This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an (...) esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87). (shrink)

Since the publication of David Lewis’ Counterfactuals, the standard line on subjunctive conditionals with impossible antecedents (or counterpossibles) has been that they are vacuously true. That is, a conditional of the form ‘If p were the case, q would be the case’ is trivially true whenever the antecedent, p, is impossible. The primary justification is that Lewis’ semantics best approximates the English subjunctive conditional, and that a vacuous treatment of counterpossibles is a consequence of that very elegant theory. Another justification (...) derives from the classical lore than if an impossibility were true, then anything goes. In this paper we defend non-vacuism, the view that counterpossibles are sometimes non-vacuously true and sometimes non-vacuously false. We do so while retaining a Lewisian semantics, which is to say, the approach we favor does not require us to abandon classical logic or a similarity semantics. It does however require us to countenance impossible worlds. An impossible worlds treatment of counterpossibles is suggested (but not defended) by Lewis (Counterfactuals. Blackwell, Oxford, 1973), and developed by Nolan (Notre Dame J Formal Logic 38:325–527, 1997), Kment (Mind 115:261–310, 2006a: Philos Perspect 20:237–302, 2006b), and Vander Laan (In: Jackson F, Priest G (eds) Lewisian themes. Oxford University Press, Oxford, 2004). We follow this tradition, and develop an account of comparative similarity for impossible worlds. (shrink)

It is widely agreed that contraposition, strengthening the antecedent and hypothetical syllogism fail for subjunctive conditionals. The following putative counter-examples are frequently cited, respectively.

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)

In this paper Richard Jeffrey's 'Logic of Decision' is extended by examination of agents' attitudes to the sorts of possibilities identified by indicative conditional sentences. An expression for the desirability of conditionals is proposed and, along with Adams' thesis that the probability of a conditional equals the conditional probability of its antecedent given its consequent, is defended by informally deriving it from Jeffrey's notion of desirability and some weak constraints on rational preference for conditional possibilities. Finally a statement is given (...) of a representation theorem establishing the conditions under which a rational agent's preferences for conditionals determines the existence of unique measures (up to choice of scale) of her degrees of belief and desire. (shrink)

ABSTRACT: This paper traces the earliest development of the most basic principle of deduction, i.e. modus ponens (or Law of Detachment). ‘Aristotelian logic’, as it was taught from late antiquity until the 20th century, commonly included a short presentation of the argument forms modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens, and modus tollendo ponens. In late antiquity, arguments of these forms were generally classified as ‘hypothetical syllogisms’. However, Aristotle did not discuss such arguments, nor did he call any (...) arguments ‘hypothetical syllogisms’. The Stoic indemonstrables resemble the modus ponens/tollens arguments. But the Stoics never called them ‘hypothetical syllogisms’; nor did they describe them as ponendo ponens, etc. The tradition of the four argument forms and the classification of the arguments as hypothetical syllogisms hence need some explaining. In this paper, I offer some explanations by tracing the development of certain elements of Aristotle’s logic via the early Peripatetics to the logic of later antiquity. I consider the questions: How did the four argument forms arise? Why were there four of them? Why were arguments of these forms called ‘hypothetical syllogisms’? On what grounds were they considered valid? I argue that such arguments were neither part of Aristotle’s dialectic, nor simply the result of an adoption of elements of Stoic logic, but the outcome of a long, gradual development that begins with Aristotle’s logic as preserved in his Topics and Prior Analytics; and that, as a result, we have a Peripatetic logic of hypothetical inferences which is a far cry both from Stoic logic and from classical propositional logic, but which sports a number of interesting characteristics, some of which bear a cunning resemblance to some 20th century theories. (shrink)

This paper gives a framework for understanding causal counterpossibles, counterfactuals imbued with causal content whose antecedents appeal to metaphysically impossible worlds. Such statements are generated by omissive causal claims that appeal to metaphysically impossible events, such as “If the mathematician had not failed to prove that 2+2=5, the math textbooks would not have remained intact.” After providing an account of impossible omissions, the paper argues for three claims: (i) impossible omissions play a causal role in the actual world, (ii) causal (...) counterpossibles have broad applications in philosophy, and (iii) the truth of causal counterpossibles provides evidence for the nonvacuity of counterpossibles more generally. (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)

