This article surveys recent developments in the epistemology of modality.

Recently, von Fintel (2001) and Gillies (2007) have argued that certain sequences of counterfactuals, namely reverse Sobel sequences, should motivate us to abandon standard truth conditional theories of counterfactuals for dynamic semantic theories. I argue that we can give a pragmatic account of our judgments about counterfactuals without giving up the standard semantics. In particular, I introduce a pragmatic principle governing assertability, and I use this principle to explain a variety of subtle data concerning reverse Sobel sequences.

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

I argue that the suppositional view of conditionals, which is quite popular for indicative conditionals, extends also to subjunctive or counterfactual conditionals. According to this view, conditional judgements should not be construed as factual, categorical judgements, but as judgements about the consequent under the supposition of the antecedent. The strongest evidence for the view comes from focusing on the fact that conditional judgements are often uncertain; and conditional uncertainty, which is a well-understood notion, does not function like uncertainty about matters (...) of fact. I argue that the evidence for this view is as strong for subjunctives as it is for indicatives. (shrink)

Grounding necessitarianism (GN) is the view that full grounds necessitate what they ground. Although GN has been rather popular among philosophers, it faces important counterexamples: For instance, A=[Socrates died] fully grounds C=[Xanthippe became a widow]. However, A fails to necessitate C: A could have obtained together with B=[Socrates and Xanthippe were never married], without C obtaining. In many cases, the debate essentially reduces to whether A indeed fully grounds C – as the contingentist claims – or if instead C is (...) fully grounded in A+, namely A plus some supplementary fact S (e.g. [Xanthippe was married to Socrates]) – as the necessitarian claims. Both sides typically agree that A+ necessitates C, while A does not; they disagree on whether A or A+ fully grounds C. This paper offers a novel defence of the claim that, in these typical cases, unlike A+, A fails to fully ground C – thereby bringing further support to GN. First and foremost, unlike A+, A fails to fully ground C because it fails to contain just what is relevant to do so, in two distinct senses – explanatory and generative relevance. Second, going for A, rather than A+, as a full ground undermines not just grounding necessitarianism, but modally weaker views which even contingentists may want to preserve. (shrink)

This paper investigates the implicative conditional, a connective intended to describe the logical behavior of an empirically defined class of natural language conditionals, also namedimplicative conditionals, which excludes concessive and some other conditionals. The implicative conditional strengthens the strict conditional with the possibility of the antecedent and of the contradictory of the consequent.$${p\Rightarrow q}$$p⇒qis thus defined as$${\lnot } \Diamond {(p \wedge \lnot q) \wedge } \Diamond {p \wedge } \Diamond {\lnot q}$$¬◊(p∧¬q)∧◊p∧◊¬q. We explore the logical properties of this conditional in (...) a reflexive normal Kripke semantics, provide an axiomatic system and prove it to be sound and complete for our semantics. The implicative conditional validates transitivity and contraposition, which we take to be integral parts of reasoning and communication. But it only validates restricted versions of strengthening the antecedent, right weakening, simplification, and rational monotonicity. Apparent counterexamples to some of these properties are explained as due to contextual factors. Finally, the implicative conditional avoids the paradoxes of material and strict implication, and validates some connexive principles such as Aristotle’s theses and weak Boethius’ thesis, as well as some highly entrenched principles of conditionals, such as conjunction of consequents, disjunction of antecedents, modus ponens, cautious monotonicity and cut. (shrink)

In this paper I urge friends of truth-value gaps and truth-value gluts – proponents of paracomplete and paraconsistent logics – to consider theories not merely as sets of sentences, but as pairs of sets of sentences, or what I call ‘bitheories,’ which keep track not only of what holds according to the theory, but also what fails to hold according to the theory. I explain the connection between bitheories, sequents, and the speech acts of assertion and denial. I illustrate the (...) usefulness of bitheories by showing how they make available a technique for characterising different theories while abstracting away from logical vocabulary such as connectives or quanti- fiers, thereby making theoretical commitments independent of the choice of this or that particular non-classical logic. (shrink)

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)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical Syllogism. The improved proof (...) relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...) connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

This paper is intended to show that, at least in a considerably wide class of cases, indicative conditionals are adequately formalized as strict conditionals. The first part of the paper outlines three arguments that support the strict conditional view, that is, three reasons for thinking that an indicative conditional is true just in case it is impossible that its antecedent is true and its consequent is false. The second part of the paper develops the strict conditional view and defends it (...) from some foreseeable objections. (shrink)

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...) to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (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)

