Philosophy Conditionals
by
Christopher Gauker
  • LAST REVIEWED: 22 September 2016
  • LAST MODIFIED: 29 June 2011
  • DOI: 10.1093/obo/9780195396577-0023

Introduction

In English, a conditional is a sentence of the form, “If p, then q” (or of a synonymous form). The part of the sentence following “if” is the antecedent, while the part following “then” is the consequent. An indicative conditional is a conditional having an antecedent in indicative mood, such as “If Fred is here, then he can help you.” A subjunctive conditional is a conditional having an antecedent in the subjunctive mood, such as “If I were in Paris, then I would be happy.” (In English, the present-tense subjunctive mood, as it occurs in the antecedent of a conditional, is usually indistinguishable from the past tense, and the past-tense subjunctive is indistinguishable from the past perfect.) What are called counterfactual conditionals are usually just subjunctive conditionals, though some authors draw a distinction. An important touchstone in discussions of conditionals is the so-called material conditional, which, by stipulation, is true if and only if either the antecedent is false or the consequent is true. The philosophical problem of conditionals is, in part, the problem of explaining the conditions under which a conditional sentence is true, or true relative to pertinent parameters. It is also the problem of characterizing the class of logically valid arguments containing conditionals. For instance, we would like to know whether the argument “I will meet you tomorrow; therefore, if I die tonight, then I will meet you tomorrow” is logically valid. The philosophical problem of conditionals has proven to be difficult and controversial, and for that reason the problem of conditionals has been used as a primary motivation for several different approaches to semantic theory.

General Overviews

All three of the texts below summarize several aspects of the state of play in the discussion of conditionals. But while Edgington 1995 and Bennett 2003 aim to defend particular theories, Nute and Cross 2003 attempt to remain neutral.

  • Bennett, Jonathan. A Philosophical Guide to Conditionals. New York: Oxford University Press 2003.

    DOI: 10.1093/0199258872.001.0001Save Citation »Export Citation »E-mail Citation »

    Bennett advocates the probabilistic approach of Adams in his treatment of indicative conditionals, but advocates the Stalnaker-Lewis approach for subjunctive conditionals. In the course of his argument, Bennett touches on many of the major issues concerning conditionals, and for that reason his book can serve as general introduction.

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    • Edgington, Dorothy. “On Conditionals.” Mind 104 (1995): 235–329.

      DOI: 10.1093/mind/104.414.235Save Citation »Export Citation »E-mail Citation »

      This is a survey of the subject of conditionals aimed at defending Adams’s probabilistic theory.

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      • Nute, Donald, and Charles B. Cross. “Conditional Logic.” In The Handbook of Philosophical Logic. Vol. 4. 2d ed. Edited by Dov Gabbay and Franz Guenthner, 1–98. Dordrecht, The Netherlands: Kluwer Academic, 2003.

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        This is a technically precise survey and comparison of semantic theories of conditionals. It focuses on variations of the possible-worlds approach and on the belief-revision approach.

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        Collections

        Neither of these anthologies collects the most recent work; however, some of the important articles will more easily be obtained in these anthologies than in their original sources. Harper, et. al. 1981 covers a broader ranger of topics, but Jackson 1991 is a more concentrated selection of classics.

        • Harper, William H., Robert Stalnaker, and Glenn Pearce, eds. Ifs: Conditionals, Belief, Decision, Chance, and Time. Dordrecht, The Netherlands: D. Reidel, 1981.

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          This collection includes some of the early, previously published work by Stalnaker and Lewis, as well as some papers by others not found elsewhere.

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          • Jackson, Frank, ed. Conditionals. Oxford: Oxford University Press, 1991.

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            This collection includes some of the important papers by Stalnaker and Lewis as well as classics by Goodman and Grice and a few other important contributions.

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            Logical Foundations

            Much contemporary work on the semantics of conditionals is grounded in the semantics for modal logic. Lewis and Langford 1932 in effect posed the problem, and Kripke 1959 put forward the basic elements of the contemporary solution.

            • Kripke, Saul. “A Completeness Theorem in Modal Logic.” Journal of Symbolic Logic 24 (1959): 1–14.

              DOI: 10.2307/2964568Save Citation »Export Citation »E-mail Citation »

              This paper deserves mention, although it has nothing to say about the logic of natural language conditionals, because it, together with its sequels, legitimized in the eyes of many the use of the concept of possible world in semantic theorizing.

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              • Lewis, Clarence Irving, and Cooper Harold Langford. Symbolic Logic. New York: The Century Company, 1932.

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                In an appendix, Lewis and Langford define a number of axiom systems governing modal operators and what they called “strict implication.” No one holds that the logic of strict implication, as captured by any of these theories, is the logic of natural language conditionals. But through this work, Lewis and Langford highlighted the idea that a theory of conditionals is responsible for accounting for the logic of conditionals.

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                Early Work

                Stalnaker 1968 and Lewis 1973a (cited under The Possible Worlds Approach) revolutionized the study of conditionals, but before that there was already a large body of literature on the meaning of conditionals. Little of that is still read, and a lot of those authors wrote without a clear conception of what is required of a precise, recursive semantic theory. What follows is a short list of works that introduced some of the main ideas still discussed. Ramsey 1990 (published in 1931) introduced what is now known as the Ramsey test; Chisholm 1946 and Goodman 1947 introduced the idea that conditionals are to be evaluated against the background of accepted hypotheses; Grice 1989 defended the conception of indicative conditionals as material conditionals; von Wright 1957 introduced the idea that assertions of conditionals are conditional assertions; Todd 1964 anticipated the approach of Stalnaker and Lewis; Adams 1965 proposed an explication of conditionals in terms of conditional probabilities.

                • Adams, Ernest. “On the Logic of Conditionals.” Inquiry 8 (1965): 166–197.

                  DOI: 10.1080/00201746508601430Save Citation »Export Citation »E-mail Citation »

                  This is the article in which Adams introduced the idea that the semantics for a language containing conditionals needs to be formulated in terms of probabilities rather than truth values. It contains an especially useful counterexample to the equation of indicative conditionals with material conditionals (the switch example).

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                  • Chisholm, Roderick. “The Contrary-to-Fact Conditional.” Mind 55 (1946): 289–307.

