In this paper, I argue that inductive inferences can be reinterpreted as deductive through a metaphysical lens of modal necessity. Instead of viewing deduction as a limit case of induction where the conclusion is certain rather than probable, we can rethinking inductive inferences as a particular type of deductive inferences where the conclusion is necessitated by premises in specific modal ranges.

In this paper, we put forth an analysis of sensitivity which aims to discern individual from merely statistical evidence. We argue that sensitivity is not to be understood as a factive concept, but as a purely epistemic one. Our resulting analysis of epistemic sensitivity gives rise to an account of legal proof on which a defendant is only found liable based on epistemically sensitive evidence.

In this paper, I raise a novel objection to David Lewis’s Humean account of laws. The objection is that non-universal laws are metaphysically possible, but Lewis’s account cannot accommodate them. I then propose and defend an extension of Lewis’s view that gives us an account of Humean non-universal laws.

This paper addresses the question of what constitutes an apt interpreted model for the purpose of analyzing causation. I first collect universally adopted aptness principles into a basic account, flagging open questions and choice points along the way. I then explore various additional aptness principles that have been proposed in the literature but have not been widely adopted, the motivations behind their proposals, and the concerns with each that stand in the way of universal adoption. I conclude that the remaining (...) work of articulating aptness for a SEM analysis of causation is tied up with issues to do with modality, ontology, and mereology. Continuing this work is therefore likely to shed light on the relationship between these areas and causation more generally. (shrink)

This paper defends a theory of fictional truth. According to this theory, there is a fact of the matter concerning the number of hairs on Sherlock Holmes' head, and likewise for any other meaningful question one could ask about what's true in a work of fiction. We argue that a theory of this form is needed to account for the patterns in our judgments about attitude reports that embed fictional claims. We contrast our view with one of the dominant approaches (...) to fictional truth, which originates with David Lewis. Along the way we explore the relationship between fiction, counterfactuals, and vagueness. (shrink)

In this paper, I argue that David Lewis’s possible world semantics for counterfactual discourse and for fictional discourse are apparently inconsistent and in need of revision. The problem emerges for Lewis’s account once one considers how to evaluate ambifictional counterfactuals. Since this is likely not a concept familiar to most, and since it does not appear that the problem has been previously recognized in the critical literature, I will begin by rehearsing Lewis’s possible worlds semantics for counterfactuals and fiction. Then (...) I will explicate the distinction between intrafictional, extrafictional, interfictional, and ambifictional propositions. Next, I will state what an ambifictional counterfactual proposition is, and explain why this kind of discourse confounds Lewis’s system. I will conclude, finally, with a brief discussion of how the Lewisian would be best advised to resolve the paradox. (shrink)

Patrick Todd's The Open Future defends the view that all future contingent statements, like ‘It will rain tomorrow’, are false.1 Not only is ‘It will rain tomor.

After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In this contribution, we take (...) Linear Temporal Logic (LTL) as case study for this defeasible aspect. LTL has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of LTL, called defeasible linear temporal logic (LTL ~ ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with LTL. We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of LTL ~ sentences. Based on Sistla and Clarke's work on the complexity of the classical LTL language, we show the bounded-model property of two fragments of LTL ~ language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments. (shrink)

Counterfactuals have become an important area of interdisciplinary interest, especially in logic, philosophy of language, epistemology, metaphysics, psychology, decision theory, and even artificial intelligence. In this study, we propose a new form of analysis for counterfactuals: analysis by algorithmic complexity. Inspired by Lewis-Stalnaker's Possible Worlds Semantics, the proposed method allows for a new interpretation of the debate between David Lewis and Robert Stalnaker regarding the Limit and Singularity assumptions. Besides other results, we offer a new way to answer the problems (...) raised by Goodman and Quine regarding vagueness, context-dependence, and the non- monotonicity of counterfactuals. Engaging in a dialogue with literature, this study will seek to bring new insights and tools to this debate. We hope our method of analysis can make counterfactuals more understandable in an intuitively plausible way, and a philosophically justifiable manner, aligned with the way we usually think about counterfactual propositions and our imaginative reasoning. (shrink)

According to methodological anti-exceptionalism, logic follows a scientific methodology. There has been some discussion about which methodology logic has. Authors such as Priest, Hjortland and Williamson have argued that logic can be characterized by an abductive methodology. We choose the logical theory that behaves better under a set of epistemic criteria. In this paper, I analyze some important discussions in the philosophy of logic, and I show that they presuppose different methodologies, involving different notions of evidence and different epistemic values. (...) I argue that, rather than having a specific methodology such as abductivism, logic can be characterized by methodological pluralism. This position can also be seen as the application of scientific pluralism to the realm of logic. (shrink)

According to an influential recent view, S is propositionally justified in believing p iff S is in no position to know that S is in no position to know p. I argue that this view faces compelling counterexamples.

