It is argued that indicative conditionals are best viewed as having truth conditions (and so they are in part factual) but that these truth conditions are ‘gappy’ which leaves an explanatory gap that can only be filled by epistemic considerations (and so indicative conditionals are in part epistemic). This dual nature of indicative conditionals gives reason to rethink the relationship between logic viewed as a descriptive discipline (focusing on semantics) and logic viewed as a discipline with a normative import (focusing (...) on epistemic notions such as ‘reasoning’, ‘beliefs’ and ‘assumptions’). In particular, it is argued that the development of formal models for epistemic states can serve as a starting point for exploring logic when viewed as a normative discipline. (shrink)

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of (...) indicatives and relies on the notion of causal (in)dependence. (shrink)

The debate over Hypothetical Syllogism is locked in stalemate. Although putative natural language counterexamples to Hypothetical Syllogism abound, many philosophers defend Hypothetical Syllogism, arguing that the alleged counterexamples involve an illicit shift in context. The proper lesson to draw from the putative counterexamples, they argue, is that natural language conditionals are context-sensitive conditionals which obey Hypothetical Syllogism. In order to make progress on the issue, I consider and improve upon Morreau’s proof of the invalidity of Hypothetical Syllogism. The improved proof (...) relies upon the semantic claim that conditionals with antecedents irrelevant to the obtaining of an already true consequent are themselves true. Moreover, this semantic insight allows us to provide compelling counterexamples to Hypothetical Syllogism that are resistant to the usual contextualist response. (shrink)

The so-called ‘Adams’ Thesis’ is often understood as the claim that the assertibility of an indicative conditional equals the corresponding conditional probability—schematically: $${({\rm AT})}\qquad\qquad\quad As(A\rightarrow B)=P({B|A}),{\rm provided}\quad P(A)\neq 0.$$ The Thesis is taken by many to be a touchstone of any theorizing about indicative conditionals. Yet it is unclear exactly what the Thesis is . I suggest some precise statements of it. I then rebut a number of arguments that have been given in its favor. Finally, I offer a new (...) argument against it. I appeal to an old triviality result of mine against ‘Stalnaker’s Thesis’ that the probability of a conditional equals the corresponding conditional probability. I showed that for all finite-ranged probability functions, there are strictly more distinct values of conditional probabilities than there are distinct values of probabilities of conditionals, so they cannot all be paired up as Stalnaker’s Thesis promises. Conditional probabilities are too fine-grained to coincide with probabilities of conditionals across the board. If the assertibilities of conditionals are to coincide with conditional probabilities across the board, then assertibilities must be finer-grained than probabilities. I contend that this is implausible—it is surely the other way round. I generalize this argument to other interpretations of ‘ As ’, including ‘acceptability’ and ‘assentability’. I find it hard to see how any such figure of merit for conditionals can systematically align with the corresponding conditional probabilities. (shrink)

RÉSUMÉ: Les philosophes, au cours des cinquante dernières années, se sont efforcés de démontrer qu’un professeur peut, d’une manière cohérente et exacte, annoncer à ses étudiants qu’un examen surprise aura lieu lors d’une journée non spécifiée d’une période donnée, le problème étant qu’une telle annonce peut sembler s’annuler ellemême lorsqu’elle est soumise à une induction régressive. Deux grandes approches, l’une épistémique et l’autre logique, one été développées à ce propos. Le présent article adopte une approche logique, mais repose aussi d’une (...) manière cruciale sur une compréhension épistémique du problème, pour essayer de montrer que l’annonce du professeur peut effectivement être cohérente et exacte. (shrink)

In contemporary discussions of the Ramsey Test for conditionals, it is commonly held that (i) supposing the antecedent of a conditional is adopting a potential state of full belief, and (ii) Modus Ponens is a valid rule of inference. I argue on the basis of Thomason Conditionals (such as ' If Sally is deceiving, I do not believe it') and Moore's Paradox that both claims are wrong. I then develop a double-indexed Update Semantics for conditionals which takes these two results (...) into account while doing justice to the key intuitions underlying the Ramsey Test. The semantics is extended to cover some further phenomena, including the recent observation that epistemic modal operators give rise to something very like, but also very unlike, Moore's Paradox. (shrink)