Why believe Hume's Dictum, according to which there are, roughly speaking, no necessary connections between wholly distinct entities? Schaffer suggests that HD, at least as applied to causal or nomological connections, is motivated as required by the best account of of counterfactuals---namely, a similarity-based possible worlds account, where the operative notion of similarity requires 'miracles'---more specifically, worlds where entities of the same type that actually exist enter into different laws. The main cited motivations for such an account of similarity are (...) first, that some salient contexts presuppose CF asymmetry, and second, that accounts of CFs failing to presuppose CF asymmetry are epistemologically problematic, such that under conditions of determinism, the variations in initial micro-conditions needed to implement a given counterfactual antecedent would result in so many changes to macro-states that evaluation of CFs would be rendered practically impossible. Against the first reason, I argue that no non-artificial contexts presuppose CF asymmetry; against the second, I observe that such micro-variation is compatible, in principle, with significant similarity as regards macroscopic states of affairs---enough, in particular, to allow CFs to be appropriately evaluated. (shrink)

Max Cresswell and Hilary Putnam seem to hold the view, often shared by classical logicians, that paraconsistent logic has not been made sense of, despite its well-developed mathematics. In this paper, I examine the nature of logic in order to understand what it means to make sense of logic. I then show that, just as one can make sense of non-normal modal logics (as Cresswell demonstrates), we can make `sense' of paraconsistent logic. Finally, I turn the tables on classical logicians (...) and ask what sense can be made of explosive reasoning. While I acknowledge a bias on this issue, it is not clear that even classical logicians can answer this question. (shrink)

Stephen Mumford and Rani Lill Anjum have recently attacked causal necessitarianism – the doctrine that causes necessitate their effects – on the grounds that causation does not survive what they describe as the test of antecedent strengthening. This article shows that there are credible conditional logics which do not sanction this test, thereby providing an escape route for proponents of causal necessitarianism from Mumford and Anjum's argument.

This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed to (...) be merely (p⊃q) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q. (shrink)

We present an analysis of counterfactuals in terms of stories and combine it with an account similar to Walton’s account of truth in fiction to yield truth conditions for counterfactuals. We discuss unusual features of this account, and compare it to other main approaches. In particular, we argue that our analysis succeeds in accounting for counterpossibles and counterfactuals with true antecedents while the other two main approaches fail, and we give reasons for thinking that it is important to have an (...) adequate account of these two areas. (shrink)

This paper defends the thesis that counterfactuals are strict conditionals. Its purpose is to show that there is a coherent view according to which counterfactuals are strict conditionals whose antecedent is stated elliptically. Section 1 introduces the view. Section 2 outlines a response to the main argument against the thesis that counterfactuals are strict conditionals. Section 3 compares the view with a proposal due to Aqvist, which may be regarded as its direct predecessor. Sections 4 and 5 explain how the (...) view di ers from the theories of counterfactuals advocated by Stalnaker and Lewis, and from some contextualist strict conditional accounts of counterfactuals that have emerged recently. Finally, section 6 addresses the thorny issue of disjunctive antecedents. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably strict theorist faces a question: why do (...) we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

We here attempt to address certain criticisms of the philosophical import of the so-called Brazilian approach to paraconsistency by providing some epistemic elucidations of the whole enterprise of the logics of formal inconsistency. In the course of this discussion, we substantiate the view that difficulties in reasoning under contradictions in both the Buddhist and the Aristotelian traditions can be accommodated within the precepts of the Brazilian school of paraconsistency.

A widely accepted claim about counterfactuals is that they differ from strict conditionals, that is, there is no adequate representation of them as sentences of the form   . To justify this claim, Stalnaker and Lewis have argued that some fallacious inferences would turn out valid if counterfactuals were so represented. However, their argument has a flaw, as it rests on a questionable assumption about the relation between surface grammar and logical form. Without that assumption, no consequence of the (...) alleged kind is obtained, hence the claim may be rejected. (shrink)

Jonathan Lowe has argued that a particular variation on C.I. Lewis' notion of strict implication avoids the paradoxes of strict implication. We show that Lowe's notion of implication does not achieve this aim, and offer a general argument to demonstrate that no other variation on Lewis' notion of constantly strict implication describes the logical behaviour of natural-language conditionals in a satisfactory way.

I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...) collapsing filter on the standard model) match with many intuitions underlying Wittgensteins philosophy of mathematics, such as its strict finitism and the insistence on the decidability of any meaningful mathematical question. (shrink)

In chapter 8 of Miller 2003, I argued against the idea that Jackson and Pettit's notion of program explanation might help Sturgeon's non-reductive naturalist version of moral realism respond to the explanatory challenge posed by Harman. In a recent paper in the AJP[Nelson 2006, Mark Nelson has attempted to defend the idea that program explanation might prove useful to Sturgeon in replying to Harman. In this note, I suggest that Nelson's argument fails.

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that it is equivalent (...) to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic. (shrink)

(No abstract is available for this citation).

Both Lowe and Tsai have presented their own versions of the theory that both indicative and subjunctive conditionals are strict conditionals. We critically discuss both versions and we find each version wanting.

