Truth-Conditional Accounts of Indicative Conditionals

This paper is a guide to the main ideas and innovations in Robert Stalnaker's "Indicative Conditionals". The paper is for a volume of essays on twenty-one classics of formal semantics edited by Louise McNally, Yael Sharvit and Zoltàn Gendler Szabò.

This paper presents a new theory of the truth conditions for indicative conditionals. The theory allows us to give a fairly unified account of the semantics for indicative and subjunctive conditionals, though there remains a distinction between the two classes. Put simply, the idea behind the theory is that the distinction between the indicative and the subjunctive parallels the distinction between the necessary and the a priori. Since that distinction is best understood formally using the resources of two-dimensional modal logic, (...) those resources will be brought to bear on the logic of conditionals. (shrink)

This is a handbook article about conditionals.

This is a handbook article about indicative conditionals.

Richard Bradley offers a quick and convincing argument that no Boolean semantic theory for conditionals can validate a very natural principle concerning the relationship between cre- dences and conditionals. We argue that Bradley’s principle, Preservation, is, in fact, invalid; its appeal arises from the validity of a nearby, but distinct, principle, which we call Local Preservation, and which Boolean semantic theories can non-trivially validate.

A part of Stalnaker (1968)’s influential theory of conditionals has been neglected, namely the role for an accessibility relation between worlds. I argue that the accessibility relation does not play the role intended for it in the theory as stated, and propose a minimal revision which solves the problem, and brings the theory in line with the formulation in Stalnaker & Thomason 1970.

This collection introduces the reader to some of the most interesting current work on conditionals. Particular attention is paid to possible world semantics for conditionals, the role of conditional probability in helping us to understand conditionals, implicature and the material conditional, and subjunctive versus indicative conditionals. Contributors include V.H. Dudman, Dorothy Edgington, Nelson Goodman, H.P. Grice, David Lewis, and Robert Stalnaker.

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

Lewis argued that ‘there is no way to interpret a conditional connective so that, with sufficient generality, the probabilities of conditionals will equal the appropriate conditional probabilities’. However, as Lewis and others have subsequently recognized, Lewis' triviality results go through only on the assumption that ‘if’ is not context-sensitive. This leaves a question that has not been adequately addressed: what are the prospects of a context-sensitive theory of ‘if’ that complies with Stalnaker's thesis? I offer one interesting constraint on any (...) such theory. I argue that no context-sensitive theory satisfies Stalnaker's thesis if it satisfies three plausible assumptions: first, that the truth of an indicative is determined by the world of evaluation and by the set of worlds in the relevant epistemic context in which the antecedent is true; second, that one can learn an indicative conditional without learning that the antecedent and consequent are both true; third, that belief revision is conservative in the sense that it does not reduce the probabilities to zero unnecessarily. The result gives us a clearer picture of the real costs of a truth-conditional context-sensitive Stalnaker's thesis-compliant semantics. (shrink)

The dominance conditional 'If I drink the contents of cup A, I will drink more than if drink the contents of cup B' is true if we know that the first cup contains more than the second. In the first part of the paper, I show that only one kind of theory of indicative conditionals can explain this fact — a Stalnaker-type semantics. In the second part of the paper, I show that dominance conditionals can help explain a long-standing mystery: (...) the question of how one-boxers and two-boxers are guided by conditionals to their respective answers to the Newcomb problem. I will suggest that both implicitly appeal to a decision theoretic principle I will call the Dominance Norm (DN), a principle that connects indicative dominance conditionals with rational courses of action. Finally, I show that DN in combination with a Stalnaker-type theory of indicatives commits us to the two-boxing answer in the Newcomb problem. (shrink)

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...) of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction introduction (...) do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material. (shrink)

The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. In (...) this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false. (shrink)

