This paper sketches a dispositionalist conception of laws and shows how the dispositionalist should respond to certain objections. The view that properties are essentially dispositional is able to provide an account of laws that avoids the problems that face the two views of laws (the regularity and the contingent nomic necessitation views) that regard properties as categorical and laws as contingent. I discuss and reject the objections that (i) this view makes laws necessary whereas they are contingent; (ii) this view (...) cannot account for certain kinds of laws of nature and their properties. (shrink)

Many authors have argued in favour of an ontology of properties as powers, and it has been widely argued that this ontology allows us to address certain philosophical problems in novel and illuminating ways, for example, causation, representation, intentionality, free will and liberty. I argue that the ontology of powers, even if successful as an account of fundamental natural properties, does not provide the insight claimed as regards the aforementioned non-fundamental phenomena. I illustrate this argument by criticizing the powers theory (...) of causation presented by Mumford and Anjum and showing that related criticisms can be directed at other abuses of powers. (shrink)

Those who favour an ontology based on dispositions are thereby able to provide a dispositional essentialist account of the laws of nature. In part 1 of this paper I sketch the dispositional essentialist conception of properties and the concomitant account of laws. In part 2, I characterise various claims about the modal character of properties that fall under the heading ‘quidditism’ and which are consequences of the categoricalist view of properties, which is the alternative to the dispositional essentialist view. I (...) argue that quidditism should be rejected. In part 3, I address a criticism of a strong dispositional essentialist view, viz. that ‘structural’ (i.e. geometrical, numerical, spatial and temporal) properties must be regarded as categorical. (shrink)

This is the second part of a two-part paper. It can be read independently of the first part provided that the reader is prepared to go along with the unorthodox views on game theory which were advanced in Part I and are summarized below. The body of the paper is an attempt to study some of the positive implications of such a viewpoint. This requires an exploration of what is involved in modeling “rational players” as computing machines.

Robert Aumann argues that common knowledge of rationality implies backward induction in finite games of perfect information. I have argued that it does not. A literature now exists in which various formal arguments are offered in support of both positions. This paper argues that Aumann's claim can be justified if knowledge is suitably reinterpreted.

Recently, Brian Ellis came up with a neat and novel idea about laws of nature, which at first I misunderstood. Then I participated, with Brian Ellis and Caroline Lierse, in writing a joint paper, “The World as One of a Kind: Natural Necessity and Laws of Nature” (Ellis, Bigelow and Lierse, forthcoming). In this paper, the Ellis idea was formulated in a different way from that in which I had originally interpreted it. Little weight was placed on possible worlds or (...) individual essences. Much weight rested on natural kinds. I thought Ellis to be suggesting that laws of nature attribute essential properties to one grand individual, The World. In fact, Ellis is hostile towards individual essences for any individuals at all, including The World. He is comfortable only with essential properties of kinds, rather than individuals. The Ellis conjecture was that laws of nature attribute essential properties to the natural kind of which the actual world is one (and presumably the only) member. (shrink)

The existence of non-local correlations between outcomes of measurements in quantum entangled systems strongly suggests that we are dealing with some form of causation here. An assessment of this conjecture in the context of the collapse interpretation of quantum mechanics is the primary goal of this paper. Following the counterfactual approach to causation, I argue that the details of the underlying causal mechanism which could explain the non-local correlations in entangled states strongly depend on the adopted semantics for counterfactuals. Several (...) relativistically-invariant interpretations of spatiotemporal counterfactual conditionals are discussed, and the corresponding causal stories describing interactions between parts of an entangled system are evaluated. It is observed that the most controversial feature of the postulated causal connections is not so much their non-local character as a peculiar type of circularity that affects them. (shrink)