I argue that there is nothing about the structure of inference to the best explanation (IBE) that prevents it from establishing a contradiction in general, though there are some potential limitations on when it can be used for this purpose. Studying the relationship between IBE and contradictions is worthwhile for three reasons. First, it enhances our understanding of IBE. We see that, in many cases, IBE does not require explanations to be consistent, though there are some cases where consistency may (...) be required. Second, the argument has implications for the debate over scientific realism. Many scientific theories appear to be inconsistent. The best argument for scientific realism, however, appeals to IBE. My argument thus shows that a certain kind of realist faces a threat from inconsistent theories. Third, the argument is important for dialetheism. Dialetheists maintain that some contradictions are true. Many of the arguments in favour of dialetheism appeal to explanatory considerations. What I say here provides support for defending dialethism using an IBE-based methodology. (shrink)

Aristotle is essentially human; that is, for all possible worlds metaphysically consistent with our own, if Aristotle exists, then he is human. This is a claim about the essential property of an object. The claim that objects have essential properties has been hotly disputed, but for present purposes, we can bracket that issue. In this essay, we are interested, rather, in the question of whether properties themselves have essential properties (or features) for their existence. We call those who suppose they (...) do “property essentialists”; those who do not, “property anti-essentialists,” or “quidditists.” We offer two complementary arguments. Our total argument is under-girded by two assumptions: transworld identity theory and “received view” counterfactual semantics, a la David Lewis. We then argue that, if one presumes that these are true, then one risks running headlong into paradox if one also accepts property anti-essentialism. That's the first argument. By contrast, if one accepts these same assumptions in conjunction with property essentialism, then the paradox is avoided. This is the second argument. We take it that our arguments work to show that, between property essentialism and quidditism, the property essentialist is on better footing. Plausibly, properties themselves do have essential properties for their existence. (shrink)

It has been argued that an advantage of the safety account over the sensitivity account is that the safety account preserves epistemic closure, while the sensitivity account implies epistemic closure failure. However, the argument fails to take the method-relativity of the modal conditions on knowledge, viz., sensitivity and safety, into account. In this paper, I argue that the sensitivity account and the safety account are on a par with respect to epistemic closure once the method-relativity of the modal conditions is (...) taken into account. Therefore, epistemic closure is no longer an arbiter in the debate. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

A counterpossible is a counterfactual with an impossible antecedent. Counterpossibles present a puzzle for standard theories of counterfactuals, which predict that all counterpossibles are semantically vacuous. Moreover, counterpossibles play an important role in many debates within metaphysics and epistemology, including debates over grounding, causation, modality, mathematics, science, and even God. In this article, we will explore various positions on counterpossibles as well as their potential philosophical consequences.

The literature on indicative conditionals contains two appealing views. The first is the selectional view: on this view, conditionals operate by selecting a single possibility, which is used to evaluate the consequent. The second is the informational view: on this view, conditionals don’t express propositions, but rather impose constraints on information states of speakers. Both views are supported by strong arguments, but they are incompatible on their standard formulations. Hence it appears that we have to choose between mutually exclusive options. (...) But the options are not exclusive. This paper develops a theory of the semantics and assertability of conditionals that is both selectional and informational. The theory vindicates the signature inferences of both selectional and informational theories, including so-called Conditionals Excluded Middle and principles about the interplay between conditionals and ‘might’. It also predicts some interesting and puzzling facts about the assertion of conditionals. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

As is well-known, David Lewis’ counterfactual theory of causation is subject to serious counterexamples in ‘exceptional’ cases. What has not received due attention in the literature so far is that Lewis’ theory fails to provide necessary and sufficient conditions for causation in ‘ordinary’ cases, too. In particular, the theory suffers from the ‘problem of large causes’. It is argued that this problem may be fixed by imposing a minimization constraint, whilst this solution brings along substantial costs as well. In particular, (...) a precise formulation of minimization requires defining an ‘essential part of an event’ and/or an ‘essential subevent’. Although the possibility of such a definition is ultimately left open, some doubts are raised on whether the counterfactualists’ resources are fit for this purpose, and whether the challenge can be met without substantially departing from Lewis’ intention, which was to provide a reductive account of causation. (shrink)