                    DOI: 10.1093/mind/LV.219.289Save Citation »Export Citation »E-mail Citation »

                    In this paper Chisholm floated the idea that a counterfactual conditional could be true if there is a certain sort of true universal generalization that, together with the antecedent, implies the consequent. It is this sort of theory that Goodman 1947 subsequently showed to be problematic.

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                    • Goodman, Nelson. “The Problem of Counterfactual Conditionals.” Journal of Philosophy 44 (1947): 113–128.

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                      Goodman dramatized the puzzle of counterfactual conditionals. He proposed that a counterfactual is true if the antecedent, together with additional “cotenable” conditions, leads by law to the consequent. But he also acknowledged that this account appears to be question-begging when we attempt to explicate the concept of cotenability, inasmuch as deciding whether one hypothesis is cotenable with another requires a decision regarding the truth of another counterfactual. Reprinted in Nelson Goodman, Fact, Fiction and Forecast, 4th ed. (Cambridge, MA: Harvard University Press, 1983). Also in Jackson 1991 (cited under Collections).

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                      • Grice, Paul. Studies in the Way of Words. Cambridge, MA: Harvard University Press, 1989.

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                        This book contains the published text of lectures that Grice delivered in 1967, which circulated in mimeograph for many years. In the fourth of these (not the more famous second), Grice argues that English indicative conditionals are material conditionals. He claims that appearances to the contrary are due to conversational implicatures.

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                        • Ramsey, Frank L. “General Propositions and Causality.” In F. P. Ramsey: Philosophical Papers. Edited by D. H. Mellor, 145–163. Cambridge, UK: Cambridge University Press, 1990.

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                          In a footnote, Ramsey puts forward the very influential idea that we should accept a conditional just in case, upon adding the antecedent to our stock of beliefs, we should add the consequent as well. This test of acceptability is known as the Ramsey test. Originally published in 1931.

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                          • Todd, William. “Counterfactual Conditionals and the Presuppositions of Induction.” Philosophy of Science 31 (1964): 101–110.

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                            Todd’s paper is seldom cited, but it anticipates in an informal way the basic possible-worlds analysis usually credited to Stalnaker and Lewis.

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                            • von Wright, G. H. “On Conditionals.” In Logical Studies. By G. H. von Wright 127–165. London: Routledge and Kegan Paul, 1957.

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                              Von Wright contends that, in the case of what he calls “potential conditionals,” we should not look for a proposition expressed by a conditional but should content ourselves with an account of the act of asserting a conditional. An act of asserting a conditional is an act of conditionally asserting the consequent. Conditional asserting is equated with asserting the corresponding material conditional without asserting or denying either antecedent or consequent.

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                              The Possible Worlds Approach

                              Stalnaker 1968 is Stalnaker’s pathbreaking presentation of his theory of conditionals. Lewis 1973a is Lewis’s monograph (anticipated by Lewis 1971, and summarized in Lewis 1973b), which uses a semantic apparatus similar to that of Stalnaker 1968. Both employ a form of possible worlds semantics. Both presume that possible worlds can be ordered in a many-dimensional similarity space in which distance measures similarity. On Stalnaker’s theory, a conditional “If p, then q” is true at a world w if and only if the nearest p-world to w is a q-world. (Stalnaker and Thomason 1970 is a formally precise exposition.) Lewis, on the other hand, defines systems of concentric “spheres” of worlds centering on a world w, and holds that a counterfactual conditional is true at a world if and only if either the antecedent is impossible or the corresponding material conditional is true throughout one of the spheres centering on w. This work by Stalnaker and Lewis gave new life to the debate about conditionals, both by bringing to bear the devices of possible worlds semantics and by raising questions about which forms of argument should be considered logically valid. More generally, they significantly raised the bar on technical precision. Pollock 1976 and Nute 1980 represent yet other ways of putting an ordering of possible worlds to work in accounting for conditionals.

                              • Lewis, David. “Completeness and Decidability of Three Logics of Counterfactual Conditionals.” Theoria 37 (1971): 74–85.

                                DOI: 10.1111/j.1755-2567.1971.tb00061.xSave Citation »Export Citation »E-mail Citation »

                                This paper includes a formulation of a semantics for Lewis’s preferred logic of conditionals in terms of a Stalnaker-like selection function, and thus affords a more direct comparison of his theory and Stalnaker’s than can be found in Lewis 1973a.

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                                • Lewis, David. Counterfactuals. Cambridge, MA: Harvard University Press, 1973a.

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                                  This book is a very thorough presentation of Lewis’s theory, including both intuitive motivations, comparisons to other theories, and a treatment of the logics generated by it and its variants.

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                                  • Lewis, David. “Counterfactuals and Comparative Possibility.” Journal of Philosophical Logic 2 (1973b): 418–446.

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                                    This is Lewis’s presentation of his theory in the form of a journal article. Also in Harper, et al. 1981 (cited under Collections).

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                                    • Nute, Donald. Topics in Conditional Logic. Dordrecht, The Netherlands: D. Reidel, 1980.

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                                      This is a technically precise treatment of logics of conditionals within the basic framework established by Stalnaker and Lewis. Nute favors a theory that, like Stalnaker’s, employs a selection function. The difference is that the range of the selection function consists of sets of worlds rather than individual worlds.

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                                      • Pollock, John L. Subjunctive Reasoning. Dordrecht, The Netherlands: D. Reidel, 1976.

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                                        Pollock holds that a subjunctive conditional is true if and only if for every world w such that the antecedent might be true at w, the consequent is true at w. He then analyzes “might” in terms of “subjunctive generalizations,” which he analyzes without reference to subjunctive conditionals.

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                                        • Stalnaker, Robert. “A Theory of Conditionals.” In Studies in Logical Theory: Essays. Edited by Nicholas Rescher, 98–112. American Philosophical Quarterly Monograph Series 2. Oxford: Blackwell, 1968.

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                                          This is the groundbreaking paper in which Stalnaker proposes that “If p, then q” is true at a world w if and only if the nearest world to w in which p is true is a world in which q is true. The paper is noteworthy also for proposing to test this theory on the basis of the forms of argument involving conditionals that it renders valid. Also in Harper, et al., 1981 and Jackson 1991 (cited under Collections).

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                                          • Stalnaker, Robert, and Richmond Thomason. “A Semantic Analysis of Conditional Logic.” Theoria 36 (1970): 23–42.

