chapter is to spell out the views about some of these foundational questions that are expressed or at least implicit in Kripke’s lectures. In Section 2, I discuss the general contrast between modal realism and actualism and questions about the kind of explanation that possible worlds provide for modal discourse and modal facts. In Section 3, I look at Kripke’s views about how possible worlds are specified, in particular at the role of individuals in specifying possible worlds. In Section 4, I consider the problems about merely possible individuals. (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)

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)

Philosophers have long analyzed the truth-condition of counterfactual conditionals in terms of the possible-worlds semantics advanced by Lewis [13] and Stalnaker [23]. In this paper, I argue that, from the perspective of philosophical semantics, the causal modeling semantics proposed by Pearl [17] and others (e.g., Briggs [3]) is more plausible than the Lewis-Stalnaker possible-worlds semantics. I offer two reasons. First, the possible-worlds semantics has suffered from a specific type of counterexamples. While the causal modeling (...) semantics can handle such examples with ease, the only way for the possible-worlds semantics to do so seems to cost it its distinctive status as a philosophical semantics. Second, the causal modeling semantics, but not the possible-worlds semantics, has the resources enough for accounting for both forward-tracking and backtracking counterfactual conditionals. (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)

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)

Standard accounts of counterfactuals with metaphysically impossible antecedents take them to by trivially true. But recent work shows that nontrivial countermetaphysicals are frequently appealed to in scientific modeling and are indispensable for a number of metaphysical projects. I focus on three recent discussions of counterpossible counterfactuals, which apply counterpossibles in both scientific and metaphysical modeling. I show that a sufficiently developed modal counterpart theory can provide a semantics for a wide range of counterpossibles without any inconsistent possibilities or other forms (...) of impossible worlds. But such a view faces problems: in order for the metaphysical views I discuss to bear weight, there must be a significant difference between the metaphysical possibilities and impossibilities. I will show how the counterpart-theoretic view delineates the possible from impossible, while still making room for the impossible. (shrink)

What is our epistemic access to metaphysical modality? Timothy Williamson suggests that the epistemology of counterfactuals will provide the answer. This paper challenges Williamson's account and argues that certain elements of the epistemology of counterfactuals that he discusses, namely so called background knowledge and constitutive facts, are already saturated with modal content which his account fails to explain. Williamson's account will first be outlined and the role of background knowledge and constitutive facts analysed. Their key role (...) is to restrict our imagination to rule out irrelevant counterfactual suppositions. However, background knowledge turns out to be problematic in cases where we are dealing with metaphysically possible counterfactual suppositions that violate the actual laws of physics. As we will see, unless Williamson assumes that background knowledge corresponds with the actual, true laws of physics and that these laws are metaphysically necessary, it will be difficult to address this problem. Furthermore, Williamson's account fails to accommodate the distinction between conceivable yet metaphysically impossible scenarios, and conceivable and metaphysically possible scenarios. This is because background knowledge and constitutive facts are based strictly on our knowledge of the actual world. Williamson does attempt to address this concern with regard to metaphysical necessities – as they hold across all possible worlds – but we will see that even in this case the explanation is questionable. These problems, it will be suggested, cannot be addressed in a counterfactual account of the epistemology of modality. The paper finishes with an analysis of Williamson's possible rejoinders and some discussion about the prospects of an alternative account of modal epistemology. (shrink)

