If one flips an unbiased coin a million times, there are 2 1,000,000 series of possible heads/tails sequences, any one of which might be the sequence that obtains, and each of which is equally likely to obtain. So it seems (1) 'If I had tossed a fair coin one million times, it might have landed heads every time' is true. But as several authors have pointed out, (2) 'If I had tossed a fair coin a million times, it wouldn't have (...) come up heads every time' will be counted as true in everyday contexts. And according to David Lewis' influential semantics for counterfactuals, (1) and (2) are contradictories. We have a puzzle. We must either (A) deny that (2) is true, (B) deny that (1) is true, or (C) deny that (1) and (2) are contradictories, thus rejecting Lewis' semantics. In this paper I discuss and criticize the proposals of David Lewis and more recently J. Robert G. Williams which solve the puzzle by taking option (B). I argue that we should opt for either (A) or (C). (shrink)

Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in ‘Cynthia will pass her exam’, will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are (...) jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents. (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)

Counterfactual skepticism says that most ordinary counterfactuals are false. While few endorse counterfactual skepticism, the precise costs of the view are disputed and not generally well-understood. I have two aims in this paper. My first and primary aim is to establish, on grounds acceptable to all parties, that counterfactual skepticism is not benign. I argue it leads to significant skepticism about the future: if counterfactual skepticism is true, then we can have only very limited knowledge about the future. I give (...) three arguments to this conclusion, taking as premises principles connecting knowledge of indicative conditionals to knowledge of disjunctions; and principles linking knowledge of indicative conditionals to knowledge of counterfactual conditionals.My second aim is to examine the consequences for non-skeptical theories. My arguments indicate that not only are many ordinary counterfactuals true, but that we also know them. How can this be reconciled with the very real tension between counterfactuals and chance? I consider two solutions, one purely epistemic and one contextualist. Together they suggest something like contextualism about knowledge is required to fully resolve the skeptical threat. (shrink)

David Lewis introduced the idea of a quasi-miracle to overcome a problem in his initial account of counterfactuals. Here we put the notion of a quasi-miracle to a different and new use, showing that it offers a novel account of the phenomenon of poetic justice, where characters in a narrative get their due by happy accident. The key to understanding poetic justice is to see what makes poetically just events remarkable coincidences. We argue that remarkable coincidence is to be understood (...) in terms of a distinctive type of experience quasi-miracles offer. Cases of poetic justice offer a dual awareness of the accidental nature of the events and of a non-accidental process, involving intention, which it appears would explain them. We also extend this account to incorporate how we might experience magic tricks. An account of poetic justice as quasi-miraculous allows us to account for the experience of encounters with poetic justice, as involving the incongruity of seeing design in accident. (shrink)

This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different epistemology of possibility, which (...) does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw. (shrink)

This dissertation begins by addressing the question of when a causal model is apt for deciding questions of actual causation with respect to some target situation. I first provide relevant background about causal models, explain what makes them promising as a tool for analyzing actual causation, and motivate the need for a theory of aptness as part of such an analysis (Chapter 1). I then define what it is for a model on a given interpretation to be accurate of, that (...) is, say only true things about, some target situation. This involves a systematization of various representational principles mentioned and/or discussed throughout the literature into a method of interpretation, which I propose be taken as standard (Chapter 2). Next, I explain and address two reasons for which accuracy as I’ve defined it is insufficient for aptness. The first reason – already discussed in the literature – is the problem of structural isomorphs. In response, I propose the aptness condition of Explicit Partial Mediation (Chapter 3). The second reason – which has yet to be noticed – is the problem of the indeterminacy of accuracy. As I demonstrate, a model is accurate of a target situation only relative to a set of background possibilities – what I call a modal profile. It follows that a model represents a situation only relative to some modal profile or other. I go on to discuss the ramifications of this observation for a theory of actual causation in terms of models. I argue that the relativity be taken at face value and built into our metaphysical account of causation, resulting in a view that I call causal relativism (Chapter 4). I explore one advantage of this view in detail: that the resulting account can defend the principle of strong proportionality against several objections (Chapter 5). Finally, I apply the earlier discussion of aptness to attempts to provide a semantics of counterfactuals in terms of causal models – an interventionist semantics. I show how just as a similarity semantics relies on an opaque notion of similarity, an interventionist semantics relies on an analogous notion of aptness. The challenge of articulating aptness thus undermines the claim that an interventionist semantics avoids representational problems inherent in a similarity semantics (Chapter 6). I close with a recap and suggestions for future research (Chapter 7). -/- . (shrink)

This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.