                                            DOI: 10.1111/j.1755-2567.1970.tb00408.xSave Citation »Export Citation »E-mail Citation »

                                            In this paper, Stalnaker and Thomason develop the semantics of Stalnaker 1968 in a formally precise way. The language for which Stalnaker and Thomason provide a precise semantics includes not only a conditional connective but also modal connectives and quantifiers.

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                                            The Differences between Stalnaker and Lewis

                                            Both Stalnaker and Lewis analyze subjunctive conditionals in terms of a relation of nearness between possible worlds. (Lewis takes the object of his analysis to be not subjunctive conditionals per se, but what he calls counterfactual conditionals.) Lewis rejects two assumptions that Stalnaker makes about the nearness relation. One of these is that for any proposition p there is a uniquely nearest possible world in which p (as opposed to there being several, all equally near). The other is that for any proposition p there is always a nearest possible world in which p (rather than an infinite sequence of ever-nearer worlds in which p, up to some limit). Stalnaker, but not Lewis, extends his analysis to indicative conditionals. Lewis assumes that most conditionals in indicative mood are material conditionals. Jackson 1987 defends this construal, and in the 1986 postscript to Lewis 1976 (cited under The Probability of Conditionals), Lewis endorses Jackson’s defense. Stalnaker 1975 argues that the difference between indicative conditionals and subjunctive conditionals is pragmatic; the difference is only that when we employ a subjunctive conditional we indicate that the nearest possible world in which the antecedent holds falls outside the “context set,” which is the set of possible worlds that models the speaker’s presuppositions. Thomason and Gupta 1980 suggest that indicatives and subjunctives contain the same underlying conditional operator; the difference lies in the application of tense operators. Stalnaker 1981 defends the uniqueness assumption. Nolan 2003 defends Stalnaker’s extension of his analysis to indicative conditionals but offers a different account of the pragmatic differences between indicatives and subjunctives.

                                            • Jackson, Frank. Conditionals. Oxford: Blackwell, 1987.

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                                              Jackson addresses apparent counterexamples to the treatment of indicative conditionals as material conditionals, saying that when we assert an indicative conditional we expect the probability of the corresponding material conditional to be high, and we also expect the probability of the material conditional given the antecedent to be high. This second condition is the “robustness” condition. Jackson addresses the problems that this theory faces in dealing with compounds formed from conditionals.

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                                              • Nolan, Daniel. “Defending a Possible Worlds Account of Indicative Conditionals.” Philosophical Studies 116 (2003): 215–269.

                                                DOI: 10.1023/B:PHIL.0000007243.60727.d4Save Citation »Export Citation »E-mail Citation »

                                                Nolan defends a treatment of indicative conditionals in terms of the nearest-worlds approach. What distinguishes indicative conditionals from subjunctive conditionals on his account is that in evaluating an indicative conditional we hold fixed our background knowledge so far as is compatible with entertaining the truth of the antecedent.

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                                                • Stalnaker, Robert. “Indicative Conditionals.” Philosophia 5 (1975): 269–286.

                                                  DOI: 10.1007/BF02379021Save Citation »Export Citation »E-mail Citation »

                                                  Stalnaker defends extending his analysis to indicative conditionals. A consequence of Stalnaker’s analysis is that the argument from “Either p or q” to “If not-p then q” is invalid. To defend this consequence, Stalnaker defines a notion of reasonable inference and claims that the argument in question is a reasonable inference even if it is not valid. For critical discussion of this claim, see Gauker 2005 (cited under Contextualist Approaches), chapter 4. Also in Harper, et al. 1981 and in Jackson 1991 (cited under Collections).

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                                                  • Stalnaker, Robert. “A Defense of Conditional Excluded Middle.” In Ifs. Edited by William H. Harper, Robert Stalnaker, and Glenn Pearce, 87–104. Dordrecht, The Netherlands: D. Reidel, 1981.

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                                                    A consequence of Stalnaker’s assumption that for any proposition p there is a uniquely nearest world in which p holds is that the sentence “Either if p then q or if p then not-q” is logically valid. In this paper Stalnaker defends that consequence against Lewis’s purported counterexamples.

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                                                    • Thomason, Richmond H., and Anil Gupta. “A Theory of Conditionals in the Context of Branching Time.” Philosophical Review 89 (1980): 65–90.

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                                                      Thomason and Gupta add tense operators to a language of conditionals and propose to give priority to past history in comparing the similarity of possible worlds. They propose that the difference between indicative conditionals and subjunctive conditionals about the past lies in the scope of the pastness operator. Also in Harper, et al. 1981 (cited under Collections).

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                                                      Ordering of Worlds

                                                      On the Stalnaker-Lewis approach, the truth conditions for a conditional (both kinds for Stalnaker, counterfactuals for Lewis) are defined in terms of a similarity relation between possible worlds. Thus, some of the critical discussion has focused on whether a suitable similarity relation can be defined. Fine 1975 showed that when similarity is judged naively, this approach yields intuitively wrong truth values for conditionals. Lewis 1979 responded with an account of similarity tailored to the needs of his theory of conditionals. Krasner and Heller 1994 and Elga 2001 argue that Lewis’s account of similarity still does not meet all desiderata.

                                                      • Elga, Adam. “Statistical Mechanics and the Asymmetry of Counterfactual Dependence.” Philosophy of Science 68.3 (September 2001): S313–S324.

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                                                        One of the results that Lewis had hoped to explain in Lewis 1979 was why the future counterfactually depends on the past, and not the other way around. Elga’s paper argues that Lewis failed to do that.

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                                                        • Fine, Kit. “Review of David Lewis’s Counterfactuals.” Mind 84 (1975): 451–458.

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                                                          In this review, Fine makes the observation that if similarity of worlds is judged naively, then on Lewis’s theory intuitively true counterfactuals will have to be deemed false. An example is the sentence, “If Nixon had pushed the button, then there would have been a nuclear holocaust.”

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                                                          • Krasner, Daniel, and Mark Heller. “The Miracle of Counterfactuals: Counterexamples to Lewis’s Theory of World Ordering.” Philosophical Studies 76 (1994): 27–43.

                                                            DOI: 10.1007/BF00989718Save Citation »Export Citation »E-mail Citation »

                                                            This paper produces counterexamples to Lewis’s account (in Lewis 1979) of the structure of systems of spheres of worlds.

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                                                            • Lewis, David. “Counterfactual Dependence and Time’s Arrow.” Noûs 13 (1979): 455–476.