In the article I discuss possible amendments and corrections to Lewis’s semantics for counterfactuals that are necessary in order to account for the indeterministic and non-local character of the quantum world. I argue that Lewis’s criteria of similarity between possible worlds produce incorrect valuations for alternate-outcome counterfactuals in the EPR case. Later I discuss an alternative semantics which rejects the notion of miraculous events and relies entirely on the comparison of the agreement with respect to individual facts. However, a controversy (...) exists whether to include future indeterministic events in the criteria of similarity. J. Bennett has suggested that an indeterministic event count toward similarity only if it is a result of the same causal chain as in the actual world. I claim that a much better agreement with the demands of the quantum-mechanical indeterminism can be achieved when we stipulate that possible worlds which differ only with respect to indeterministic facts that take place after the antecedent-event should always be treated as equally similar to the actual world. In the article I analyze and dismiss some common-sense counterexamples to this claim. Finally, I critically evaluate Bennett’s proposal regarding the truth-conditions for true-antecedent counterfactuals. (shrink)

In the paper, the proof of the non-locality of quantum mechanics, given by Bedford and Stapp (1995), and appealing to the GHZ example, is analyzed. The proof does not contain any explicit assumption of realism, but instead it uses formal methods and techniques of the Lewis calculus of counterfactuals. To ascertain the validity of the proof, a formal semantic model for counterfactuals is constructed. With the help of this model it can be shown that the proof is faulty, because it (...) appeals to the unwarranted principle of “elimination of eliminated conditions” (EEC). As an additional way of showing unreasonableness of the assumption (EEC), it is argued that yet another alleged and highly controversial proof of non-locality of QM, using the Hardy example, can be made almost trivial with the help of (EEC). Finally, a general argument is produced to the effect that the locality condition in the form accepted by Stapp and Bedford is consistent with the quantum-mechanical predictions for the GHZ case under the assumption of indeterminism. This result undermines any future attempts of proving the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence in the GHZ case, quite independently of the negative assessment of the particular derivation proposed by Stapp and Bedford. (shrink)

The article deals with one particular problem created by the counterfactual analysis of causality à la Lewis, namely the context-sensitivity problem or, as I prefer to call it, the background condition problem. It appears that Lewis’ counterfactual definition of causality cannot distinguish between proper causes and mere causal conditions – i.e. factors necessary for the effect to occur, but commonly not seen as causally efficacious. The proposal is put forward to amend the Lewis definition with a condition, based on the (...) notion of cotenability, which would eliminate the problem. It is shown that the corrected definition of causality leads to the transitivity of the causal relation. Possible objections to the proposed solution, involving the assumption of indeterminism and the preemption cases, are given a thorough consideration. (shrink)

The difficulty of defining rational behavior in game situations is that the players'' strategies will depend on their expectations about other players'' strategies. These expectations are beliefs the players come to the game with. Game theorists assume these beliefs to be rational in the very special sense of beingobjectively correct but no explanation is offered of the mechanism generating this property of the belief system. In many interesting cases, however, such a rationality requirement is not enough to guarantee that an (...) equilibrium will be attained. In particular, I analyze the case of multiple equilibria, since in this case there exists a whole set of rational beliefs, so that no player can ever be certain that the others believe he has certain beliefs. In this case it becomes necessary to explicitly model the process of belief formation. This model attributes to the players a theory of counterfactuals which they use in restricting the set of possible equilibria. If it were possible to attribute to the players the same theory of counterfactuals, then the players'' beliefs would eventually converge. (shrink)

I outline a discourse-based account of presuppositions that relies on insights from the writings of Peter Strawson, as well as on insights from more recent work by Robert Stalnaker and Barbara Abbott. One of the key elements of my account is the idea that presuppositions are “assertorically inert”, in the sense that they are background propositions, rather than being part of the “at issue” or asserted content. Strawson is often assumed to have defended the view that the falsity of a (...) presupposition leads to catastrophe, in the sense that a false presupposition “wrecks the assertive enterprise”. I argue that the discourse-based account in terms of assertoric inertia can explain how cases of presupposition failure can sometimes be non-catastrophic; there are cases in which the assertive enterprise operates smoothly, despite presupposition failure. The chief problem facing this line of argument is to account for cases in which presupposition failure is catastrophic. If presuppositions are assertorically inert, then how can their falsity ever wreck the assertive enterprise? I offer a principled account that delineates the circumstances in which false presuppositions are, and those in which they are not, catastrophic. (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.