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

This paper explores the interaction of well-motivated (if controversial) principles governing the probability conditionals, with accounts of what it is for a sentence to be indefinite. The conclusion can be played in a variety of ways. It could be regarded as a new reason to be suspicious of the intuitive data about the probability of conditionals; or, holding fixed the data, it could be used to give traction on the philosophical analysis of a contentious notion—indefiniteness. The paper outlines the various (...) options, and shows that ‘rejectionist’ theories of indefiniteness are incompatible with the results. Rejectionist theories include popular accounts such as supervaluationism, non-classical truth-value gap theories, and accounts of indeterminacy that centre on rejecting the law of excluded middle. An appendix compares the results obtained here with the ‘impossibility’ results descending from Lewis ( 1976 ). (shrink)

§0. A familiar if obscure idea: an indicative conditional presents its consequent as holding in the actual world on the supposition that its antecedent so holds, whereas a subjunctive conditional merely presents its consequent as holding in a world, typically counterfactual, in which its antecedent holds. Consider this pair.

Something about this argument sounds funny. As we’ll see, though, it takes some care to identify exactly what Moore has done wrong. Iwill assume that Moore knows premise (2) to be true. One could inquire into how he knows it, and whether that knowledge can be defeated; but Iwon’t. I’ll focus instead on what epistemic relations Moore has to premise (1) and to his conclusion (3). It may matter which epistemic relations we choose to consider. Some philosophers will diagnose Moore’s (...) argument using Contextualist machinery. They’ll say. (shrink)

The work of the late Paul Grice (1913–1988) exerts a powerful influence on the way philosophers, linguists, and cognitive scientists think about meaning and communication. With respect to a particular sentence φ and an “utterer” U, Grice stressed the philosophical importance of separating (i) what φ means, (ii) what U said on a given occasion by uttering φ, and (iii) what U meant by uttering φ on that occasion. Second, he provided systematic attempts to say precisely what meaning is by (...) providing a series of more refined analyses of utterer’s meaning, sentence meaning, and what is said. Third, Grice produced an account of how it is possible for what U says and what U means to diverge. Fourth, by characterizing a philosophically important distinction between the “genuinely semantic” and “merely pragmatic” implications of a statement, Grice clarified the relationship between classical logic and the semantics of natural language. Fifth, he provided some much needed philosophical ventilation by deploying his notion of “implicature” to devastating effect against certain overzealous strains of “Ordinary Language Philosophy,” without himself abandoning the view that philosophy must pay attention to the nuances of ordinary talk. Sixth, Grice undercut some of the most influential arguments for a philosophically significant notion of “presupposition.” Today, Grice’s work lies at the center of research on the semantics-pragmatics distinction and shapes much discussion of the relationship between language and mind. In a nutshell, Grice has forced philosophers and linguists to think very carefully about the sorts of facts a semantic theory is supposed to account for and to reflect upon the most central theoretical notions, notions that otherwise might be taken for granted or employed without due care and attention. To be sure, Grice’s own positive proposals have their weaknesses; but in the light of his work any theory of meaning that is to be taken at all seriously must now draw a sharp line between genuinely semantic facts and facts pertaining to the nature of human interaction.. (shrink)

Various writers have proposed that the notion of a possible world is a functional concept, yet very little has been done to develop that proposal. This paper explores a particular functionalist account of possible worlds, according to which pluralities of possible worlds are the bases for structures which provide occupants for the roles which analyse our ordinary modal concepts. It argues that the resulting position meets some of the stringent constraints which philosophers have placed upon accounts of possible worlds, while (...) also trivializing the question what possible worlds are. The paper then discusses a range of problems facing the functionalist position. (shrink)

Proponents of the projection strategy take an epistemic rule for the evaluation of English conditionals, the Ramsey test, as clue to the truth-conditional semantics of conditionals. They also construe English conditionals as stronger than the material conditional. Given plausible assumptions, however, the Ramsey test induces the semantics of the material conditional. The alleged link between Ramsey test and truth conditions stronger than those of the material conditional can be saved by construing conditionals as ternary, rather than binary, propositional functions with (...) a hidden contextual parameter. But such a ternary construal raises problems of its own. (shrink)

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.

In "Backward causation and the Stalnaker-Lewis approach to counterfactuals," Analysis 62 (2002): 191–97, Michael Tooley argues that if a certain kind of backward causation is possible, then a Stalnaker-Lewis style comparative world similarity account of the truth conditions of counterfactuals cannot be sound. Tooley’s target is one particular type of semantics, but, as I show, the significance of Tooley’s example goes well beyond its consequences for any one semantics for the conditional.