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                                                              In this paper, Lewis answers the objection in Fine 1975 by describing an ordering of possible worlds that he expects would, in conjunction with his account of truth conditions, generate intuitively correct judgments regarding the truth values of counterfactual conditionals. Reprinted with a postscript in Lewis’s Philosophical Papers, Vol. 2 (Oxford: Oxford University Press, 1987). Also in Jackson 1991 (cited under Collections).

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                                                              Goodmanian Theories

                                                              A number of authors have tried to develop the basic idea presented in Goodman 1947 (cited under Early Work), which was that a counterfactual is true if the antecedent together with certain “cotenable” hypotheses imply the consequent. Rescher 1964, Turner 1981, and Kratzer 1981 all take on the task of defining cotenability, and Lewis 1981 explores the relation between Kratzer’s theory and the sort of theory he favors. Loewer 1979 defines logical consistency on the assumption that the relation of cotenability is given. Hinckfuss 1990 relativizes truth to sets of hypotheses.

                                                              • Hinckfuss, Ian. “Relevant Facts and Suppositions: A New Analysis of Conditionals.” Logique et Analyse 131–132 (1990): 215–241.

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                                                                Hinckfuss supposes that a conditional expresses a truth only given a set of relevant facts and a set of suppositions. Since the set of relevant facts is supposed to be not closed under entailment, the truth of p and q is not sufficient for the truth of “If p, then q.”

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                                                                • Kratzer, Angelika. “Partition and Revision: The Semantics of Counterfactuals.” Journal of Philosophical Logic 10 (1981): 201–216.

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                                                                  In Kratzer’s theory, worlds are associated with sets of propositions and the truth conditions of conditionals relative to a world are defined in terms of the subsets of the associated set that are consistent with the antecedent. Kratzer’s theory has come to be known as “premise semantics.”

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                                                                  • Lewis, David. “Ordering Semantics and Premise Semantics for Counterfactuals.” Journal of Philosophical Logic 10 (1981): 217–234.

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                                                                    Lewis argues that Kratzer’s semantics is equivalent to a variety of semantics formulated in terms of ordered sets of possible worlds.

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                                                                    • Loewer, Barry M. “Cotenability and Counterfactual Logics.” Journal of Philosophical Logic 8 (1979): 99–115.

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                                                                      Loewer accepts that, for the reasons Goodman gave, the truth conditions of counterfactual conditionals cannot be formulated in terms of cotenability. Nonetheless, he uses the notion of cotenability in a definition of a “good” set of sentences and defines logical consistency as membership in a good set.

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                                                                      • Rescher, Nicholas. Hypothetical Reasoning. Amsterdam: North-Holland, 1964.

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                                                                        Rescher addresses Goodman’s objection to Goodman’s own proposal by describing ways of forming consistent sets of sentences containing an assumption contrary to one’s own beliefs.

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                                                                        • Turner, Raymond. “Counterfactuals without Possible Worlds.” Journal of Philosophical Logic 10 (1981): 453–493.

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                                                                          Turner proposes to address Goodman’s cotenability problem in terms of an ordering of hypotheses by plausibility.

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                                                                          Conditional Assertion

                                                                          The suggestion in von Wright 1957 (cited under Early Work) that conditionals are conditional assertions has not much found favor. Edgington 1995 (cited under General Overviews) considers this idea on the way to her defense of the probabilistic approach. Belnap 1979 and Barker 1995 defend the approach, while Dummett 1958–1959 and Jeffrey 1963 criticize it.

                                                                          • Barker, Stephen J. “Towards a Pragmatic Theory of ‘If.’” Philosophical Studies 79 (1995): 185–211.

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                                                                            Barker defends the theory of conditional assertion by appeal to an analogy to conditional commands and conditional questions.

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                                                                            • Belnap, Nuel D., Jr., “Conditional Assertion and Restricted Quantification.” Noûs 4 (1979): 1–12.

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                                                                              Belnap extends the theory of conditional assertion to a language containing connectives other than conditionals.

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                                                                              • Dummett, Michael. “Truth.” Proceedings of the Aristotelian Society 59 (1958–1959): 141–162.

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                                                                                Dummett criticizes the thesis that conditionals are conditional assertions on the grounds that falsehood is nothing other than lack of truth.

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                                                                                • Jeffrey, Richard. “On Indeterminate Conditionals.” Philosophical Studies 14 (1963): 37–43.

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                                                                                  Jeffrey argues that if conditionals obey a reasonable logic then nothing is achieved by supposing that a conditional is “indeterminate” in value if the antecedent is false.

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                                                                                  The Probabilistic Theory

                                                                                  The probabilistic theory is directed primarily at indicative conditionals. The claim is that the semantics of indicative conditionals can be formulated only in the context of a semantics that eschews truth conditions altogether and treats logical implication as a relation of probability preservation. In this context, one can identify the probability of an indicative conditional “If p, then q” as the conditional probability of q given p. Adams 1975 is the canonical statement of the theory. It is defended in various ways in Gibbard 1981 and Edgington 1986. Adams 1989 places the theory in the context of a more general theory of probability logic.

                                                                                  • Adams, Ernest W. The Logic of Conditionals. Dordrecht, The Netherlands: D. Reidel, 1975.

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                                                                                    Adams extends the argument (begun in Adams 1965, cited under Early Work) for formulating the semantics of indicative conditionals in terms of probabilities. Here he also provides a fuller, precise treatment of probabilistic entailment, and he puts forward a hypothesis, also formulated in terms of probabilities, about counterfactual conditionals.

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                                                                                    • Adams, Ernest W. A Primer of Probability Logic. Stanford, CA: CSLI, 1989.

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                                                                                      This book aims at a general theory of probabilistic reasoning, both deductive and nonmonotonic. The logic of conditionals is dealt with in this context. Unfortunately, Adams’s treatment is still limited to conditionals not embedded under other connectives.

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                                                                                      • Edgington, Dorothy. “Do Conditionals Have Truth Conditions?” Critica 18 (1986): 3–30.

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                                                                                        Also included in Jackson 1991 (cited under Collections). Defenses of Adams’s analysis have featured arguments, such as those here, to the effect that indicative conditionals cannot have truth conditions at all. See also Bennett 2003 and Edgington 1995 (cited under General Overviews).

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                                                                                        • Gibbard, Alan. “Two Recent Theories of Conditionals.” In Ifs. Edited by William H. Harper, Robert Stalnaker, and Glenn Pearce, 211–247. Dordrecht, The Netherlands: D. Reidel, 1981.