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...) argue that while propensity theories face challenges, these challenges do not undermine their validity as prospective interpretations of probability in science. (shrink)

There is some consensus on the claim that imagination as suppositional thinking can have epistemic value insofar as it’s constrained by a principle of minimal alteration of how we know or believe reality to be – compatibly with the need to accommodate the supposition initiating the imaginative exercise. But in the philosophy of imagination there is no formally precise account of how exactly such minimal alteration is to work. I propose one. I focus on counterfactual imagination, arguing that this can (...) be modeled as simulated belief revision governed by Laplacian imaging. So understood, it can be rationally justified by accuracy considerations: it minimizes expected belief inaccuracy, as measured by the Brier score. (shrink)

I want to model a finite, fallible cognitive agent who imagines that p in the sense of mentally representing a scenario—a configuration of objects and properties—correctly described by p. I propose to capture imagination, so understood, via variably strict world quantifiers, in a modal framework including both possible and so-called impossible worlds. The latter secure lack of classical logical closure for the relevant mental states, while the variability of strictness captures how the agent imports information from actuality in the imagined (...) non-actual scenarios. Imagination turns out to be highly hyperintensional, but not logically anarchic. Section 1 sets the stage and impossible worlds are quickly introduced in Sect. 2. Section 3 proposes to model imagination via variably strict world quantifiers. Section 4 introduces the formal semantics. Section 5 argues that imagination has a minimal mereological structure validating some logical inferences. Section 6 deals with how imagination under-determines the represented contents. Section 7 proposes additional constraints on the semantics, validating further inferences. Section 8 describes some welcome invalidities. Section 9 examines the effects of importing false beliefs into the imagined scenarios. Finally, Sect. 10 hints at possible developments of the theory in the direction of two-dimensional semantics. (shrink)

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)

In his famous work on vagueness, Russell named “fallacy of verbalism” the fallacy that consists in mistaking the properties of words for the properties of things. In this paper, I examine two (clusters of) mainstream paraconsistent logical theories – the non-adjunctive and relevant approaches –, and show that, if they are given a strongly paraconsistent or dialetheic reading, the charge of committing the Russellian Fallacy can be raised against them in a sophisticated way, by appealing to the intuitive reading of (...) their underlying semantics. The meaning of “intuitive reading” is clarified by exploiting a well-established distinction between pure and applied semantics. If the proposed arguments go through, the dialetheist or strong paraconsistentist faces the following Dilemma: either she must withdraw her claim to have exhibited true contradictions in a metaphysically robust sense – therefore, inconsistent objects and/or states of affairs that make those contradictions true; or she has to give up realism on truth, and embrace some form of anti-realistic (idealistic, or broadly constructivist) metaphysics. Sticking to the second horn of the Dilemma, though, appears to be promising: it could lead to a collapse of the very distinction, commonly held in the literature, between a weak and a strong form of paraconsistency – and this could be a welcome result for a dialetheist. (shrink)

I present a formal theory of the logic and aboutness of imagination. Aboutness is understood as the relation between meaningful items and what they concern, as per Yablo and Fine’s works on the notion. Imagination is understood as per Chalmers’ positive conceivability: the intentional state of a subject who conceives that p by imagining a situation—a configuration of objects and properties—verifying p. So far aboutness theory has been developed mainly for linguistic representation, but it is natural to extend it to (...) intentional states. The proposed framework combines a modal semantics with a mereology of contents: imagination operators are understood as variably strict quantifiers over worlds with a content-preservation constraint. (shrink)

