We propose a new account of indicativeconditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, (...) provided that (ii) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)
This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicativeconditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.
I propose an account of indicativeconditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a (...) Lewisian system of spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: that a conditional is logically independent from its antecedent; that a sequence of antecedents behaves like a single conjunctive antecedent ; and that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. (shrink)
It is argued that indicativeconditionals 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 indicativeconditionals are in part epistemic). This dual nature of indicativeconditionals 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)
While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the ?defective truth-table? in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous (...) inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us?namely that when conditional-free ? entails conditional-free ?, ?if ? then ?? is a trivial, uninformative truth?we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicativeconditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional. (shrink)
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)
I defend the view that the truth conditions of the ordinary indicative conditional are those of the material conditional. This is done via a discussion of assertability and by appeal to conventional implicature rather than conversational implicature.
Conditionals are sentences of the form 'If A, then B', and they play a central role in scientific, logical, and everyday reasoning. They have been in the philosophical limelight for centuries, and more recently, they have been receiving attention from psychologists, linguists, and computer scientists. In spite of this, many key questions concerning conditionals remain unanswered. While most of the work on conditionals has addressed semantical questions - questions about the truth conditions of conditionals - this (...) book focuses on the main epistemological questions that conditionals give rise to, such as: what are the probabilities of conditionals? When is a conditional acceptable or assertable? What do we learn when we receive new conditional information? In answering these questions, this book combines the formal tools of logic and probability theory with the experimental approach of cognitive psychology. It will be of interest to students and researchers in logic, epistemology, and psychology of reasoning. (shrink)
Recent ideas about epistemic modals and indicativeconditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's  semantic consequence (...) relation for a language with epistemic modals and indicativeconditionals. In the other direction, the formal semantics for indicativeconditionals due to Kolodny and MacFarlane  gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)
I discuss an argument given by Dorothy Edgington for the conclusion that indicativeconditionals cannot express propositions. The argument is not effective against Robert Stalnaker's context-dependent propositional theory. I isolate and defend the feature of Stalnaker's theory that allows it to evade the argument.
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)
This paper falls into two parts. In the first part, I argue that consideration of general indicativeconditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content (...) – assumed to be merely (p⊃q) – and the conversational implicature contents which utterance of if p, q may gain in certain contexts. I also defend the pragmatic approach against a recent objection by Edgington that appeal to pragmatics cannot explain what we are inclined to say about the believability conditions, as opposed to the assertability conditions, of indicative if p, q. (shrink)
In this article, I present a schema for generating counterexamples to the argument form known as Hypothetical Syllogism with indicativeconditionals. If my schema for generating counterexamples to HS works as I think it does, then HS is invalid for indicativeconditionals.
We will look at several theories of indicativeconditionals grouped into three categories: those that base its semantics on its logical counterpart (the material conditional); intensional analyses, which bring in alternative possible worlds; and a third subgroup which denies that indicativeconditionals express propositions at all. We will also look at some problems for each kind of approach.
An agent who receives information in the form of an indicative conditional statement and who trusts her source will modify her credences to bring them in line with the conditional. I will argue that the agent, upon the acquisition of such information, should, in general, expand her prior credence function to an indeterminate posterior one; that is, to a set of credence functions. Two different ways the agent might interpret the conditional will be presented, and the properties of the (...) resulting indeterminate posteriors compared. The cause of the expansion from a single prior credence function to a set of credence functions forming the indeterminate posterior one will be explained. The expansion undermines the Bayesian dogma that the result of assimilating new information into a determinate prior credence functions is always a determinate posterior one. (shrink)
There is a new Bayesian, or probabilistic, paradigm in the psychology of reasoning, with new psychological accounts of the indicative conditional of natural language. In psychological experiments in this new paradigm, people judge that the probability of the indicative conditional, P(if A then C), is the conditional probability of C given A, P(C | A). In other experiments, participants respond with what has been called the 'de- fective' truth table: they judge that if A then C is true (...) when A holds and C holds, is false when A holds and C does not, and is neither true nor false when A does not hold. We argue that these responses are not 'defective' in any negative sense, as many psychologists have implied. We point out that a number of normative researchers, including de Finetti, have proposed such a table for various coherent interpretations of the third value. We review the relevant general tables in the normative literature, in which there is a third value for A and C and the logically compound forms of the natural language conditional, negation, conjunction, disjunction, and the material conditional. We describe the results of an experiment on which of these tables best describes ordinary people's judgements when the third value is interpreted as indicating uncertainty. (shrink)
One very popular kind of semantics for subjunctive conditionals is aclosest-worlds account along the lines of theories given by David Lewisand Robert Stalnaker. If we could give the same sort of semantics forindicative conditionals, we would have a more unified account of themeaning of ``if ... then ...'' statements, one with manyadvantages for explaining the behaviour of conditional sentences. Such atreatment of indicativeconditionals, however, has faced a battery ofobjections. This paper outlines a closest-worlds account of (...) indicativeconditionals that does better than some of its cousins in explaining thebehaviour of such conditionals. The paper then discusses objectionsoffered by Dorothy Edgington and Frank Jackson to closest-worldsaccounts of indicativeconditionals, and shows that these objections canbe met by the account outlined. (shrink)
Stalnaker's 1975 motivates an account of the truth conditions of indicativeconditionals that seems in tension with the truth-conditions he offers. This paper discusses how best to resolve this tension.