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                                                                                          This paper defends the probabilistic analysis of indicative conditionals and the possible worlds analysis of subjunctive conditionals. However, it is perhaps most important as the source of the “Sly Pete” example. This is a story in which we seem to have equally good reasons to accept two conditionals that share an antecedent but have incompatible consequents. The puzzle is discussed in some detail in Bennett 2003 (cited under General Overviews).

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                                                                                          The Belief-Revision Theory

                                                                                          First in Gärdenfors 1978, and subsequently, more fully, in Gärdenfors 1988, Gärdenfors developed a theory of conditionals grounded in the concept of a belief set. The key idea, inspired by the Ramsey test, is that a conditional may belong to a set of beliefs if and only if the addition of the antecedent to that set of beliefs requires the addition of the consequent. A logic is determined inasmuch as certain conditions on the update of belief sets are supposed to hold, and these can entail that if any belief set contains a number of premises, then it cannot contain the negation of the conclusion as well. The primary technical challenge that the theory faces, a so-called triviality theorem, is in showing that all of a number of reasonable conditions on update can be satisfied together. Rott 1989, Hansson 1992, and Morreau 1992 question a variety of the assumptions underlying Gärdenfors’s triviality theorem. A thorough review of the issue may be found in Nute and Cross 2003 (cited under General Overviews).

                                                                                          • Hansson, Sven Ove. “In Defense of the Ramsey Test.” Journal of Philosophy 70 (1992): 522–540.

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                                                                                            Hansson proposes to avoid Gärdenfors’s reductio by distinguishing between belief sets and sets of sentences that a belief set “supports.”

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                                                                                            • Gärdenfors, Peter. “Conditionals and Changes of Belief.” In The Logic and Epistemology of Scientific Change. Edited by Ilkka Niiniluoto and Raimo Tuomela, 381–404. Acta Philosophica Fennica 30.2–4. Amsterdam: North-Holland, 1978.

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                                                                                              This is Gärdenfors early, hopeful statement of his approach.

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                                                                                              • Gärdenfors, Peter. Knowledge in Flux: Modeling the Dynamics of Epistemic States. Cambridge, MA: MIT Press, 1988.

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                                                                                                This is the culmination of Gärdenfors’s own work in the area, which poses the central challenge that all subsequent work has attempted to address.

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                                                                                                • Morreau, Michael. “Epistemic Semantics for Counterfactuals.” Journal of Philosophical Logic 21 (1992): 33–62.

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                                                                                                  Morreau proposes to avoid Gärdenfors’s reductio by denying that the set of belief set is closed under expansions.

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                                                                                                  • Rott, Hans. “Conditionals and Theory Change: Revisions, Expansions and Additions.” Synthese 81 (1989): 91–113.

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                                                                                                    Rott proposes to avoid Gärdenfors’s reductio by abandoning the assumption that if not-A is not in a belief set, then the result of expanding a belief-set by adding A is a subset of the result of expanding a belief-set by adding “A or B.”

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                                                                                                    Dynamic Semantics

                                                                                                    A near neighbor of the belief-revision theory is the theory of dynamic semantics, which holds that a semantic theory may take the form of an account of the ways in which accepting a sentence results in an update of one’s beliefs. Veltman 1986 defines the truth conditions of conditionals in terms of a tree structure that reflects possible information updates; von Fintel 1999 uses the idea to account for purported asymmetries in the order in which conditionals may be uttered; Gillies 2004 defines an indicative conditional as a test rather than as an update; Veltman 2005 uses a similar idea in a treatment of counterfactual conditionals.

                                                                                                    • Gillies, Thony. “Epistemic Conditionals and Conditional Epistemics.” Noûs 38 (2004): 585–616.

                                                                                                      DOI: 10.1111/j.0029-4624.2004.00485.xSave Citation »Export Citation »E-mail Citation »

                                                                                                      Gillies holds that while some sentences specify an alteration that is to be made to a set of beliefs upon acceptance, others merely provide a test on a set of beliefs, to make sure that it is as it should be. An indicative conditional, Gillies proposes, is such a test.

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                                                                                                      • Veltman, Frank. “Data Semantics and the Pragmatics of Indicative Conditionals.” In On Conditionals. Edited by Elizabeth Closs Traugott, Alice ter Meulen, Judy Snitzer Reilly, and Charles A. Ferguson, 147–168. Cambridge, UK: Cambridge University Press, 1986.

                                                                                                        DOI: 10.1017/CBO9780511753466Save Citation »Export Citation »E-mail Citation »

                                                                                                        Veltman defines an information model as a partially ordered set of information states. An indicative conditional is true in such a model at a state s if and only if at every state s′ beyond s, if the antecedent is true at s′, then the consequent is not false at s′.

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                                                                                                        • Veltman, Frank. “Making Counterfactual Assumptions.” Journal of Semantics 22 (2005): 159–180.

                                                                                                          DOI: 10.1093/jos/ffh022Save Citation »Export Citation »E-mail Citation »

                                                                                                          Veltman, like Gillies, holds that a conditional is a test. But Veltman uses this idea differently, to obtain a theory of counterfactual conditionals rather than indicative conditionals.

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                                                                                                          • von Fintel, Kai. “Counterfactuals in a Dynamic Context.” In Ken Hale: A Life in Language. Edited by Michael Kenstowicz, 123–152. Cambridge, MA: MIT Press, 1999.

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                                                                                                            Working within the basic conception introduced by Stalnaker, von Fintel wants to allow that successive counterfactual conditionals may update the space of worlds with respect to which a counterfactual is evaluated.