The basic form of the exclusion problem is by now very, very familiar. 2 Start with the claim that the physical realm is causally complete: every physical thing that happens has a sufficient physical cause. Add in the claim that the mental and the physical are distinct. Toss in some claims about overdetermination, give it a stir, and voilá—suddenly it looks as though the mental never causes anything, at least nothing physical. As it is often put, the physical does all (...) the work, and there is nothing left for the mental to do. (shrink)

This paper studies the use of hypothetical and value-based reasoning in US Supreme-Court cases concerning the United States Fourth Amendment. Drawing upon formal AI & Law models of legal argument a semi-formal reconstruction is given of parts of the Carney case, which has been studied previously in AI & law research on case-based reasoning. As part of the reconstruction, a semi-formal proposal is made for extending the formal AI & Law models with forms of metalevel reasoning in several argument schemes. (...) The result is compared with Rissland’s (1989) analysis in terms of dimensions and Ashley’s (2008) analysis in terms of his process model of legal argument with hypotheticals. (shrink)

This article discusses a familiar version of trope theory as opposed to a familiar version of the theory of universals, examining how these two rivals address the problem of “attribute agreement”—a problem that has been at the root of the very reason for developing these theories in the first place. The article shows that there is not much of a difference between the ways these two theories handle the problem, and in a more general way it argues that there is (...) little reason for preferring one theory over the other. It is not interested in this claim only for the sake of the debate between trope theory and the theory of universals. Indeed, the reasons why it claims that it is so difficult to choose one theory over the other can be applied to other cases as well (where they might lead to claims of metaphysical equivalence). (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

Gabbay has gathered an enormous amount of results; some of them important and novel, others important but already known, many rather routine, however. The organization of this material shows grave defects, both in the exposition and in its logical structure. Intensional logic appears as a vast collection of (often duplicated) loosely connected results. This may be a true reflection of the present state of the subject, but it does not contribute to a better understanding of it, let alone advance it.

A variation of Bell's theorem that deals with the indeterministic case is formulated and proved within the logical framework of Lewis's theory of counterfactuals. The no-faster-than-light-influence condition is expressed in terms of Lewis would counterfactual conditionals. Objections to this procedure raised by certain philosophers of science are examined and answered. The theorem shows that the incompatibility between the predictions of quantum theory and the idea of no faster-than-light influence cannot be ascribed to any auxiliary or tacit assumption of either determinism (...) or the related idea that outcomes of unperformed measurements are determinate within nature. In addition, the theorem provides an example of an application of Lewis's theory of counterfactuals in a rigorous scientific context. (shrink)

One of the most dominant approaches to semantics for relevant (and many paraconsistent) logics is the Routley-Meyer semantics involving a ternary relation on points. To some (many?), this ternary relation has seemed like a technical trick devoid of an intuitively appealing philosophical story that connects it up with conditionality in general. In this paper, we respond to this worry by providing three different philosophical accounts of the ternary relation that correspond to three conceptions of conditionality. We close by briefly discussing (...) a general conception of conditionality that may unify the three given conceptions. (shrink)

Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.

Team semantics is a highly general framework for logics which describe dependencies and independencies among variables. Typically, the dependencies considered in this context are properties of sets of configurations or data records. We show how team semantics can be further generalized to support languages for the discussion of interventionist counterfactuals and causal dependencies, such as those that arise in manipulationist theories of causation. We show that the “causal teams” we introduce in the present paper can be used for modelling some (...) classical counterfactual scenarios which are not captured by the usual causal models. We then analyse the basic properties of our counterfactual languages and discuss extensively the differences with respect to the Lewisian tradition. (shrink)

I aim to show that standard theories of counterfactuals are mistaken, not in detail, but in principle, and I aim to say what form a tenable theory must take. Standard theories entail a categorical interpretation of counterfactuals, on which to state that, if it were that A, it would be that C is to state something, not relative to any supposition or hypothesis, but categorically. On the rival suppositional interpretation, to state that, if it were that A, it would be (...) that C is to state that it would be that C relative to the supposition that it were that A. The two interpretations make incompatible predictions concerning the correct evaluation of counterfactuals. I argue that the suppositional interpretation makes the correct prediction. (shrink)