This guide accompanies the following articles: Sonia Roca‐Royes, ‘Essentialism vis‐à‐vis Possibilia, Modal Logic, and Necessitism.’Philosophy Compass 6/1 (2011): 54–64. doi: 10.1111/j.1747‐9991.2010.00363.x. Sonia Roca‐Royes, ‘Essential Properties and Individual Essences.’Philosophy Compass 6/1 (2011): 65–77. doi: 10.1111/j.1747‐9991.2010.00364.x. Author’s Introduction Intuitively, George Clooney could lose a finger and he would still be him. Also intuitively, he could not lose his humanity without ceasing to be altogether. So while he could have one less finger, he could not be other than human. These intuitions suggest that (...) there are two kinds of properties: on the one hand, there are essential properties and, on the other, there are accidental properties. Essentialism is the view that captures those intuitions and claims that some of an object’s properties are essential and some are accidental. Essential properties are often appealed to in metaphysical arguments. Consider the famous Goliath–Lumpl example. Goliath is a clay‐statue, and Lumpl is the piece of clay from which Goliath is made. Are Goliath and Lumpl the same entity, or are they distinct, despite coinciding in the same spatial region (at least for a period of time)? An argument in favour of their distinctness appeals to essential properties. Let s be Goliath’s shape. Lumpl’s current shape is therefore also s. It seems that Lumpl could lose its current shape and still exist. Yet, if Goliath – the statue – were melted, for instance, it would cease to exist. Behind this reasoning is the belief that having shape s is essential to Goliath but not to Lumpl. Goliath and Lumpl can therefore be distinguished by their essential properties. Consequently, and by Leibniz’s Indiscernibility of Identicals– according to which identicals cannot be distinguished – Goliath and Lumpl are distinct objects. The essentialist intuition appealed to in this argument is that shapes are essential to statues but not to pieces of clay. Of course, this particular argument – like any other – can be resisted. It is all the same a good illustration of how essentialism is put to work in metaphysics. A good understanding of the broad phenomenon of essentialism is therefore an unavoidable task, since the credit of a lot of metaphysical arguments partially depends on it. Although the topic has been studied for millenniums, the two papers that this guide accompanies are focused on contemporary issues in essentialism, and so will do this guide too. Author Recommends Fine, Kit. ‘Essence and Modality.’Philosophical Perspectives 8 (1994): 1–16. One of the most cited and influential papers against the modal account of the notion of essence and in favour of what has subsequently been referred to in the literature as ‘the Finean account of the notion of essence’. Forbes, Graeme. The Metaphysics of Modality. Oxford: Clarendon Press, 1985. A foundational work in modality and essentialism. The first two chapters provide a valuable introduction to propositional and first order modal logic. Chapters 5–8 constitute a comprehensive essentialist theory and contain some of the most cited arguments for individual essences. Kripke, Saul. Naming and Necessity, Cambridge, MA: Harvard UP, 1972/1980. Another foundational work. With this book – which is, among other things, a defence of a Direct Theory of Reference – Kripke rescues, after Quine’s powerful attacks against it, and using the semantic rigidity of proper names, (Aristotelian) essentialism. Mackie, Penelope. How Things Might Have Been: Individuals, Kinds and Essential Properties. Oxford: Clarendon Press, 2006. An extremely valuable recent contribution to the field. Here, Mackie defends that, although essentialism is a real phenomenon, there are much fewer essential properties than is standardly believed, and labels this view ‘Minimalist Essentialism’. Beyond the intrinsic interest of the defence of Minimalist Essentialism, the book is also highly recommended for its clear reconstructions – and discussions – of some of the most influential essentialist arguments. In addition, the book’s bibliography is very comprehensive and updated, and it might be a useful resource for students. Plantinga, Alvin. The Nature of Necessity. Oxford: OUP, 1974. Yet another foundational work. Here, Plantinga offers his essentialist theory which, like Forbes’, also incorporates individual essences although of a very different sort from Forbes’. Plantinga believes in purely non‐qualitative individual essences, whereas Forbes’ aims at purely qualitative ones. The book is also excellent to provide a solid background to those unfamiliar with the topic. Roca‐Royes. ‘Essentialism vis‐à‐vis Possibilia, Modal Logic and Necessitism.’Philosophy Compass, 6/1 (2011): 54–64, doi: 10.1111/j.1747‐9991.2010.00363.x. This is one of the two papers this guide accompanies. It contains a comparative examination of two opposed responses to the problem of possibilia. One solution crucially appeals to individual essences and another – compatible with them, but not dependent on them – makes existence a necessary‐whenever‐possible property. Salmon, Nathan. Reference and Essence. Princeton: Princeton UP, 1981. Against what Kripke’s Naming and Necessity might have induced us to believe, Salmon’s Reference and Essence argues that essentialism cannot be derived from the Direct Theory of Reference. Our commitments to essentialism should therefore come from somewhere else. It also contains one of the most cited and influential arguments against the transitivity of the accessibility relation between worlds, which relies on flexible essential properties. Online Materials The Stanford Encyclopedia of Philosophy publishes extremely valuable entries on a vast variety of topics which are conveniently updated and revised. On essentialism, the following are to be highlighted: Teresa Robertson, ‘Essential vs. Accidental Properties’: Takashi Yagisawa, ‘Possible Objects’: Penelope Mackie, ‘Transworld Identity’: PhilPapers is an interactive directory of online philosophical publications to which one can subscribe, and which allows authors to submit their latest work. One might find it useful to check this on a regular basis, since contents are constantly updated. The following link is to the site’s resources on essentialism:. Sample Syllabus Because the phenomenon of essentialism is very broad, one can design an entire course on it, thereby having enough time to see some of the issues in considerable depth. The sample syllabus suggested here is of one such course, focusing exclusively on contemporary issues in essentialism. Less deeply, the topic of essentialism can also be introduced in a general course on metaphysics or on modality. To this effect, focusing on some of the topics suggested in weeks 1–6 below would perhaps be more appropriate than focusing on the more complex issues suggested for weeks 7–10. Week 1. Introduction to Essentialism. Two Notions of Essential Property: The Modal Account and the Finean Account Fine, Kit. ‘Essence and Modality.’Philosophical Perspectives 8 (1994): 1–16. Robertson, Teresa. ‘Essential vs. Accidental Properties.’Stanford Encyclopedia of Philosphy (Fall 2008 Edition). Ed. Edward N. Zalta. URL:. Roca‐Royes, Sonia. ‘Essential Properties and Individual Essences.’Philosophy Compass, 6/1 (2011): 65–77. Sections 1–2. Week 2. Essentialist Principles, I: Three Arguments for the Essentiality of Origin Kripke, Saul. Naming and Necessity. Cambridge, MA: Harvard UP, 1972/1980. Lecture III. Mackie, Penelope. ‘Identity, Time and Necessity.’Proceedings for the Aristotelian Society 98 (1998): 59–78. Rohbraugh, Guy and deRosset, Louis. ‘A New Route to the Necessity of Origin.’Mind 133 (2004): 705–25. Week 3. Essentialist Principles, II: Essentiality of Kind Brody, Baruch. ‘Natural Kinds and Real Essences.’Journal of Philosophy 64 (1967): 431–46. Mackie, Penelope. How Things Might Have Been: Individuals, Kinds and Essential Properties. Oxford: Clarendon Press, 2006. Chapters 7 and 8. Wiggins, David. Sameness and Substance Renewed. Cambridge: Cambridge UP, 2001. Chapter 3. Week 4. Essentialist Principles, III: Natural Kind Essentialism Kripke, Saul. ‘Identity and Necessity.’Identity and Individuation, Ed. M. K. Munitz. New York: New York University Press, 1971. 