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                                                                                                            Contextualist Approaches

                                                                                                            Many theorists have had the thought that somehow the truth conditions of a conditional must be relativized to context. Even from the standpoint of the Stalnaker-Lewis theory, one might allow that truth is relative to a contextually determined space of possible worlds and a similarity metric on that space. Döring 1997 argues that this relativization is implicit in Stalnaker’s appeal to the Ramsey test. However, a more thoroughly contextualist treatment will utilize the relativization of context to dispense with the appeal to the similarity relation on sets of possible worlds. Moreover, a thorough relativization will not, as Goodmanian approaches do, simply define absolute truth conditions for conditionals by letting the antecedent and a fixed background generate a set of hypotheses relative to which the consequent is evaluated; rather, it will relativize the truth conditions of conditionals to variable contexts. Barwise 1986 and Lycan 2001 both seem to introduce such relativizations in the context of an informal account of the meaning of conditionals. Likewise, Tichy 1984 and Lowe 1995 acknowledge the need for such a relativization, although they do not make it explicit in their accounts of truth conditions. Tichy 1984 diagnoses purported counterexamples to the argument form Contraposition as resting on a surreptitious shift in the context relative to which the premise and the conclusion are evaluated, and Lowe 1995 finds such a shift between the premises in purported counterexamples to Hypothetical Syllogism. The Goodmanian approaches of both Kratzer 1981 and Hinckfuss 1990 (cited under Goodmanian Theories) also relativize the truth conditions of conditionals to context. The first attempt to defend a semantics of conditionals by means of a recursive definition of semantic value relative to a context for a simple language is Gauker 1987, which was superseded by the different approach taken in Gauker 2005.

                                                                                                            • Barwise, Jon. “Conditionals and Conditional Information.” In On Conditionals. Edited by Elizabeth Closs Traugott, Alice ter Meulen, Judy Snitzer Reilly, and Charles A. Ferguson, 21–54. Cambridge, UK: Cambridge University Press, 1986.

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                                                                                                              Barwise holds that conditionals express “constraints” on situations (in his sense of “situation”). However, on any particular occasion on which a conditional sentence is used to make an assertion, it will be grounded in a particular situation that will restrict the class of situations on which the conditional imposes its constraints.

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                                                                                                              • Döring, Frank. “The Ramsey Test and Conditional Semantics.” Journal of Philosophical Logic 26 (1997): 359–376

                                                                                                                DOI: 10.1023/A:1017935520602Save Citation »Export Citation »E-mail Citation »

                                                                                                                In Stalnaker 1968 (cited under The Possible Worlds Approach), Stalnaker had claimed that his theory of conditionals amounts to an endorsement of the Ramsey test. Döring argues that it does not do that unless we inject an element of context-relativity into the semantics in a way Stalnaker did not do.

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                                                                                                                • Gauker, Christopher. “Conditionals in Context.” Erkenntnis 27 (1987): 293–319.

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                                                                                                                  This is probably the earliest attempt to defend a theory of conditionals formulated as a recursive definition of semantic value relative to a context for a simple language. (McGee 1985, cited under Valid Forms of Argument Containing Conditionals, has a recursive definition, but McGee does not defend it.) As in Lowe 1983 (cited under Lowe versus Wright on Hypothetical Syllogism) and Tichy 1984, that relativization is used to explain away apparent counterexamples to Hypothetical Syllogism and Contraposition.

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                                                                                                                  • Gauker, Christopher. Conditionals in Context. Cambridge, MA: MIT Press, 2005.

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                                                                                                                    Gauker defines contexts as structures built up from linguistic entities and defines them in such a way that contexts may contain other contexts. Logically valid arguments are those that preserve “assertibility in a context.” Gauker defines the conditions under which indicative and subjunctive conditionals are assertible relative to a context. Considering a wide variety of argument forms, Gauker argues that his theory generates the correct logic for natural language conditionals.

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                                                                                                                    • Lowe, E. J. “The Truth about Counterfactuals.” Philosophical Quarterly 45 (1995): 41–59.

                                                                                                                      DOI: 10.2307/2219847Save Citation »Export Citation »E-mail Citation »

                                                                                                                      Lowe denies that there is a logical difference between indicative and subjunctive conditionals and analyzes “If p, then q” as true if and only if necessarily either not-p or q and either possibly p or necessarily q. He accommodates context-relativity by allowing the domain of worlds over which necessity is defined to vary with context.

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                                                                                                                      • Lycan, William G. Real Conditionals. Oxford: Oxford University Press, 2001.

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                                                                                                                        Lycan translates sentences of English into sentences of first-order logic. He supposes that a context picks out a set R of “events.” “If p, then q” says that for every event in R, if p is “in” it, then so is q. As Lycan acknowledges, his theory has the result that modus ponens is invalid (because the event in which p is true may not be in R).

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                                                                                                                        • Tichy, Pavel. “Subjunctive Conditionals: Two Parameters vs. Three.” Philosophical Studies 45 (1984): 147–179.

                                                                                                                          DOI: 10.1007/BF00372476Save Citation »Export Citation »E-mail Citation »

                                                                                                                          Tichy holds that conditionals must be evaluated relative to a “contextually determined” parameter, and at one point he endorses a relativization of the truth of conditionals to “a class of indicative auxiliary premises.” However, in the formal presentation of his own theory, he proposes that the antecedent of a conditional contains contextually determined “tacit content.”

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                                                                                                                          Material Conditionals

                                                                                                                          Grice 1989 (cited under Early Work) attempted to defend from apparent counterexamples the thesis that natural-language indicative conditionals are material conditionals. Other authors, including those below, have attempted to argue that indicative conditionals must be material conditionals. Hanson 1991 and Barker 1997 make a case for the identification of conditionals with material conditionals by appeal to other logical features of language. See also Jackson 1987 (cited under The Differences between Stalnaker and Lewis).

                                                                                                                          Valid Forms of Argument Containing Conditionals

                                                                                                                          Arguments for or against an analysis of conditionals often turn on questions of which forms of argument containing conditionals ought to be validated. This is often what is at issue in the papers listed in this bibliography. A fairly comprehensive review of the forms of argument that have been at issue is in Gauker 2005 (cited under Contextualist Approaches), chapter 3. The following are a few additional sources not listed elsewhere in this bibliography. McGee 1985 and Lycan 1993 question the validity of modus ponens, while Katz 1999 defends it. MacKay and van Inwagen 1977 and Cross 2009 take stands on other questions of what is valid.

                                                                                                                          Lowe versus Wright on Hypothetical Syllogism

                                                                                                                          One of Stalnaker’s seemingly most persuasive arguments for his analysis of conditionals (in Stalnaker 1968, cited under The Possible Worlds Approach) was that it seemed to account for the apparent invalidity of Hypothetical Syllogism for counterfactual conditionals (also called Transitivity). In this exchange between Wright and Lowe, it emerges that the right way to defend Hypothetical Syllogism against purported counterexamples is to relativize the content of conditional sentences to context. Lowe 1983 disputes the purported counterexamples to Hypothetical Syllogism without yet appealing to context-relativity. Wright 1983 disputes the purported counterexamples by relativizing the truth of a counterfactual to a contextually determined range of worlds. Wright 1984, responding to the provocation of Lowe 1984, clarifies Wright’s position. Lowe 1990 takes Wright’s proposal on board in an account of the truth-conditions of conditionals.