A comprehensive theory ofeven if needs to account for consequent ‘entailing’even ifs and in particular those of theif-focused variety. This is where the theory ofeven if ceases to be neutral between conditional theories. I have argued thatif-focusedeven ifs,especially if andonly if can only be accounted for through the suppositional theory ofif. Furthermore, a particular interpretation of this theory — the conditional assertion theory — is needed to account foronly if and a type of metalinguistic negation ofQ if P. We therefore (...) have evidence that the currently accepted approaches to conditionals are basically wrong about the semantic forms they attribute toif P, Q.11. (shrink)

The phrase ‘autoepistemic logic’ was introduced in Moore [1985] to refer to a study inspired in large part by criticisms in Stalnaker [1980] of a particular nonmonotonic logic proposed by McDermott and Doyle.1 Very informative discussions for those who have not encountered this area are provided by Moore [1988] and the wide-ranging survey article Konolige [1994], and the scant remarks in the present introductory section do not pretend to serve in place of those treatments as summaries of the field. A (...) good deal of the material omitted here pertains to the specifically nonmonotonic nature of autoepistemic logic as standardly developed, but as we shall urge, there is from one point of view nothing distinctively nonmonotonic about the basic motivating ideas of the subject. (shrink)

The hypothetical syllogism is invalid in standard interpretations of conditional sentences. Many arguments of this sort are quite compelling, though, and you can wonder what makes them so. I shall argue that it is our parsimony in regard to connections among events and states of affairs. All manner of things just might, for all we know, be bound up with one another in all sorts of ways. But ordinarily it is better, being simpler, to assume they are unconnected. In so (...) doing, we jump to the conclusions of some compelling but invalid arguments. (shrink)

IntroductionThe project of giving an account of meaning in natural languages goes largely by assigning truth-conditional content to sentences. I will call the view that sentences have truth-conditional content propositionalism as it is common to identify the truth-conditional content of a sentence with the proposition it expresses. This content plays an important role in our explanations of the speech-acts, attitude ascriptions, and the meaning of sentences when they appear as parts of longer sentences. Much work in philosophy of language and (...) linguistics semantics over the last half-century has aimed to characterize the truth-conditional content of different aspects of language.There are different kinds of worries one might have about this project. There are general methodological worries about truth-conditional semantics that have had some currency in the philosophical literature. In my view, the enormous progress in semantics made in its brief history suggests these are misplaced. Ho .. (shrink)

Bayesians have a seemingly attractive account of rational credal states in terms of coherence. An agent's set of credences are synchronically coherent just in case they conform to the probability calculus. Some Bayesians impose a further putative coherence constraint called regularity: roughly, if X is possible, then it is assigned positive probability. I look at two versions of regularity – logical and metaphysical – and I canvass various defences of it as a rationality norm. Combining regularity with synchronic coherence, we (...) have a set of constraints known as strict coherence.I argue that strict coherence is untenable. In particular, I attack regularity as a rationality norm. First, I rebut each of the various defences of regularity. Then I argue directly against regularity: it conflicts with the Bayesian decision‐theoretic treatment of rational action. Thus, seemingly plausible theoretical and pragmatic norms turn out to be inconsistent.[Barbossa is about to kill Will,but Jack Sparrow shows up:]Barbossa: It's not possible!Jack: Not probable.To be uncertain is to be uncomfortable,but to be certain is to be ridiculous. (shrink)

Byrne's approach to the semifactual conditional captures the reasoning data. However, we argue that it does not account for the processes or principles by which people arrive at representations of even-if conditionals, upon which their reasoning is said to be based. Drawing upon recent work on the suppositional conditional we present such an account.

A number of papers have argued in favour of the material account of indicative conditionals, but typically they either concentrate on defending the account from the charge that it has counterintuitive consequences, or else focus on some particular positive argument in favour of the theory. In this paper, I survey the various positive arguments that can be given, presenting simple versions where possible and showing the connections between them. I conclude with some methodological considerations.

