Lewis (1973) gave a short argument against conditional excluded middle, based on his treatment of ‘might’ counterfactuals. Bennett (2003), with much of the recent literature, gives an alternative take on ‘might’ counterfactuals. But Bennett claims the might-argument against CEM still goes through. This turns on a specific claim I call Bennett’s Hypothesis. I argue that independently of issues to do with the proper analysis of might-counterfactuals, Bennett’s Hypothesis is inconsistent with CEM. But Bennett’s Hypothesis is independently objectionable, so we should (...) resolve this tension by dropping the Hypothesis, not by dropping CEM. (shrink)

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong.I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne’s challenges. I argue that this is closer to the spirit of Lewis’s first (non-chancy) proposal (...) than is Lewis’s own suggested modification. (shrink)

John Hawthorne in a recent paper takes issue with Lewisian accounts of counterfactuals, when relevant laws of nature are chancy. I respond to his arguments on behalf of the Lewisian, and conclude that while some can be rebutted, the case against the original Lewisian account is strong. I develop a neo-Lewisian account of what makes for closeness of worlds. I argue that my revised version avoids Hawthorne's challenges. I argue that this is closer to the spirit of Lewis's first (non-chancy) (...) proposal than is Lewis's own suggested modification. (shrink)

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate all (...) these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals. (shrink)

Many philosophical theories make comparisons between objects, events, states of affairs, worlds, or systems, and many such theories deliver plausible verdicts only if some of the elements they compare are ranked as ‘best.’ When the relevant ordering does not have such ‘best’ or ‘tied for best’ elements the theory wrongly falls silent or gives badly counterintuitive results. This paper develops ordering supervaluationism---a very general technique that allows any such theory to handle these problematic cases. Just as ordinary supervaluation helps us (...) save and generalize ‘uniqueness assuming’ theories, ordering supervaluationism helps us save and generalize ‘limit assuming’ theories. With so many otherwise attractive limit assuming theories, this is a sensible, methodologically conservative approach. (shrink)

Bell's Theorem is proved for locality and conservation formulated in terms of subjunctive conditionals with chance consequents, rather than the usual conditional probability formulation. This brings into sharp focus the minimal counterfactual assumptions needed for Bell's theorem.

Reidel, 1976. This book is out of print, but can be downloaded as a pdf file (3.3 MB).

It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of CEM (...) are derivable. We also investigate the systems CIw and CI of consequential implication, corresponding to the modal logics K and KD respectively, with occasional remarks about stronger systems. While unrestricted CEM produces modal collapse in all these systems, CEM restricted to contingent formulas yields the Alt2 axiom (semantically, each world can see at most two worlds), which corresponds to the symmetry of consequential implication. It is proved that in all the main systems considered, a given instance of CEM is derivable if and only if the result of replacing consequential implication by the material biconditional in one or other of its disjuncts is provable. Several related results are also proved. The methods of the paper are those of propositional modal logic as applied to a special sort of conditional. (shrink)

Common sense suggests that counterfactuals are capable of truth and falsity, and that their truth values depend on more than just the actual course of events. Projectivists, like Mackie, deny the first; reductivists, like Lewis, deny the second. I criticize Mackie's and Lewis's theories, thereby defending realism. There are parallel issues and positions concerning the other concepts of the natural necessity family. A realist theory may also have a positive part, consisting of an account of some of the conceptual relations (...) within this family. I try to cast light on the counterfactual by postulating a relation of accessibility between possible worlds - accessibility at the 'point' at which an event occurs. (shrink)

This is the second volume of philosophical essays by one of the most innovative and influential philosophers now writing in English. Containing thirteen papers in all, the book includes both new essays and previously published papers, some of them with extensive new postscripts reflecting Lewis's current thinking. The papers in Volume II focus on causation and several other closely related topics, including counterfactual and indicative conditionals, the direction of time, subjective and objective probability, causation, explanation, perception, free will, and rational (...) decision. Throughout, Lewis analyzes global features of the world in such a way as to show that they might turn out to supervene on the spatiotemporal arrangement of local qualities. (shrink)

Counterfactuals is David Lewis' forceful presentation of and sustained argument for a particular view about propositions which express contrary to fact conditionals, including his famous defense of realism about possible worlds and his theory of laws of nature.