Christopher Hill contends that the metaphysical modalities can be reductively explained in terms of the subjunctive conditional and that this reductive explanation yields two tests for determining the metaphysical modality of a proposition. He goes on to argue that his reductive account of the metaphysical modalities in conjunction with his account of modal knowledge underwrites the further conclusion that conceivability does not provide a reliable test for metaphysical possibility. I argue (1) that Hill’s reductive explanation of the metaphysical modalities in (...) terms of the subjunctive conditional does not yield a reductive explanation of knowledge of metaphysical modality in terms of knowledge of subjunctive conditionals, and (2) that his account of modal knowledge is at odds with his contention that conceivability does not provide epistemic access to metaphysical possibility. (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)

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)

The arbitrariness of a signal has long been seen as a theoretically important but difficult to pin down notion. In this article, we suggest there are at least two different notions of arbitrariness at play in philosophical and scientific debates concerning the use of arbitrary signals, and work towards improved analyses of both. We then consider how these different types of arbitrariness can co-occur and come apart. Finally, we examine the connections between these two types of arbitrariness and the cognitive (...) complexity of signal users with an eye towards better evaluating one possible form of human-nonhuman communicative continuity. We show that each type of arbitrariness bears its own nuanced relationship to cognitive complexity, demonstrating the theoretical importance of keeping these two notions separate. (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)

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)

Divers (2014) argues that a Lewisian theory of modality which includes both counterpart theory and modal realism cannot account for the truth of certain intuitively true modal sentences involving cross-world comparatives. The main purpose of this paper is to defend the Lewisian theory against Divers’s challenge by developing a response strategy based on a degree-theoretic treatment of comparatives and by showing that this treatment is compatible with the theory.

During the last quarter of a century, a number of philosophers have become attracted to the idea that necessity can be analyzed in terms of a hyperintensional notion of essence. One challenge for proponents of this view is to give a plausible explanation of our modal knowledge. The goal of this paper is to develop a strategy for meeting this challenge. My approach rests on an account of modality that I developed in previous work, and which analyzes modal properties in (...) terms of the notion of a metaphysical law. I discuss what information about the metaphysical laws is required for modal knowledge. Moreover, I describe two ways in which we might be able to acquire this information. The first way employs inference to the best explanation. The metaphysical laws, including the essential truths, play a crucial role in causal and grounding explanations and we can gain knowledge of these laws by abductive inferences from facts of which we have perceptual or a priori knowledge. The second way of gaining information about the metaphysical laws rests on knowledge that is partly constitutive of competence with the concepts that are needed to express the relevant information. Finally, I consider how knowledge of the metaphysical laws can be used to establish modal claims, paying special attention to the much-discussed connection between conceiving and possibility. (shrink)

La filosofía de la ciencia se desarrolló durante la primera mitad del siglo xx bajo el supuesto de que la ciencia podía caracterizarse por la estructura lógica tanto del conocimiento articulado en las teorías más exitosas como de sus explicaciones. En la segunda mitad del siglo xx se cuestiona fuertemente esa idea, pero se sigue asumiendo que la filosofía de la ciencia debe hacerse siguiendo los cánones de una epistemología fundamentalista que considera que el avance de la ciencia pasa por (...) una ontología cada vez mas austera guiada por la idea de "mientras menos mejor". Desde esta perspectiva fundamentalista, el que las diferentes ciencias hablen de diferentes tipos de cosas es un obstáculo al entendimiento, producto de la imperfección del conocimiento actual. Este ideal nos invita a pensar que la epistemología debe hacerse reflexionando sobre el conocimiento articulado en nuestras teorías más austeras y nos compromete con propuestas reduccionistas problemáticas que no permiten explicar la diversidad de recursos epistémicos que de hecho utilizan los científicos. En este libro promovemos una epistemología que no sigue el lema de "mientras menos mejor", sino el de "organizar nuestros recursos epistémicos de manera que se genere entendimiento". Así, la misma estructura de las explicaciones y las prácticas (que incluye métodos y normas respecto de lo que se considera plausible y valioso) es lo que nos da la pauta para responder a la pregunta de qué es lo que hay. Esta estrategia epistémica nos obliga a hacer una filosofía de la ciencia muy cercana a la ciencia, reconociendo la pluralidad de sus métodos, objetivos y prácticas, sin reducir la filosofía de la ciencia a la sociología o a cualquier otra ciencia en particular. (shrink)

Possibilistic logic and modal logic are knowledge representation frameworks sharing some common features, such as the duality between possibility and necessity, and the decomposability of necessity for conjunctions, as well as some obvious differences since possibility theory is graded. At the semantic level, possibilistic logic relies on possibility distributions and modal logic on accessibility relations. In the last 30 years, there have been a series of attempts for bridging the two frameworks in one way or another. In this paper, we (...) compare the relational semantics of epistemic logics with simpler possibilistic semantics of a fragment of such logics that only uses modal formulas of depth 1. This minimal epistemic logic handles both all-or-nothing beliefs and explicitly ignored facts. We also contrast epistemic logic with the S5-based rough set logic. Finally, this paper presents extensions of generalized possibilistic logic with objective and non-nested multimodal formulas, in the style of modal logics KD45 and S5. (shrink)