I interpret Mill?s view on logic as the instrumentalist view that logical inferences, complex statements, and logical operators are not necessary for reasoning itself, but are useful only for our remembering and communicating the results of the reasoning. To defend this view, I first show that we can transform all the complex statements in the language of classical first-order logic into what I call material inference rules and reduce logical inferences to inferences which involve only atomic statements and the material (...) inference rules. Then I explain why we introduce logical operators and logical inference rules into a system of the latter kind. In the end I determine what kind of negation is justified from this point of view. (shrink)

In the recent literature on Moore's Proof of an external world, it has emerged that different diagnoses of the argument's failure are prima facie defensible. As a result, there is a sense that the appropriateness of the different verdicts on it may depend on variation in the kinds of context in which the argument is taken to be a move, with different characteristic aims. In this spirit, Martin Davies has recently explored the use of the argument within two different epistemic (...) projects called respectively ‘deciding what to believe’ and ‘settling the question’. Depending on which project is in hand, according to Davies, the diagnoses of its failure—if indeed it fails—will differ. I believe that, by introducing the idea that the effectiveness of a valid argument may be epistemic project-relative, Davies has pointed the way to an important reorientation of the debates about Moore's Proof. But I wish to take issue with much of the detail of his proposals. I argue that Davies's characterization of his two projects is misleading (§1), and his account of their distinction defective (§2). I then canvass some suggestions about how it may be improved upon and about how further relevant kinds of epistemic projects in which Moore's argument may be taken to be a move can be characterized, bringing out how each of these projects impinges differently on the issue of the Proof's failure and of its diagnosis (§§3 and 4). In conclusion (§5) I offer an overview of the resulting terrain. (shrink)

In his 1987 book _Conditionals, Frank Jackson presents an argument to the effect that the indicative conditionals of natural language have the same truth conditions as the material conditional of truth-functional logic. This Jackson refers to as the "paradox of indicative conditionals." I offer a solution to this paradox by arguing that some conditionals that appear to be in the indicative mood are actually subjunctives, to which the paradox does not apply. I support this proposed solution with some historical observations (...) on the evolution of the English verb phrase. (edited). (shrink)

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)

Let us call a statement of the form ‘If A was, is, or will be the case, then C was, is, or will be the case’ an indicative conditional. And let us call a statement of the form ‘If A had been, were, or were to be the case, then C would have been, would be, or would come to be the case’ a subjunctive, or counterfactual, conditional.

A number of epistemologists have recently concluded that a piece of reasoning may be epistemically permissible even when it is impossible for the reasoning subject to present her reasoning as an argument without begging the question. I agree with these epistemologists, but argue that none has sufficiently divorced the notion of begging the question from epistemic notions. I present a proposal for a characterization of begging the question in purely pragmatic terms.

I present some counterexamples to Adams's Thesis and explain how they undermine arguments that indicative conditionals cannot be truth-evaluable propositions.

The work of Hugh MacColl (1837–1909) suffered the same fate after his death as before it:despite being vaguely alluded to and in part even commended, on the whole it has remained an unknown quantity. Even worse, those of his ideas which have played a decisive role in the history of logic have been credited to his successors; this is especially the case with the definition of strict implication and the first formal development of formal modal logic. This paper takes an (...) initial step towards a rectification of this unfortunate misrepresentation, presenting a bibliography of MacColl’s most significant publications with particular regard to their reception. (shrink)

It is known that indicative and subjunctive conditionals interact differently with a rigidifying "actually" operator. The paper studies this difference in an abstract setting. It does not assume the framework of possible world semantics, characterizing "actually" instead by the type of logically valid formulas to which it gives rise. It is proved that in a language with such features all sentential contexts that are congruential (in the sense that they preserve logical equivalence) are extensional (in the sense that they preserve (...) material equivalence). For a subjunctive conditional, the natural conclusion to draw is that it is non-congruential. It is much harder to defend the claim that an indicative conditional is non-congruential. The pressure to treat the indicative conditional as truth-functional is correspondingly greater. The implications of these results for attempts to interpret the indicative conditional as an epistemic or doxastic operator are assessed. (shrink)

What has sometimes been called the "standard" argument for fatalism never achieved the critical popularity of Richard Taylor's (1962) infamous argument. But it has enjoyed far greater longevity. In De Fato Cicero (1960) tells us it was known in ancient Greece as the "idle argument", for it purports to show the futility of attempting to control one's fate and, hence, those persuaded by it could be led to a life of inaction and idleness. Even with such antiquated credentials, however, the (...) argument continues to exercise fine contemporary minds (e.g. Schlesinger 1993). (shrink)

It is argued that expressivists can solve their problems in accounting for the unity and autonomy of logic – logic is topic independent and does not derive from a general ‘logic’ of mental states – by adopting an analysis of the logical connectives that takes logically complex sentences to express complex combinations of simple attitudes like belief and disapproval and dispositions to form such simple attitudes upon performing suppositional acts, and taking acceptance and rejection of sentences to be the common (...) mental denominator in descriptive and evaluative discourse, and structural requirements governing these to be the basis for logic. Such an account requires that attitudes like belief, intention and disapproval can come in hypothetical mode – plausibly linked to the capacity to mentally simulate or emulate one's own attitudes – and, if correct, suggests that these form the basic building blocks for our capacity to understand logically complex sentences. (shrink)