This paper investigates the interpretation of counterfactual conditionals. The main goal of the paper is to provide an account of the semantic role of similarity in the evaluation of counterfactuals. The paper proposes an analysis according to which counterfactuals are treated as predications “ de re ” over past situations in the actual world. The relevant situations enter semantic composition via the interpretation of tense. Counterfactuals are treated as law-like conditionals with de re predication over particular facts. Similarity with respect (...) to particular facts is ensured by the semantics of tense in interaction with the modal, while the modal itself is responsible for invoking laws. In the paper, various arguments are provided to support a local view of similarity over the global approach found in semantics along the line of Lewis’s and Stalnaker’s. Arguments are also provided tying the evaluation of similarity to the interpretation of tense. Finally, arguments are provided to show that in key cases, the approaches make comparable predictions. (shrink)

The natural interpretation of counterfactuals with disjunctive antecedents involves selecting from each of the disjuncts the worlds that come closest to the world of evaluation. It has been long noticed that capturing this interpretation poses a problem for a minimal change semantics for counterfactuals, because selecting the closest worlds from each disjunct requires accessing the denotation of the disjuncts from the denotation of the disjunctive antecedent, which the standard boolean analysis of or does not allow (Creary and Hill, Philosophy of (...) Science 43:341–344, 1975; Nute, Journal of Philosophy 72:773–778, 1975; Fine, Mind 84(335):451–458, 1975; Ellis et al. Journal of Philosophical Logic 6:335–357, 1977). This paper argues that the failure to capture the natural interpretation of disjunctive counterfactuals provides no reason to abandon a minimal change semantics. It shows that the natural interpretation of disjunctive counterfactuals is expected once we refine our assumptions about the semantics of or and the logical form of conditionals, and (i) we assume that disjunctions introduce propositional alternatives in the semantic derivation, in line with independently motivated proposals about the semantics of or (Aloni, 2003a; Simons, Natural Language Semantics 13:271–316, 2005; Alonso-Ovalle, Disjunction in Alternative Semantics. PhD thesis, 2006); and (ii) we treat conditionals as correlative constructions, as advocated in von Fintel (1994), Izvorski (Proceedings of NELS 26, 1996), Bhatt and Pancheva (2006), and Schlenker (2004). (shrink)

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

The purpose of this note is to dispute Michael Ayers' claim that "there is no special problem of subjunctive conditionals".

Kit Fine (1994. “Essence and Modality”, Philosophical Perspectives 8: 1-16) argues that the standard modal account of essence as de re modality is ‘fundamentally misguided’ (p. 3). We agree with his critique and suggest an alternative counterfactual analysis of essence. As a corollary, our counterfactual account lends support to non-vacuism the thesis that counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are not always vacuously true.

In this book the author gives a broad overview of different areas of research in nonmonotonic reasoning, and presents some new results and ideas based on his research. The guiding principles are: clarification of the different research activities in the area, which have sometimes been undertaken independently of each other; and appreciation of the fact that these research activities often represent different means to the same ends, namely sound theoretical foundations and efficient computation. The book begins with a discussion of (...) the various types of nonmonotonic reasoning, their applications and their logics. Theorem proving techniques for these logics are also described. The following chapters deal with formulations of nonmonotonic inheritance, and nonmonotonic reasoning based on nonmonotonic rules. The final chapter discusses the achievements in the field in the light of the Yale shooting example. The book will be welcomed by researchers in theoretical computer science and artificial intelligence. (shrink)

Modal realism -- Time, space, world -- Existence -- Actuality -- Modal realism and modal tense -- Transworld individuals and their identity -- Existensionalism -- Impossibility -- Proposition and relief -- Fictional worlds -- Epistemology.

I argue that most counterfactuals are false.

I. Causal Thesis: Dispositions have a causal basis. II. Distinctness Thesis: Dispositions are distinct from their causal basis. III. Impotence Thesis: Dispositions are not causally active.