                                                                                                                          • Lowe, E. J. “A Simplification of the Logic of Conditionals.” Notre Dame Journal of Formal Logic 24 (1983): 357–366.

                                                                                                                            DOI: 10.1305/ndjfl/1093870380Save Citation »Export Citation »E-mail Citation »

                                                                                                                            Lowe observes that the premises of these purported counterexamples appear to equivocate on the choice of “suppressed premises.”

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                                                                                                                            • Lowe, E. J. “Wright versus Lewis on the Transitivity of Counterfactuals.” Analysis 44 (1984): 183–185.

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                                                                                                                              Lowe interprets Wright 1983 as relativizing validity to context and presses his own “suppressed premises” diagnosis of the apparent counterexamples.

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                                                                                                                              • Lowe, E. J. “Conditionals, Context, and Transitivity.” Analysis 50 (1990): 80–87.

                                                                                                                                DOI: 10.2307/3328851Save Citation »Export Citation »E-mail Citation »

                                                                                                                                Lowe takes on board Wright’s relativization of the truth of conditionals to context, proposing that a conditional is true relative to a set of worlds if and only if the strict conditional evaluated relative to that set of worlds is true.

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                                                                                                                                • Wright, Crispin. “Keeping Track of Nozick.” Analysis 43 (1983): 134–140.

                                                                                                                                  DOI: 10.2307/3327431Save Citation »Export Citation »E-mail Citation »

                                                                                                                                  In the context of a critique of Nozick’s conception of knowledge, Wright defends the validity of Hypothetical Syllogism by suggesting that in the apparent counterexamples the two premises will be evaluated as true only relative to different ranges of possible worlds.

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                                                                                                                                  • Wright, Crispin. “Comment on Lowe.” Analysis 44 (1984): 183–184.

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                                                                                                                                    Wright replies to Lowe that he had relativized truth, not validity, to context of utterance.

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                                                                                                                                    The Probability of Conditionals

                                                                                                                                    A natural thought, expressed in Stalnaker 1970, would be to combine a theory of the truth conditions of conditionals with the claim that the probability of a conditional “If p, then q” equals the conditional probability of q given p. Lewis 1976 showed that under very reasonable conditions that equation cannot hold, and this result was generalized in various ways in Lewis 1986, Hájek 1989, and Döring 1994. This result does not directly challenge Ernst Adams’s program (in Adams 1975, cited under The Probabilistic Theory), which proposes to dispense with truth conditions altogether in favor of probability assignments.

                                                                                                                                    The Difference between Indicative and Subjunctive Conditionals

                                                                                                                                    It is generally acknowledged that our semantic theories must distinguish between two kinds of conditionals. Most theorists draw the distinction on the basis of mood––indicative versus subjunctive. V. H. Dudman has argued that this is a mistake. The traditional distinction classifies conditionals of the form “If … does … , then … will … ,” together with “If … did … , then … did … ”; while Dudman holds that they should be classified with conditionals of the form “If … had … , then … would … .” Dudman 1984 and Dudman 1994 present a kind of informal semantics in defense of Dudman’s taxonomy, while Dudman 1988 criticizes the distinction between the subjunctive and indicative moods that underlies the traditional distinction. Bennett 1988 is Bennett’s defense of Dudman, and Bennett 1995 is Bennett’s repudiation of his earlier defense. Cross 2002 takes on Dudman’s swift argument in Dudman 2000. Both Bennett 2003 (Cited under General Overviews), chapter 2, and Gauker 2005 (cited under Contextualist Approaches), chapter 7, review this subject and conclude that the division based on mood is correct.

                                                                                                                                    “Even if” Conditionals

                                                                                                                                    “Even if” conditionals seem to have logical properties different from ordinary conditionals. Inasmuch as we would expect a theory of “even if” to be a product of theories of “even” and of “if,” giving a plausible theory of “even if” constrains our theories of “if,” although the question has not always been approached in this way. Bennett 1982 treats “even” as making only a pragmatic, not a semantic, contribution. Both Barker 1991 and Lycan 1991 dispute this and offer characterizations of the semantic contribution of “even.” Kay 1990 is not about conditionals, but offers a sophisticated treatment of the meaning of “even.” Gauker 2005 (cited under Contextualist Approaches), chapter 8, details a semantic theory for “even,” which is then combined with Gauker’s account of “if.”

                                                                                                                                    Quantified Conditionals

                                                                                                                                    The combination of quantifiers and conditionals is not entirely straightforward. Lewis 1975 is an influential treatment. Higginbotham 2003 explores some of the fine points, and von Fintel 1998 illustrates the polemical uses of Lewis’s treatment. See also Stalnaker and Thomason 1970 (cited under The Possible Worlds Approach and Gauker 2005 (cited under Contextualist Approaches).

                                                                                                                                    • Higginbotham, James. “Conditionals and Compositionality.” Philosophical Perspectives 17 (2003): 181–194.

                                                                                                                                      DOI: 10.1111/j.1520-8583.2003.00008.xSave Citation »Export Citation »E-mail Citation »

                                                                                                                                      Higginbotham examines the difference between pairs of sentences such as “Every professor will retire early if offered a generous pension” and “Every professor offered a generous pension will retire early.”

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                                                                                                                                      • Lewis, David. “Adverbs of Quantification.” In Formal Semantics of Natural Language. Edited by Edward Keenan, 3–15. Cambridge, UK: Cambridge University Press, 1975.

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                                                                                                                                        Lewis argues that in sentences such as “Often, if a donkey kicks a man who owns it, he beats it,” we should not think of the quantifier as binding a sentence containing a conditional operator; rather, the “if”-clause restricts the application of an operator such as “often” or “in every case.”

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                                                                                                                                        • von Fintel, Kai. “Quantifiers and ‘If’-Clauses.” Philosophical Quarterly 48 (1998): 209–214.

                                                                                                                                          DOI: 10.1111/1467-9213.00095Save Citation »Export Citation »E-mail Citation »

                                                                                                                                          Von Fintel criticizes Barker 1997 (cited under Material Conditionals) based on Lewis 1975.