Conditionals somehow express conditional beliefs. However, conditional belief is a bi-propositional attitude that is generally not truth-evaluable, in contrast to unconditional belief. Therefore, this article opts for an expressivistic semantics for conditionals, grounds this semantics in the arguably most adequate account of conditional belief, that is, ranking theory, and dismisses probability theory for that purpose, because probabilities cannot represent belief. Various expressive options are then explained in terms of ranking theory, with the intention to set out a general interpretive scheme (...) that is able to account for the most variegated usage of conditionals. The Ramsey test is only the first option. Relevance is another, familiar, but little understood item, which comes in several versions. This article adds a further family of expressive options, which is able to subsume also counterfactuals and causal conditionals, and indicates at the end how this family allows for partial recovery of truth conditions for conditionals. (shrink)

The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan thesis (...) sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)

ArgumentThis paper argues that ancient Babylonian signs (omens) reflect a mode of inferential reasoning as a function of their syntactic and logical structure as conditionals. Taking into account the institutional context that produced a systematic written body of omens, the paper is principally interested in the cognitive disposition of such texts. Investigating what constitutes system in these works, formal aspects of the material are examined in terms of the nature of conditionals and the logic of conditional statements. It is argued (...) that conditional statements about ominous phenomena speak as much to a notion of conceivability and possibility as to empirical physical actuality. It is claimed that the epistemological character of the Babylonian compendia of signs cannot be understood without due attention to epistemic possibility and further, that the cuneiform omen texts comprise a different kind of scientific knowledge from that limited to a knowledge of physical phenomena and their laws. (shrink)

V.H. Dudman has argued that a better semantic account of the conditional emerges from placing grammar ‘in the driver's seat’. His account of their grammar identifies two main categories, which differ from those postulated by traditional theorists, and which he claims correspond to two very different and deep‐rooted styles of thought. I show that it is unlikely that a perfect match exists between styles of thought and grammatical categories in the way that Dudman postulates. I consider arguments by Dale and (...) Edgington in this context. More importantly, however, I also show that even if there were a perfect match, Dudman's account would still obscure semantic similarities between ‘if’‐sentences which are arguably of greater importance than the ones he highlights. This, I suggest, has implications extending far beyond Dudman's work. (shrink)

God, by definition, is all-powerful, all-good, all-wise, and all-knowing. Therein lies a problem for the theist, of course, for every one of these attributes has been the subject of fierce debate. In this paper I want to return to the debate by introducing a new problem for the idea that anyone could have the kind of perfect knowledge God is supposed to have. What distinguishes my problem from others is that the sort of knowledge it focuses on is self-knowledge, hence (...) knowledge of a particularly intimate kind. My claim is that God cannot have infallible knowledge of at least some of his own perfections, in particular his being all-wise or ideally rational. Such ignorance is not only inconsistent with the usual conception of God's omniscience, given that whatever knowledge God possesses is traditionally thought to be be a priori and infallible, but, more importantly, is inconsistent with the fundamental idea that God at least knows infallibly or incorrigibly that he has what it takes to be God: qualities such as omnibenevolence, omnipotence, and supreme wisdom. In short, my claim is that God must have a deep “blindspot” about his own nature, something which is inconsistent with a traditional picture of that nature. (shrink)

I advance a pragmatic account of begging the question according to which a use of an argument begs the question just in case it is used as a statement of inference and it fails to state an inference the arguer or an addressee can perform given what they explicitly believe. Accordingly, what begs questions are uses of arguments as statements of inference, and the root cause of begging the question is an argument’s failure to state an inference performable by the (...) reasoners the arguer targets. In these ways, my account is distinguished from other pragmatic accounts. By taking the defect of a question-begging use of an argument to be its failure to state its purported inference, my account highlights in a unique way why question-begging is not an epistemic defect, and why it is not a fallacy, understood as a mistake in reasoning. These points have been made elsewhere, but I believe that their plausibility is enhanced by considering begging the question as nullifying the role of an argument as a statement of inference. Since question-begging uses of arguments fail to state their purported inferences, using an argument in a question-begging-way is not a ratiocinative mistake. This undermines accounts of begging the question that adopt an epistemic approach. (shrink)