We propose a novel interpretation of Lewis on the analysis of modality that is constructed from primary sources, comprehensive and unprecedented. Our guiding precepts are to distinguish semantics from metaphysics, while respecting the inter-relations between them, and to discern whatever may be special, semantically or metaphysically, about the modal case. Following detailed presentation, we amplify and advocate our interpretation by providing a conforming genealogy of Lewis’s theory of modality and applying it to construct a detailed and newly illuminating version of (...) the Lewisian theory of modality de re. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species (...) of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

The article aims at formulating a philosophical framework and by this giving some means at hand to save human libertarian freedom, God’s omniscience and God’s ”eternity’. This threefold aim is achieved by 1) conceiving of an agent as having different possibilities to act, 2) regarding God’s knowledge -- with respect to agents -- not only as being ”propositional’ in character but also as being ”experiential’: God knows an agent also from the ”first person perspective’, as the agent knows herself, and, (...) 3), formulating ”eternity’ and ”temporality’ as being homeomorphically related to each other. This gives rise to a coherent interplay that saves both human libertarian freedom and God’s omniscient ”view from eternity’. (shrink)

In this paper it is shown that Lewis' MWD (might/would duality) and imaging principles lead to wildly implausible probability assignments for would counterfactuals.

We show that Carmo and Jones’ condition 5 conflicts with the other conditions on their models for contrary-to-duty obligations. We then propose a resolution to the conflict.

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...) only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (shrink)

We bring out syntactic and semantic similarities of two types of conditionals with fronted antecedents [normal indicative conditionals and biscuit conditionals ] and two types of left dislocation constructions in German, which mark two types of topicality. On the basis of these similarities we argue that NCs and BCs are aboutness topics and relevance topics, respectively. Our analysis extends the approach to aboutness topicality of Endriss to relevance topics to derive the semantic and pragmatic contribution of left-dislocated DPs and applies (...) it to an analysis of conditionals as pluralities of possible worlds. We show how this uniform approach to the interpretation of topicality accounts for the nominal left dislocation constructions as well as for the semantic and pragmatic effects observed in connection with the two types of conditionals. We furthermore discuss the potential of our proposal to deal with subjunctive biscuit conditionals, if-clauses modifying speech acts different from assertions, conditionals with right-dislocated if-clauses, and nested conditionals. (shrink)

This paper seeks to determine the significance, if any, of epidemiological evidence to prove the specific causation element of liability in negligence or other relevant torts—in particular, what importance can be attached to a relative risk > 2, where that figure represents a sound causal inference at the general level. The paper discusses increased risk approaches to epidemiological evidence and concludes that they are a last resort. The paper also criticizes the proposal that the probability of causation can be estimated (...) with reference to the RR, such that RR > 2 is necessary and sufficient for causation. It is argued, following arguments by Sander Greenland and others, that RR > 2 is not necessary for proof of specific causation, except under restrictive biological assumptions that are not known to be satisfied for any important disease, and therefore must never be required. However, the paper argues that in some circumstances RR > 2 can be sufficient to prove causation at law. This position is defended against the widely held judicial and academic view that epidemiological evidence must be accompanied by something else, particular to the case at hand, if it is to have probative force for specific causation. It is argued that far from being epistemically irrelevant, to achieve correct and just outcomes it is in fact mandatory to take epidemiological evidence into account in deciding specific causation. Failing to consider such evidence when it is available leads to error and injustice. The conclusion is that in certain circumstances epidemiological evidence of RR > 2 is not necessary to prove specific causation but that it is sufficient. This “sufficiency” is confined to circumstances where there is no other evidence, as a way of getting clear on what the epidemiological evidence says. Once we have worked out what it says, this must be weighed against the other relevant evidence, if there is any. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

Counterfactual conditionals have been appealed to in various ways to show how the mind can be causally efficacious. However, it has often been overestimated what the truth of certain counterfactuals actually indicates about causation. The paper first identifies four approaches that seem to commit precisely this mistake. The arguments discussed involve erroneous assumptions about the connection of counterfactual dependence and genuine causation, as well as a disregard of the requisite evaluation conditions of counterfactuals. In a second step, the paper uses (...) the insights of the foregoing analyses to formulate a set of counterfactuals-based conditions that are characterized as sufficient to establish singular causal claims. The paper concludes that there are ample reasons to believe that some mental events satisfy all these conditions with respect to certain further events and, hence, that mental events sometimes are causes. (shrink)