This paper presents the first possible world semantics for concessive conditionals (i.e., even if A, C conditionals) constructed in a compositional way. First, the meaning of if is formalized through a semantics that builds on the proposal given by Stalnaker (1968). A major difference from Stalnaker’s approach is that irrelevant conditionals (i.e., conditionals where the antecedent and the consequent have no connection) are false in this new setting. Second, the meaning of even is analyzed through a formal semantics based on (...) the notion of scale. This analysis overcomes the problems arising in standard approaches, in which even is analyzed with the help of pragmatic presuppositions. Finally, the two particles are combined in order to provide a formal analysis of even if. This theory predicts the major phenomena concerning the behavior of concessive conditionals and without any call to pragmatic explanations. More generally, this approach creates the possibility of a compositional analysis of other conditionals such as if then or only if forms. (shrink)

In this paper Grice's requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz's conclusion-relevant consequence relation.

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

In this paper I look at indicative nested whether-conditionals, sentences like:If I pass the exam, I will pass whether I pray or not.The behavior of ‘if’ in these examples is to be contrasted with the behavior of ‘if’ in or-to-if conditionals:If Mary is at home or at work, then if she is not at home, she is at work.I argue that no currently available semantics for indicative conditionals can explain both the behavior of ‘if’ in nested whether-conditionals and the behavior (...) of ‘if’ in or-to-ifs. We need a theory that predicts both. While no currently available theory makes the right predictions, one theory comes close—Heim’s rendition of Stalnaker’s semantics :183–221, 1992). I show how to fix Heim’s view to get the right results for all cases. In sum, the paper argues for a particular development of Stalnaker’s semantics, and shows that whether-conditionals cannot be dealt with on other approaches. (shrink)

At the center of the literature on conditionals lies the division between indicative and subjunctive conditionals, and Ernest Adams’ famous minimal pair: If Oswald didn’t shoot Kennedy, someone else did. If Oswald hadn’t shot Kennedy, someone else would have. While a lot of attention is paid to figuring out what these different kinds of conditionals mean, significantly less attention has been paid to the question of why their grammatical differences give rise to their semantic differences. In this paper, I articulate (...) and defend an answer to this question that illuminates and unifies the meanings of both kinds of conditionals. The basic idea is that epistemic and metaphysical possibilities differ with respect to their interaction with time, such that there can be present epistemic possibilities with different pasts, while present metaphysical possibilities share the same past. The interpretation of conditionals is subject to a pragmatic constraint that rules out interpretations in which their consequents are directly settled by information used to build their domains. The past + future morphology on subjunctives, but not indicatives, is what allows them to receive a metaphysical interpretation in light of this pragmatic constraint. The resulting theory predicts several surprising features of indicatives and subjunctives, which I argue are correct. (shrink)

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

Section 1 briefly examines three theories of indicative conditionals. The Suppositional Theory is defended, and shown to be incompatible with understanding conditionals in terms of truth conditions. Section 2 discusses the psychological evidence about conditionals reported by Over and Evans (this volume). Section 3 discusses the syntactic grounds offered by Haegeman (this volume) for distinguishing two sorts of conditional.

Discusses how to capture the link between the probability of indicative conditionals and conditional probability using a classical semantics for conditionals.

Adams Thesis has much evidence in its favour, but David Lewis famously showed that it cannot be true, in all but the most trivial of cases, if conditionals are proprositions and their probabilities are classical probabilities of truth. In this paper I show thatsimilar results can be constructed for a much wider class of conditionals. The fact that these results presuppose that the logic of conditionals is Boolean motivates a search for a non-Boolean alternative. It is argued that the exact (...) proposition expressed by a conditional depends on the context in which it is uttered. Consequentlyits probability of truth will depend not only on the probabilities of the various propositions it might express, but also on the probabilities of the contexts determining which proposition it does in fact express.The semantic theory developed from this is then shown to explain why agents degrees of belief satisfyAdams Thesis. Finally the theory is compared with proposals for a three-valued logic of conditionals. (shrink)