Bryne & Hajek (1997) argue that Lewis’s (1988; 1996) objections to identifying desire with belief do not go through if our notion of desire is ‘causalized’ (characterized by causal, rather than evidential, decision theory). I argue that versions of the argument go through on certain assumptions about the formulation of decision theory. There is one version of causal decision theory where the original arguments cannot be formulated—the ‘imaging’ formulation that Joyce (1999) advocates. But I argue this formulation is independently objectionable. (...) If we want to maintain the desire as belief thesis, there’s no shortcut through causalization. (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)

In this paper we argue that there is a problem with the conjunction of David Lewis' account of counterfactual conditionals and his account of laws of nature. This is a pressing problem since both accounts are individually plausible, and popular.

Aaccording to D. K. lewis (1973), would-couterfactuals and might-counterfactuals are duals. from this, it follows that the negation of a would-counterfactual is equiv- alent to the corresponding “might-not”-counterfactual and that the negation of a might-counterfactual is equivalent to the corresponding “would-not”- counterfactual. there are cases, however, where we seem to be entitled to accept the would- counterfactual and we are also equally entitled to accept the corresponding might-not-counterfactual and cases where we seem to be entitled to accept the might-counterfactual without (...) being equally entitled to reject the corresponding would-not-counterfactual. In this paper, I will show that a distinction between two types of rejections for counterfactuals (p-rejection and s-rejection) and the recognition that might-not-counterfactuals may play the role of p-rejections (by an application to counterfactuals of the lewisian approach to conversational scores) could explain why the problematic cases should not be seen as cases where the duality of would- and might-counterfactuals fails. (shrink)

Conceptual analyses can be subdivided into two classes, good and evil. Em- pirical analysis is the good kind, routinely practiced in the sciences. Orthodox analysis is the malevolent version that plagues philosophical discourse. In this paper, I will clarify the difference between them, provide some reasons to prefer good over evil, and illustrate their consequences for the metaphysics of causation. By conducting an empirical analysis of causation rather than an orthodox analysis, one can segregate the genuine metaphysical problems that need (...) to be addressed from the many pseudo-problems that have long dogged traditional accounts of causation. (shrink)

*This is a project I hope to come back to one day. It stalled, a bit, on the absence of a positive theory of update I could be satisfied with* When should we believe a indicative conditional, and how much confidence in it should we have? Here’s one proposal: one supposes actual the antecedent; and sees under that supposition what credence attaches to the consequent. Thus we suppose that Oswald did not shot Kennedy; and note that under this assumption, Kennedy (...) was assassinated by someone other than Oswald. Thus we are highly confident in the indicative: if Oswald did not kill Kennedy, someone else did. (shrink)

A ‘might’ counterfactual is a sentence of the form ‘If it had been the case that A, it might have been the case that C’. Recently, John Hawthorne has argued that the truth of many ‘might’ counterfactuals precludes the truth of most ‘would’ counterfactuals. I examine the semantics of ‘might’ counterfactuals, with one eye towards defusing this argument, but mostly with the aim of understanding this interesting class of sentences better.

Whether there exist causal relations between guns firing and people dying, between pedals pressed and cars accelerating, or between carbon dioxide emissions and global warming, is typically taken to be a mind-independent, objective, matter of fact. However, recent contributions to the literature on causation, in particular theories of contrastive causation and causal modelling, have undermined this central causal platitude by relativising causal facts to models or to interests. This thesis flies against the prevailing wind by arguing that we must pay (...) greater attention to which elements of our causal talk vary with context and which elements track genuine features of the world around us. I will argue that once these elements are teased apart we will be in a position to better understand some of the most persistent problems in the philosophy of causation: pre-emption cases, absence causation, failures of transitivity and overdetermination. The result is a naturalist account of causation, concordant with the contextual variability we find in our ordinary causal talk, and parsimonious with respect to the theoretical entities posited. (shrink)

Conditional excluded middle (CEM) is the following principe of counterfactual logic: either, if it were the case that φ, it would be the case that ψ, or, if it were the case that φ, it would be the case that not-ψ. I will first show that CEM entails the identity of indiscernibles, the falsity of physicalism, and the failure of the modal to supervene on the categorical and of the vague to supervene on the precise. I will then argue that (...) we should accept these startling conclusions, since CEM is valid. (shrink)