I formulate a counterfactual version of the notorious 'Ramsey Test'. Whereas the Ramsey Test for indicative conditionals links credence in indicatives to conditional credences, the counterfactual version links credence in counterfactuals to expected conditional chance. I outline two forms: a Ramsey Identity on which the probability of the conditional should be identical to the corresponding conditional probabihty/expectation of chance; and a Ramsey Bound on which credence in the conditional should never exceed the latter.Even in the weaker, bound, form, the counterfactual (...) Ramsey Test makes counterfactuals subject to the very argument that Lewis used to argue against the indicative version of the Ramsey Test. I compare the assumptions needed to run each, pointing to assumptions about the time-evolution of chances that can replace the appeal to Bayesian assumptions about credence update in motivating the assumptions of the argument.I finish by outlining two reactions to the discussion: to indicativize the debate on counterfactuals; or to counterfactualize the debate on indicatives. (shrink)

Recent methodological debates regarding the place of feasibility considerations in normative political theory are hindered for want of a rigorous model of the feasibility frontier. To address this shortfall, I present an analysis of feasibility that generalizes the economic concept of a production possibility frontier and then develop a rigorous model of the feasibility frontier using the familiar possible worlds technology. I then show that this model has significant methodological implications for political philosophy. On the Target View, a political ideal (...) presents a long-term goal for morally progressive reform efforts and, thus, serves as an important reference point for our specification of normative political principles. I use the model to show that we can- not reasonably expect that adopting political ideals as long-term reform objectives will guide us toward the realization of morally optimal feasible states of affairs. I conclude by proposing that political philosophers turn their attention to the analysis of actual social failures rather than political ideals. (shrink)

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (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)

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility (...) theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

The paper defends Humean approaches to autonomous mental causation against recent attacks in the literature. One important criticism launched at Humean approaches says that the truth-makers of the counterfactuals in question include laws of nature, and there are laws that support physical-to-physical counterfactuals, but no laws in the same sense that support mental-to-physical counterfactuals. This paper argues that special science causal laws and physical causal laws cannot be distinguished in terms of degrees of strictness. It follows that mental-to-physical counterfactuals are (...) supported—or not supported—by laws in just the same way as are physical-to-physical counterfactuals. (shrink)

In English, discourse reference to time involves grammatical tenses interpreted as temporal anaphors. Recently, it has been argued that conditionals involve modal discourse anaphora expressed by a parallel grammatical system of anaphoric modals. Based on evidence from Kalaallisut, this paper argues that temporal and modal anaphora can be just as precise in a language that does not have either grammatical category. Instead, temporal anaphora directly targets eventualities of verbs, without mediating tenses, while modal anaphora involves anaphoric moods and/or attitudinal verbs.

Partee (1973) noted anaphoric parallels between English tenses and pronouns. Since then these parallels have been analyzed in terms of type-neutral principles of discourse anaphora. Recently, Stone (1997) extended the anaphoric parallel to English modals. In this paper I extend the story to languages of other types. This evidence also shows that centering parallels are even more detailed than previously recognized. Based on this evidence, I propose a semantic representation language (Logic of Change with Centered Worlds), in which the observed (...) parallels can be formally analyzed. (shrink)

When is a cause of a cause of an effect also a cause of that effect? The right answer is either Sometimes or Always . In favour of Always , transitivity is considered by some to be necessary for distinguishing causes from redundant non-causal events. Moreover transitivity may be motivated by an interest in an unselective notion of causation, untroubled by principles of invidious discrimination. And causal relations appear to add up like transitive relations, so that the obtaining of the (...) overarching relation is not independent of the obtaining of the intermediaries. On the other hand, in favour of Sometimes , often we seem not to treat events that are very spatiotemporally remote from an effect as its causes, even when connected to the effect in question by a chain of counterfactual or chance-raising dependence. Moreover cases of double prevention provide counterexamples to causal transitivity even over short chains. According to the argument of this paper, causation is non-transitive. Transitizing causation provides no viable account of causal redundancy. An unselective approach to causation may motivate resisting the distance counterexamples to transitivity, but it does not help with double prevention, and even makes it more intractable. The strongest point in favour of transitivity is the adding up of causal relations, and this is the point that extant non-transitizing analyses have not adequately addressed. I propose a necessary condition on causation that explains the adding up phenomenon. In doing so it also provides a unifying explanation of distance and double prevention counterexamples to transitivity. (shrink)