In this paper I offer an account of the meaning of must and can within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like must and can in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in (...) the first part, which arise from the ex falso quodlibet paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of must and can. (shrink)

This book defends the view that any adequate account of rational decision making must take a decision maker's beliefs about causal relations into account. The early chapters of the book introduce the non-specialist to the rudiments of expected utility theory. The major technical advance offered by the book is a 'representation theorem' that shows that both causal decision theory and its main rival, Richard Jeffrey's logic of decision, are both instances of a more general conditional decision theory. The book solves (...) a long-standing problem for Jeffrey's theory by showing for the first time how to obtain a unique utility and probability representation for preferences and judgements of comparative likelihood. The book also contains a major new discussion of what it means to suppose that some event occurs or that some proposition is true. The most complete and robust defence of causal decision theory available. (shrink)

Suppose the world is chancy. The worry arises that most ordinary counterfactuals are false. This paper examines David Lewis' strategy for rescuing such counterfactuals, and argues that it is highly problematic.

David Lewis's modal realism claims that nothing can exist in more than one world or time, and that statements about how something would have been are to be analysed in terms of its counterpart. I first explain why the counterpart relation depends on de re modal statements in an intensional language, so that intuitive properties of similarity relations cannot be used to show that the counterpart relation is not an equivalence relation. I then look at test sentences in (the intensional) (...) natural language, and show that none of them provide compelling evidence that a counterpart semantics is needed. (shrink)

Counterfactuals are typically thought--given the force of Sobel sequences--to be variably strict conditionals. I go the other way. Sobel sequences and (what I call) Hegel sequences push us to a strict conditional analysis of counterfactuals: counterfactuals amount to some necessity modal scoped over a plain material conditional, just which modal being a function of context. To make this worth saying I need to say just how counterfactuals and context interact. No easy feat, but I have something to say on the (...) matter. (shrink)

Skyrms's formulation of the argument against stochastic hidden variables in quantum mechanics using conditionals with chance consequences suffers from an ambiguity in its "conservation" assumption. The strong version, which Skyrms needs, packs in a "no-rapport" assumption in addition to the weaker statement of the "experimental facts." On the positive side, I argue that Skyrms's proof has two unnoted virtues (not shared by previous proofs): (1) it shows that certain difficulties that arise for deterministic hidden variable theories that exploit a nonclassical (...) probability theory extend to the stochastic case; (2) the use of counterfactual conditionals relates the Bell puzzle to Dummett's (1976) discussion of realism in quantum mechanics. (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

The score was tied in the bottom of the ninth, I was on third base, and there was only one out when Bubba hit a towering fly ball to deep left-center. Although I’m no speed-demon, the ball was hammered so far that I easily could have scored the winning run if I had tagged up. But I didn’t. I got caught up in the excitement and stupidly played it half way, standing between third and home until I saw the center (...) fielder make his spectacular catch, after which I had to return sheepishly to third. The next batter grounded out, and we lost the game in extra innings. (shrink)

I show that given Jonathan Bennett's theory of 'even if,' the following statement is logically true iff the principle of conditional excluded is valid: (SE) If Q and if P wouldn't rule out Q, then Q even if P. Hence whatever intuitions support the validity of (SE) support the validity of Conditional Excluded Middle, too. Finally I show that Bennett's objection to John Bigelow's theory of the conditional can be turned into a (perhaps) more telling one, viz. that on Bigelow's (...) theory 'if P then Q' and 'if P and Q then R' do not jointly entail 'if P then R'. (shrink)

In this essay I renew the case for Conditional Excluded Middle (CXM) in light of recent developments in the semantics of the subjunctive conditional. I argue that Michael Tooley’s recent backward causation counterexample to the Stalnaker-Lewis comparative world similarity semantics undermines the strongest argument against CXM, and I offer a new, principled argument for the validity of CXM that is in no way undermined by Tooley’s counterexample. Finally, I formulate a simple semantics for the subjunctive conditional that is consistent with (...) both CXM and Tooley’s counterexample. (shrink)

In this essay I renew the case for Conditional Excluded Middle in light of recent developments in the semantics of the subjunctive conditional. I argue that Michael Tooley's recent backward causation counterexample to the Stalnaker-Lewis comparative world similarity semantics undermines the strongest argument against CXM, and I offer a new, principled argument for the validity of CXM that is in no way undermined by Tooley's counterexample. Finally, I formulate a simple semantics for the subjunctive conditional that is consistent with both (...) CXM and Tooley's counterexample. (shrink)

I argue that most counterfactuals are false.

A criticism of Dorothy Edgington's attempt to make Gibbard's problem for indicative conditionals apply to counterfactuals.