It has seemed, to many, that there is an important connection between the ways in which some theoretical posits explain our observations, and our reasons for being ontologically committed to those posits. One way to spell out this connection is in terms of what has become known as the explanatory criterion of ontological commitment. This is, roughly, the view that we ought to posit only those entities that are indispensable to our best explanations. Our primary aim is to argue that (...) the moral nonnaturalist places herself in an invidious position if she simply accepts that the nonnatural moral facts that she posits are not explanatory. Instead, we offer the nonnaturalist an alternative strategy for dealing with moral explanations. The strategy is to retain the explanatory criterion of ontological commitment and maintain that moral properties are, in fact, explanatory. The explanations they provide are not causal explanations; instead, moral properties make a non-causal difference to the physical facts. (shrink)

We argue that explanations appealing to logical impossibilities are genuine explanations. Our defense is based on a certain picture of impossibility. Namely, that there are impossibilities and that the impossibilities have structure. Assuming this broad picture of impossibility we defend the genuineness of explanations that appeal to logical impossibilities against three objections. First, that such explanations are at odds with the perceived conceptual connection between explanation and counterfactual dependence. Second, that there are no genuinely contrastive why-questions that involve logical impossibilities (...) and, third, that explanations appealing to logical impossibilities rule nothing out. (shrink)

The standard view about counterfactuals is that a counterfactual (A > C) is true if and only if the A-worlds most similar to the actual world @ are C-worlds. I argue that the worlds conception of counterfactuals is wrong. I assume that counterfactuals have non-trivial truth-values under physical determinism. I show that the possible-worlds approach cannot explain many embeddings of the form (P > (Q > R)), which intuitively are perfectly assertable, and which must be true if the contingent falsity (...) of (Q > R) is to be explained. If (P > (Q > R)) has a backtracking reading then the contingent facts that (Q > R) needs to be true in the closest P-worlds are absent. If (P > (Q > R)) has a forwardtracking reading, then the laws required by (Q > R) to be true in the closest P-worlds will be absent, because they are violated in those worlds. Solutions like lossy laws or denial of embedding won't work. The only approach to counterfactuals that explains the embedding is a pragmatic metalinguistic approach in which the whole idea that counterfactuals are about a modal reality, be it abstract or concrete, is given up. (shrink)

I argue that Lewis's counterfactual theory of causation, given his treatment of counterfactuals in terms of world-comparative similarity faces insuperable problems in the form of the problem of effects and the problem of epiphenomena.

ABSTRACT Our goal in this paper is to extend counterfactual accounts of scientific explanation to mathematics. Our focus, in particular, is on intra-mathematical explanations: explanations of one mathematical fact in terms of another. We offer a basic counterfactual theory of intra-mathematical explanations, before modelling the explanatory structure of a test case using counterfactual machinery. We finish by considering the application of counterpossibles to mathematical explanation, and explore a second test case along these lines.

A major criticism of David Lewis’ counterfactual theory of causation is that it allows too many things to count as causes, especially since Lewis allows, in addition to events, absences to be causes as well. Peter Menzies has advanced this concern under the title “the problem of profligate causation.” In this paper, I argue that the problem of profligate causation provides resources for exposing a tension between Lewis’ acceptance of absence causation and his modal realism. The result is a different (...) problem of profligate causation—one that attacks the internal consistency of Lewisian metaphysics rather than employing common sense judgments or intuitions that conflict with Lewis’ extensive list of causes. (shrink)