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                                                                                                                                          The Meaning of “Then” in Conditionals

                                                                                                                                          Some theorists contend that there is a difference in meaning between “If p, q” and “If p, then q. Davis 1993 argues that the “then” affects truth conditions, whereas Iatridou 1994 maintains that it has to do with presuppositions.

                                                                                                                                          • Davis, Wayne A. “Weak and Strong Conditionals.” Pacific Philosophical Quarterly 64 (1993): 57–71.

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                                                                                                                                            Davis holds that, with certain exceptions, the “then” in “If p, then q” ensures that if that conditional is true, then both “If p, q” and “If not-q, not-p” are true.

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                                                                                                                                            • Iatridou, Sabine. “On the Contribution of Conditional Then.” Natural Language Semantics 2 (1994): 171–199.

                                                                                                                                              DOI: 10.1007/BF01256742Save Citation »Export Citation »E-mail Citation »

                                                                                                                                              Iatridou follows Lewis 1975 (cited under Quantified Conditionals) in assuming that “if”-clauses restrict the application of an operator. She holds that “then” carries the presupposition that the negation of the antecedent does not likewise restrict the operator.

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                                                                                                                                              The Presuppositions of Conditionals

                                                                                                                                              Conditionals raise special questions for theories of presupposition, inasmuch as a conditional as a whole may fail to carry the presuppositions of its components (which are then not “projected”). This is a large topic in its own right, of which the items below provide only a sample. It is relevant to the semantics of conditionals in part because the dynamic approach to conditionals has its origins in attempts to deal with the presuppositions of conditionals. Heim 1983 represents the tradition in dynamic semantics that conceives of meanings as rules for updating sets of possible worlds. Van der Sandt 1992 represents a very different tradition in dynamic semantics that conceives of meanings as recipes for constructing mental representations. Gauker 2008 is skeptical about the whole problematic.

                                                                                                                                              • Gauker, Christopher. “Against Accommodation: Heim, van der Sandt, and the Presupposition Projection Problem.” Philosophical Perspectives 22 (2008): 171–205.

                                                                                                                                                DOI: 10.1111/j.1520-8583.2008.00145.xSave Citation »Export Citation »E-mail Citation »

                                                                                                                                                Gauker argues that presuppositions are not projected at all.

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                                                                                                                                                • Heim, Irene. “On the Projection Problem for Presupposition.” In Proceedings of the West Coast Conference on Formal Linguistics. Edited by Daniel P. Flickinger, Michael Barlow, and Michael T. Wescoat, 114–126. Stanford, CA: Stanford Linguistics Association, Dept. of Linguistics. Stanford University, 1983.

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                                                                                                                                                  Heim treats presuppositions as admissibility conditions on update. Reprinted in Pragmatics: A Reader, edited by Steven Davis (Oxford: Oxford University Press, 1991).

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                                                                                                                                                  • van der Sandt, Rob A. “Presupposition Projection as Anaphora Resolution.” Journal of Semantics 9 (1992): 333–377.

                                                                                                                                                    DOI: 10.1093/jos/9.4.333Save Citation »Export Citation »E-mail Citation »

                                                                                                                                                    Van der Sandt treats presuppositions as content that can occupy various positions in a discourse representation.

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                                                                                                                                                    Linguistic Taxonomies

                                                                                                                                                    The syntax of conditionals does not seem to be an especially active area within linguistics. Here, however, are a couple of treatments from different traditions within linguistics. Declerck and Reed 2001 attempts to categorize many examples, whereas Iatridou 2000 seeks a more theoretical perspective.

                                                                                                                                                    • Declerck, Renaat, and Susan Reed. Conditionals: A Comprehensive Empirical Analysis. New York: Mouton de Gruyter, 2001.

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                                                                                                                                                      This book is an elaborate taxonomy of kinds of conditionals; however, it is not grounded in any particular semantic theory.

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                                                                                                                                                      • Iatridou, Sabine. “The Grammatical Ingredients of Counterfactuality.” Linguistic Inquiry 31 (2000): 231–270.

                                                                                                                                                        DOI: 10.1162/002438900554352Save Citation »Export Citation »E-mail Citation »

                                                                                                                                                        In many languages, counterfactuality is indicated by means of what is traditionally regarded as past tense and pluperfect morphology. Iatridou offers an interesting hypothesis to explain why that is so.

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                                                                                                                                                        Causation and Conditionals

                                                                                                                                                        In the Critique of Pure Reason, Immanuel Kant held that the category of causality underwrites conditional judgments. Some such thesis is often assumed as well by nonspecialists. Mackie 1962 asserts the connection as well and attempts to explain it. However, in recent times, probably only Tichy 1978 proposes a serious analysis of conditionals in terms of causality. More often the reverse order of analysis has been proposed: subjunctive conditionals are utilized in an analysis of causality. There is an extensive literature on that subject, but because it belongs more to the subject of causation than to the subject of conditionals, only Lewis 1973 is listed here.

                                                                                                                                                        • Lewis, David. “Causation.” Journal of Philosophy 70 (1973): 556–567.

                                                                                                                                                          DOI: 10.2307/2025310Save Citation »Export Citation »E-mail Citation »

                                                                                                                                                          This paper, which has spawned a large literature, asserts that c is the cause of e if and only if there is a causal chain leading from c to e, where the links in the causal chain are events such that if the first had not happened then the second would not have happened.

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                                                                                                                                                          • Mackie, J. L. “Counterfactuals and Causal Laws.” In Analytical Philosophy. Edited by R. J. Butler, 66–80. Oxford: Blackwell, 1962.

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                                                                                                                                                            Mackie has his own account of counterfactual assertions, but his paper is remembered for its observation that causal laws support counterfactuals while accidental generalizations do not.

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                                                                                                                                                            • Tichy, Pavel. “A New Theory of Subjunctive Conditionals.” Synthese 37 (1978): 433–457.

                                                                                                                                                              DOI: 10.1007/BF00873249Save Citation »Export Citation »E-mail Citation »

                                                                                                                                                              Tichy takes causal relations as primitive, and in terms of them explains the truth conditions of subjunctive conditionals.

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                                                                                                                                                              The Psychology of Conditionals

                                                                                                                                                              The study of reasoning with and about conditionals is a minor subdiscipline within cognitive psychology. Unfortunately, there has been very little cross-talk between philosophers and psychologists on this subject. Evans and Over 2005 is a representative, recent example.

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