Reasoning with indicative conditionals, i.e., with statements such as 'If the weather is bad, then the plane will be late', constitutes a significant part of ordinary reasoning. How are we to proceed in the logical treatment of ordinary language arguments involving indicative conditionals? In particular, is standard formal truth-functional sentential logic applicable to these conditionals, and if so, under what circumstances? This dissertation first examines two sharply contrasting theories proposed in response to these questions. One of them is the dominant (...) view, primarily identified with H. P. Grice and Frank Jackson, which defends the traditional truth-functional treatment of indicative conditionals and also endorses the application of formal logic to them. The other theory, upheld primarily by Ernest Adams, claims that the formal truth-functional logic is inapplicable to indicative conditionals and that their proper treatment requires a special probabilistic logic. Through a critique of both of these theories, I show that these extreme approaches are defective and unsatisfactory. I argue that the main benefit of having such philosophical theories of indicative conditionals can be achieved at a much lower cost by what may be called a common sense account of indicative conditionals. The common-sense account rejects the idea that indicative conditionals in their 'true logical form' are truth-functional material conditionals. It nonetheless endorses the applicability of formal truth-functional logic to ordinary conditional reasoning. On behalf of common-sense account, I argue that the two issues, the assumption of truth-functionality of indicative conditionals and applicability of formal truth-functional logic to them, do not rise or fall together. (shrink)

Grice's arguments that ordinary language indicative conditionals are logically equivalent to material conditionals are criticized. It is agreed that 'indirectness conditions' going beyond the material conditional can "sometimes" be detached' from ordinary language conditionals, but it is argued that this is not always possible. An example in which a speaker who knows that some mushrooms are non-poisonous tells a hearer "if you eat those mushrooms you will be poisoned", causing the hearer not to eat the mushrooms, is discussed, and it (...) is argued that this utterance should be regarded as factually unsatisfactory', and therefore, by Grice's own standards, false. (shrink)

In this dissertation a correct answer is sought to the question, 'When, in general terms, is an English conditional true?' The search was motivated largely by three apparent inadequacies in the most prominent proposed "semantics" for English conditionals. First, most such semantics counter-intuitively count as true all conditionals with necessarily false antecedents and/or necessarily true consequents. Secondly, no prominent semantics is designed to deal with "probabilistic" conditionals, conditionals like 'If he had fallen, he probably would have laughed.' Thirdly, most prominent (...) semantics counter-intuitively count as true conditionals with antecedents which do not appear to be "appropriately relevant" to their consequences. ;In Chapter I, the common view is defended that English conditionals can be divided into two semantically-distinct classes, the "indicative" and the "subjective" conditionals, although the question whether these classes are actually distinguished by mood is left open. In Chapters II through IV, the "material implication" analysis, Ernest Adams' analysis, and the theories of Peter Gardenfors and Ken Warmbrod regarding "indicative" conditionals are all criticized. In Chapter V, a new semantics for "indicative" conditionals is developed. A "probabilistic" indicative conditional, as they're typically used, is true exactly when its consequent has the appropriate probability "on" the conditional's antecedent "relative to" the conditional's "intended background," and the antecedent is "appropriately relevant" to the consequent. A non-probabilistic indicative conditional is true when the conditional's consequent is certain "on" the conditional's antecedent, relative to the conditional's "intended background," and the antecedent is "appropriately relevant" to the consequent. ;In Chapter VI, consequences of this semantics for the logic of these conditionals are worked out. In Chapter VII, the semantics of David Lewis and Robert Stalnaker for "subjective" conditionals are criticized. In Chapter VIII, a new semantics for "subjunctive" conditionals is proposed, a semantics which is only a slight variation of the semantics given in Chapter V for "indicative" conditionals. Finally, in Chapter IX, new accounts of entailment and logical probability are proposed in order to yield intuitively-correct truth values for conditionals with necessarily false antecedents and/or necessarily true consequents. (shrink)