Substructural pluralism about the meaning of logical connectives is best understood as the view that natural language connectives have all (and only) the properties conferred by classical logic, but that particular occurrences of these connectives cannot simultaneously exhibit all these properties. This is just a more sophisticated way of saying that while natural language connectives are ambiguous, they are not so in the way classical logic intends them to be. Since this view is usually framed as a means to resolve (...) paradoxes, little attention is paid to the logical properties of the ambiguous connectives themselves. The present paper sets out to fill this gap. First, I argue that substructural logicians should care about these connectives; next, I describe a consequence relation between a set of ambiguous premises and an ambiguous conclusion, and review the logical properties of ambiguous connectives; and finally, I highlight how ambiguous connectives can explain our intuitions about logical rivalry. (shrink)

This paper argues that the technical notion of conditional probability, as given by the ratio analysis, is unsuitable for dealing with our pretheoretical and intuitive understanding of both conditionality and probability. This is an ontological account of conditionals that include an irreducible dispositional connection between the antecedent and consequent conditions and where the conditional has to be treated as an indivisible whole rather than compositional. The relevant type of conditionality is found in some well-defined group of conditional statements. As an (...) alternative, therefore, we briefly offer grounds for what we would call an ontological reading: for both conditionality and conditional probability in general. It is not offered as a fully developed theory of conditionality but can be used, we claim, to explain why calculations according to the RATIO scheme does not coincide with our intuitive notion of conditional probability. What it shows us is that for an understanding of the whole range of conditionals we will need what John Heil (2003), in response to Quine (1953), calls an ontological point of view. (shrink)

This paper examines a neglected puzzle about conditionals: namely, the fact that each of a pair of conditionals with incompatible consequents, [A > C] and [B > C*], may be properly affirmable in circumstances when one does not believe, and is not entitled to infer, the denial of the conjunction of the antecedents, i.e. ~(A & B). The puzzle is why this should be so, since the conditionals entail the conjunction on the popular accounts of conditionals. I present a pragmatic (...) solution which distinguishes between two levels of affirmability. (shrink)

Riggs v. Palmerhas become famous since Dworkin used it to show that legal positivism is defective. The debate over the merits of Dworkin's claims is still very lively. Yet not enough attention has been paid to the fact that the content of the statute at issue inRiggswas given by thecounterfactual intentionof the legislature. According to arguments from legislative intent, a judicial decision is justified if it is based on the lawmaker's intention. But can legislative intentions be determined counterfactually? More generally, (...) what are the discursive commitments undertaken by a lawyer or a judge, in an exchange of legal reasons, when using this interpretive methodology? This paper addresses these issues considering, in particular, David Lewis's “resemblance” condition and “relevant similarity” between possible worlds in the evaluation of counterfactual statements. The analysis sheds some new light on the debate on theoretical disagreements and shows that Dworkin's conception of law as an argumentative practice is not necessarily at odds with legal positivism. It rather allows us to look at it under a better light. (shrink)

The gist of modal epistemology is expressed in the idea that you fail to know if you do believe truly but it is seriously possible for you to believe falsely. According to subjunctivism, this idea is captured by certain subjunctive conditionals. One formulation invokes a safety condition—“If S had believed P, then P would have been the case,” while the other invokes a sensitivity condition—“If P had been false, S would not have believed that P.” According to simple subjunctivism, such (...) conditionals do not contrapose and Sosa derives important epistemological consequences which favor safety from this difference. However, simple subjunctivism is inadequate. I return to Goodman and his analysis of factuals and propose modal stability, which is restricted sensitivity or enhanced safety as a proper epistemic condition for the non-accidental connection between the basis for the belief and the relevant facts of the matter. The idea of modal stability combines robustness (benefi ts of safety) with responsiveness to facts (benefi ts of sensitivity) and recovers the original motivation for the relevant alternatives theory—when testing for claims of knowledge that p we ask what might be the case if not-p, but we ignore irrelevant possibilities. Epistemic modal conditions should be expressed in terms of conditionals of connection which contrapose within the limits of relevance. (shrink)

E. J. Lowe argues that the mental event token cannot be identical to the complex neural event token for they have different counterfactual properties. If the mental event had not occurred, the behavior would not have ensued, while if the neural event had not occurred, the behavior would have ensued albeit slightly differently. Lowe's argument for the neural counterfactual relies on standard possible world semantics, whose evaluation of such counterfactuals is problematic. His argument for the mental counterfactual relies on a (...) premise that is plausibly false. My arguments support other counterfactuals, which are consistent with identity theories. (shrink)

Jan Heylen and Leon Horsten object to my proposed analysis of ordinary-language conditionals by appealing to certain putative counter-examples. In this reply, I explain how, by ignoring my reading of the indicative/subjunctive distinction, their objection misses its target. I also criticize their underlying methodology.