135–64. Kripke, Saul. Naming and Necessity. Cambridge, MA: Harvard UP, 1972/1980. Lecture III. Putnam, Hilary. ‘The Meaning of “Meaning”.’Minnesota Studies in the Philosophy of Science 7 (1975): 215–71. Week 5. Sufficient‐for‐Existence Properties (and Cross‐World Identification Principles) Chisholm, Roderick. ‘Identity through Possible Worlds: Some Questions.’Noûs 1.1 (1967): 1–8. Mackie, Penelope. How Things Might Have Been: Individuals, Kinds and Essential Properties. Oxford: Clarendon Press, 2006. Chapter 3. Salmon, Nathan. Reference and Essence. Princeton: Princeton UP, 1981. Chapter 7. Week 6. Individual Essences Mackie, Penelope. ‘Transworld Identity.’The Stanford Encyclopedia of Philosophy (Fall 2008 Edition). Ed. Edward N. Zalta. URL:. Section 4. Roca‐Royes, Sonia. ‘Essential Properties and Individual Essences.’Philosophy Compass 6/1 (2011): 65–77. Sections 3–4. Week 7. Flexible Essential Properties and S4 Roca‐Royes, Sonia. ‘Essentialism vis‐à‐vis Possibilia, Modal Logic, and Necessitism.’Philosophy Compass 6/1 (2011): 54–64. Section 3. Salmon, Nathan. Reference and Essence. Princeton: Princeton UP, 1981. Appendix 1. Week 8. Individual Essences and Possibilia Peacocke, Christopher. ‘Principles for Possibilia.’Noûs 36.3 (2002): 486–508. Roca‐Royes, Sonia. ‘Essentialism vis‐à‐vis Possibilia, Modal Logic, and Necessitism.’Philosophy Compass 6/1 (2011): 54–64. Section 2. Week 9. Necessitism and Essentialism: A Third Notion of Essential Property Linsky, Bernard and Zalta, Edward. ‘In Defense of the Contingently Nonconcrete.’Philosophical Studies 84 (1996): 283–94. Roca‐Royes, Sonia. ‘Essentialism vis‐à‐vis Possibilia, Modal Logic, and Necessitism.’Philosophy Compass 6/1 (2011): 54–64. Section 5. Williamson, Timothy. ‘Bare Possibilia.’Erkenntnis 48 (1998): 257–73. Week 10. Essentialism and Modal Logic: The Barcan Formula Menzel, Christopher. ‘Actualism.’The Stanford Encyclopedia of Philosophy (Summer 2010 Edition). Ed. Edward N. Zalta. URL:. Section 2. Roca‐Royes, Sonia. ‘Essentialism vis‐à‐vis Possibilia, Modal Logic, and Necessitism.’Philosophy Compass 6/1 (2011): 54–64. Section 4. Focus Questions • There is a debate as to whether essential properties– as well as individual essences and sufficient‐for‐existence properties– should be specified in purely qualitative terms or whether, by contrast, non‐purely qualitative – or even purely non‐qualitative – specifications are allowed. What are the main arguments against the availability of purely qualitative specifications? • Flexible essential properties seem to be more plausible than non‐flexible ones. Yet, together with sufficient‐for‐existence properties, they imply flexible individual essences. How plausible are these? Should we revise our intuitions supporting flexible essential properties? • What are, ultimately, the ontological differences between a necessitist approach to possibilia and an individual‐essences‐based approach? • According to necessitism, essential properties do not impose necessary conditions for an object’s existence. Can the necessitist, nonetheless, capture this role of essential properties by saying that, when it comes to possibly concrete entities, essential properties provide necessary conditions for an object’s concreteness? Can they, on a similar vein, also offer sufficient‐for‐concreteness properties as a surrogate for the (non‐necessitist’s) sufficient‐for‐existence properties? • Even after the enormous amount of literature that essentialism has generated, we are far from reaching a general agreement as to which properties are essential and which are accidental. Should this be a reason to reflect, critically, on the methodology that is being used in the arguments for or against essential properties? Is reliance on intuitions inescapable? (shrink)

Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This chapter sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher costs than its proponents typically recognize.

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.

This book argues for the importance and commonness of reasonings concerning impossibilities. Its aim is twofold – descriptive and constructive. Since hypothetical reasoning about impossibilities calls for explanation, the book provides a comprehensive guide through popular semantic theories of conditionals. Each is examined from the perspective of the question of impossibilities and the logic and metaphysics surrounding them. This provides the ground for a further aim. In the final chapter, I endeavor to combine the best features of the existing theories (...) and explore the possibility of a novel hybrid account. (shrink)

_Identity and Discrimination_, originally published in 1990 and the first book by respected philosopher Timothy Williamson, is now reissued and updated with the inclusion of significant new material. Williamson here proposes an original and rigorous theory linking identity, a relation central to metaphysics, and indiscriminability, a relation central to epistemology.__ Updated and reissued edition of Williamson’s first publication, with the inclusion of significant new material Argues for an original cognitive account of the relation between identity and (...) discrimination that has been influential in the philosophy of perception Pioneers the use of epistemic logic to solve puzzles about indiscriminability Develops the application of techniques from mathematical logic to understand issues about identity over time and across possible worlds. (shrink)

Metaphysical modalities are definable from counterfactual conditionals, and the epistemology of the former is a special case of the epistemology of the latter. In particular, the role of conceivability and inconceivability in assessing claims of possibility and impossibility can be explained as a special case of the pervasive role of the imagination in assessing counterfactual conditionals, an account of which is sketched. Thus scepticism about metaphysical modality entails a more far-reaching scepticism about counterfactuals. The account is used to question the (...) significance of the distinction between a priori and a posteriori knowledge. (shrink)

A striking feature of the traditional armchair method of philosophy is the use of imaginary examples: for instance, of Gettier cases as counterexamples to the justified true belief analysis of knowledge. The use of such examples is often thought to involve some sort of a priori rational intuition, which crude rationalists regard as a virtue and crude empiricists as a vice. It is argued here that, on the contrary, what is involved is simply an application of our general cognitive capacity (...) to handle counterfactual conditionals, which is not exclusively a priori and is not usefully conceived as a form of rational intuition. It is explained how questions of metaphysical possibility and necessity are equivalent to questions about counterfactuals, and the epistemology of the former (in particular, the role of conceiving or imagining) is a special case of the epistemology of the latter. A non-imaginary Gettier case is presented in order to show how little difference it makes. (shrink)

Rational agents face choices, even when taking seriously the possibility of determinism. Rational agents also follow the advice of Causal Decision Theory (CDT). Although many take these claims to be well-motivated, there is growing pressure to reject one of them, as CDT seems to go badly wrong in some deterministic cases. We argue that deterministic cases do not undermine a counterfactual model of rational deliberation, which is characteristic of CDT. Rather, they force us to distinguish between counterfactuals that are relevant (...) and ones that are irrelevant for the purposes of deliberation. We incorporate this distinction into decision theory to develop ‘Selective Causal Decision Theory’, which delivers the correct recommendations in deterministic cases while respecting the key motivations behind CDT. (shrink)

The numerous difficulties facing the traditional Humean regularity approach to the problem of causation have been discussed in the literature at great length. In view of the current interest in possible worlds semantics, it is not surprising that the only serious alternative treatment of causation presently available, the counterfactual approach, has been explored recently as a means of circumventing the apparently unresolvable difficulties facing regularity causal theories. It is the purpose of this paper to suggest that such a (...) strategy holds little promise. Specifically, I will argue that, in addition to giving rise to problems directly analogous to those facing regularity accounts, the counterfactual approach fails in principle to reflect important properties of causal relations as we understand them intuitively. David Lewis's possible worlds account, the most comprehensive counterfactual theory to date, is further criticized for implicit problems with natural lawhood even more serious than those typically raised for regularity accounts, for additional inadequacies in its analysis of causal relations, and for its failure to satisfy basic empiricist epistemological standards. (shrink)

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an (...) epistemicist semantics from that model theory, one of which I will find to be more plausible than the other. (shrink)

Counterfactuals abound in science, especially when one deals with models. Some models, namely highly idealized models, have assumptions that are metaphysically impossible. This means that in science one has often to deal with counterpossibles. According to the standard semantics for counterfactuals, all counterpossibles are vacuously true. But scientific practice shows that counterpossibles are not always regarded as vacuously true by scientists. To do justice of the use of counterpossibles in science, some authors think that we should adopt a semantics that (...) allows for impossible worlds. It seems difficult to reconcile the role played by highly idealized models in science with scientific realism. Nevertheless, some authors think that it is possible to provide a realist account of highly idealized models. In this view, scientific realism should not be interpreted as the claim that models aim to provide accurate representations of models’ targets, rather it should be interpreted as the claim that models aim to provide true modal information about models’ targets. This variant of scientific realism seems to imply a commitment to some form of modal realism. I develop an objection to that variant of scientific realism by elaborating on some arguments originally developed to show that there are unknowable facts. (shrink)