While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.1 Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” (...) in these sets can be anything at all; they can be numbers, or people, or sh. The set of worlds, together with the accessibility relation and the rest of the model, is used as a purely formal structure.2 One can even go beyond establishing results about formal systems and apply Kripke models to English, as Charles Chihara has recently argued.3 Chihara shows, for instance, how to use Kripke models (plus primitive modal notions) to give an account of validity for English modal sentences. In other cases worlds are not really needed at all. It is often vivid to give a counterexample thus: “There is a possible world in which P. Since your theory implies that in all worlds, not-P, your theory is wrong.” But the counterexample could just as easily be given using modal operators: “Possibly, P. Since your theory implies that it is necessary that not-P, your theory is wrong.”. (shrink)

The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form “If A had not occurred, C would not have occurred”. While counterfactual analyses have been given of type-causal concepts, most counterfactual analyses have focused on singular causal or token-causal claims of the form “event c caused event e”. Analyses of token-causation have become popular in the last thirty years, especially since the development in the (...) 1970's of possible world semantics for counterfactuals. The best known counterfactual analysis of causation is David Lewis's (1973b) theory. However, intense discussion over thirty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of counterfactuals. Recent years have seen a proliferation of different refinements of the basic idea to achieve a closer match with commonsense judgements about causation. (shrink)

Book synopsis: Philosophers have long been fascinated by the connection between cause and effect: are 'causes' things we can experience, or are they concepts provided by our minds? The study of causation goes back to Aristotle, but resurged with David Hume and Immanuel Kant, and is now one of the most important topics in metaphysics. Most of the recent work done in this area has attempted to place causation in a deterministic, scientific, worldview. But what about the unpredictable and chancey (...) world we actually live in: can one theory of causation cover all instances of cause and effect? (shrink)

Among the many philosophers who hold that causal facts1 are to be explained in terms of—or more ambitiously, shown to reduce to—facts about what happens, together with facts about the fundamental laws that govern what happens, the clear favorite is an approach that sees counterfactual dependence as the key to such explanation or reduction. The paradigm examples of causation, so advocates of this approach tell us, are examples in which events c and e— the cause and its effect— both occur, (...) but: had c not occurred, e would not have occurred either. From this starting point ideas proliferate in a vast profusion. But the remarkable disparity among these ideas should not obscure their common foundation. Neither should the diversity of opinion about the prospects for a philosophical analysis of causation obscure their importance. For even those philosophers who see these prospects as dim—perhaps because they suffer post-Quinean queasiness at the thought of any analysis of any concept of interest—can often be heard to say such things as that causal relations among events are somehow “a matter of” the patterns of counterfactual dependence to be found in them. (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)

Lewis/Stalnaker semantics has it that all counterpossibles (i.e., counterfactual conditionals with impossible antecedents) are vacuously true. Non-vacuism, by contrast, says the truth-values of counterpossibles are affected by the truth-values of the consequents. Some counterpossibles are true, some false. Williamson objects to non-vacuism. He asks us to consider someone who answered ‘11’ to ‘What is 5 + 7?’ but who mistakenly believes that he answered ‘13’. For the non-vacuist, (1) is false, (2) true: (1) If 5 + 7 were 13, x (...) would have got that sum right (2) If 5 + 7 were 13, x would have got that sum wrong Williamson is not persuaded by the initial intuitiveness of such examples: ... they tend to fall apart when thought through. For example, if 5 + 7 were 13 then 5 + 6 would be 12, and so (by another eleven steps) 0 would be 1, so if the number of right answers I gave were 0, the number of right answers I gave would be 1. (2006) That’s the whole argument—much of it implicit. Alan Baker’s critique (2007) of Brogaard and Salerno (2007) prompts us to say something less abbreviated about a less abbreviated form of Wiliamson’s argument. Then we further develop our (2007) counterfactual analysis of essense. (shrink)

The paper takes an expressivistic perspective, i.e., it takes conditionals of all sorts to primarily express conditional beliefs. Therefore it is based on what it takes to be the best account of conditional belief, namely ranking theory. It proposes not to start looking at the bewildering linguistic phenomenology, but first to systematically study the various options of expressing features of conditional belief. Those options by far transcend the Ramsey test and include relevancies of various kinds and in particular the so-called (...) “circumstances are such that” reading, under which also all conditionals representing causal relations can be subsumed. In this way a unifying perspective on the many kinds of conditionals is offered. The final section explains the considerable extent to which truth conditions for conditionals, which may seem lost in the expressivistic or epistemic perspective, may be recovered. (shrink)