This article focuses on defective conditionals ? namely indicative conditionals whose antecedents are false and whose truth-values therefore cannot be determined. The problem is to decide which formal connective can adequately represent this usage. Classical logic renders defective conditionals true whereas traditional mathematics dismisses them as irrelevant. This difference in treatment entails that, at the propositional level, classical logic validates some sentences that are intuitively false in plane geometry. With two proofs, I show that the same flaw is shared by (...) a family of trivalent logics. I go on to examine the strict conditional and its derivatives. This family is the only one to avoid the faulty inference but it does so without addressing the status of the truth-value assigned to defective conditionals. (shrink)

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. It is hence not surprising that conditional logics – logics specifically designed to account for natural language conditionals – are an active and interdisciplinary area. The present book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics. For that purpose a range of topics are discussed such as Bennett’s arguments against truth value based semantics for indicative conditionals.

After Ibn-sina, Moslem logicians started to develop and expand the Sinan logic. In discussing the conditionals they have come closer to the field of logic by avoiding some of the ontological views in the Sinan logic. However they have tried to clarity the conditionals the conditions for their truth and the quality of the validity of universality and particularity and to determine the place of affirmation and negation in conditional propositions through using an ordinary language. For the first time they (...) divided contingent propositions in to general and particular types and in explaining the conditions for their truth they made a distinction between the universal and particular conjunctive implications. With respect to the issue of the criteria for universality they distinguished between general and necessary contingents and referred to a separate criterion for each. They have also considered such criteria on the basis of the time and quality of the state of the proposition as it is stated and not as it is assumed.In addition to explaining the views of Moslem logicians this paper also undertakes to prove that Islamic logic didn't die after Ibn-Rushd; rather, alongside with the growth of Islamic philosophy it has continued its life up to the present time. (shrink)

Grice argues that indicative conditionals ‘if p then q’ have conventional, truth conditional meaning according to the material conditional ‘p  q’. In order to explain away the known paradoxes with this interpretation, he distinguishes between truth conditions and assertion conditions, attempting to demonstrate that the assumed connection between ‘p’ and ‘q’ (the Indirectness Condition) is a conversational implicature; hence a matter only relevant for the assertion conditions of a conditional. This paper argues that Grice fails to demonstrate i) that (...) the Indirectness Condition is cancellable, hence a conversational implicature, ii) that the Indirectness Condition is not part of the conventional, truth-relevant meaning of ‘if’, and accordingly, iii) semantic or logical equivalence between indicative and material conditionals. (shrink)

If you read this abstract, then you will understand what my essay is about. Under what conditions would the preceding assertion be a lie? Traditional definitions of lying are always applied to straight declaratives such as ‘The dog ate my homework’. This one sided diet of examples leaves us unprepared for sentences in which conditional probability governs assertibility. The truth-value of conditionals does not play a significant role in the sincere assertion of conditionals. Lying is insincere assertion. So the connection (...) between lying and falsehood is broken when lying with conditionals. Drawing on Frank Jackson's account of indicative conditionals. I argue that it is possible to lie with true conditionals by virtue of their false conventional implicatures. False conversational implicatures only guarantee misleading assertions, not lies. Lying remains a semantic rather than a pragmatic affair. (shrink)

According to orthodox semantics, to know the meaning of a sentence is to know its truth-conditions. Against this view I observe that we typically do not know the truth-conditions of the sentences we understand. We do not know the truth-conditions, for instance, of empty definite descriptions, non-declaratives, subjunctive conditionals, causal ascriptions, belief ascriptions, probability statements, figurative language, category mistakes, normative judgments, or vague statements. Appealing to tacit knowledge does not help, for the problem goes beyond our inability to articulate complete (...) truth-conditions: even full knowledge of the world’s condition would leave us unable to say whether an arbitrary sentence was true or false. (shrink)