Jaegwon Kim’s supervenience/exclusion argument attempts to show that non-reductive physicalism is incompatible with mental causation. This influential argument can be seen as relying on the following principle, which I call “the piggyback principle”: If, with respect to an effect, E, an instance of a supervenient property, A, has no causal powers over and above, or in addition to, those had by its supervenience base, B, then the instance of A does not cause E (unless A is identical with B). In (...) their “Epiphenomenalism: The Dos and the Don’ts,” Larry Shapiro and Elliott Sober employ a novel empirical approach to challenge the piggyback principle. Their empirical approach pulls from the experiments of August Weismann regarding the inheritance of acquired characteristics. Through an examination of Weismann’s experiments, Shapiro and Sober extract lessons in reasoning about the epiphenomenalism of a property. And according to these empirically drawn lessons, the piggyback principle is a don’t. My primary aim in this paper is to defend the piggyback principle against Shapiro and Sober’s empirical approach. (shrink)

A prominent philosophical debate concerns whether we should accept causal decision theory or evidential decision theory as our best theory of rational choice. However, instead of accepting one of these theories at the expense of the other, an alternative would be to accept that both theories play a partial role in the true account of rational choice. In this paper, I defend a pluralist account of this sort. In particular, I argue that rational permissibility is an indeterminate notion, with EDT (...) and CDT each corresponding to one sharpening of this notion. (shrink)

I argue that reflection on philosophers who could have been working among us but aren’t can lead us to give up our philosophical beliefs.

Stewart Cohen’s New Evil Demon argument raises familiar and widely discussed concerns for reliabilist accounts of epistemic justification. A now standard response to this argument, initiated by Alvin Goldman and Ernest Sosa, involves distinguishing different notions of justification. Juan Comesaña has recently and prominently claimed that his Indexical Reliabilism (IR) offers a novel solution in this tradition. We argue, however, that Comesaña’s proposal suffers serious difficulties from the perspective of the philosophy of language. More specifically, we show that the two (...) readings of sentences involving the word ‘justified’ which are required for Comesaña’s solution to the problem are not recoverable within the two-dimensional framework of Robert Stalnaker to which he appeals. We then consider, and reject, an attempt to overcome this difficulty by appeal to a complication of the theory involving counterfactuals, and conclude the paper by sketching our own preferred solution to Cohen’s New Evil Demon. (shrink)

A familiar criticism of religious belief starts from the claim that a typical religious believer holds the particular religious beliefs she does just because she happened to be raised in a certain cultural setting rather than some other. This claim is commonly thought to have damaging epistemological consequences for religious beliefs, and one can find statements of an argument in this vicinity in the writings of John Stuart Mill and more recently Philip Kitcher, although the argument is seldom spelled out (...) very precisely. This paper begins by offering a reconstruction of an argument against religious beliefs from cultural contingency, which proceeds by way of an initial argument to the unreliability of the processes by which religious beliefs are formed, whose conclusion is then used to derive two further conclusions, one which targets knowledge and the other, rationality. Drawing upon recent work in analytic epistemology, I explore a number of possible ways of spelling out the closely related notions of accidental truth, epistemic luck, and reliability upon which the argument turns. I try to show that the renderings of the argument that succeed in securing the sceptical conclusion against religious beliefs also threaten scepticism about various sorts of beliefs besides religious beliefs. (shrink)

According to the proponents of Developmental Systems Theory and the Causal Parity Thesis, the privileging of the genome as “first among equals” with respect to the development of phenotypic traits is more a reflection of our own heuristic prejudice than of ontology - the underlying causal structures responsible for that specified development no more single out the genome as primary than they do other broadly “environmental” factors. Parting with the methodology of the popular responses to the Thesis, this paper offers (...) a novel criterion for ‘causal primacy’, one that is grounded in the ontology of the unique causal role of dispositional properties. This paper argues that, if the genome is conceptualised as realising dispositional properties that are “directed toward” phenotypic traits, the parity of ‘causal roles’ between genetic and extra-genetic factors is no longer apparent, and further, that the causal primacy of the genome is both plausible and defensible. (shrink)