A conversation can be conceived as aiming to circumscribe a set of possibilities that are relevant to the goals of the conversation. This set of possibilities may be conceived as determined by the goals and objective circumstances of the interlocutors and not by their propositional attitudes. An indicative conditional can be conceived as circumscribing a set of possibilities that have a certain property: If the set of relevant possibilities is subsequently restricted to one in which the antecedent holds, then (...) it will be restricted as well to one in which the consequent holds. We will identify a number of desiderata concerning the validity of arguments; we will develop a formally precise semantics for conditionals conceived in this way that satisfies the desiderata, and we will present a deductive calculus that is sound and complete with respect to the semantics. Finally, we will argue that the semantics compares well, both formally and foundationally, with two other semantic theories of indicativeconditionals that satisfy the desiderata, namely, those of Gillies and Bledin. (shrink)
In his 1987 book _Conditionals, Frank Jackson presents an argument to the effect that the indicativeconditionals of natural language have the same truth conditions as the material conditional of truth-functional logic. This Jackson refers to as the "paradox of indicativeconditionals." 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 argues that two widely accepted principles about the indicative conditional jointly presuppose the falsity of one of the most prominent arguments against epistemological iteration principles. The first principle about the indicative conditional, which has close ties both to the Ramsey test and the “or-to-if” inference, says that knowing a material conditional suffices for knowing the corresponding indicative. The second principle says that conditional contradictions cannot be true when their antecedents are epistemically possible. Taken together, these (...) principles entail that it is impossible to be in a certain kind of epistemic state: namely, a state of ignorance about which of two partially overlapping bodies of knowledge corresponds to one’s actual one. However, some of the more popular “margin for error” style arguments against epistemological iteration principles suggest that such states are not only possible, but commonplace. I argue that the tension between these views runs deep, arising just as much for non-factive attitudes like belief, presupposition, and certainty. I also argue that this is worse news for those who accept the principles about the indicative conditional than it is for those who reject epistemological iteration principles. (shrink)
Grice's arguments that ordinary language indicativeconditionals 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)
For an indicative conditional to be true it is not generally sufficient that its antecedent be false or its consequent true. I propose to analyse such a conditional as strong, i.e. as containing a tacit quantification over a domain of possible situations, with the if-clause specifying that domain such that the conditional gets assigned the appropriate truth conditions. Now, one definition of logical consequence proceeds in terms of a natural-language conditional. Interpreting it as strong leads to a paraconsistent consequence (...) relation, though the motivation behind it is not to reason coherently about contradictions but to reason entirely without them. (shrink)
In this paper I explore a version of standard (expected utility) decision theory in which the probability parameter is interpreted as an objective chance believed by agents to obtain and values of this parameter are fixed by indicativeconditionals linking possible actions with possible outcomes. After reviewing some recent developments centering on the common-cause counterexamples to the standard approach, I introduce and briefly discuss the key notions in my own approach. (This approach has essentially the same results as (...) the causal approach in common-cause cases.) I then discuss the Rule of Dominance and find, in the context of the present proposal, that it cannot serve as an independent source of action justification. Turning next to Newcomb''s Problem, I argue that the much discussed issue of back-tracking counterfactuals is something of a red herring for decision theory. Once the twin distractions of back-tracking counterfactuals and Dominance Reasoning are set aside the 1-box solution emerges as a natural consequence of the present proposal. It is of interest that this proposal agrees with the causal approach in the standard common-cause examples and the expected-utility approach in the Newcomb case: one can be smart and rich and keep on smoking. (shrink)
A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic and so allows the conditional to embed in arbitrarily complex sentences. The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL. The expressivist framework extends the AGM (...) framework for belief revision and so provides a categorical epistemology for conditionals that complements McGee’s probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data while integrating both expressivist and semanticist perspectives. (shrink)
A few purported counterexamples to the Adams thesis have cropped up in the literature in the last few decades. I propose a theory that accounts for them, in a way that makes the connections between indicativeconditionals and counterfactuals clearer.
*This work is no longer under development* Two major themes in the literature on indicativeconditionals are that the content of indicativeconditionals typically depends on what is known;1 that conditionals are intimately related to conditional probabilities.2 In possible world semantics for counterfactual conditionals, a standard assumption is that conditionals whose antecedents are metaphysically impossible are vacuously true.3 This aspect has recently been brought to the fore, and defended by Tim Williamson, who uses (...) it in to characterize alethic necessity by exploiting such equivalences as: A⇔¬A A. One might wish to postulate an analogous connection for indicativeconditionals, with indicatives whose antecedents are epistemically impossible being vacuously true: and indeed, the modal account of indicativeconditionals of Brian Weatherson has exactly this feature.4 This allows one to characterize an epistemic modal by the equivalence A⇔¬A→A. For simplicity, in what follows we write A as KA and think of it as expressing that subject S knows that A.5 The connection to probability has received much attention. Stalnaker suggested, as a way of articulating the ‘Ramsey Test’, the following very general schema for indicativeconditionals relative to some probability function P: P = P 1For example, Nolan ; Weatherson ; Gillies. 2For example Stalnaker ; McGee ; Adams. 3Lewis. See Nolan for criticism. 4‘epistemically possible’ here means incompatible with what is known. 5This idea was suggested to me in conversation by John Hawthorne. I do not know of it being explored in print. The plausibility of this characterization will depend on the exact sense of ‘epistemically possible’ in play—if it is compatibility with what a single subject knows, then can be read ‘the relevant subject knows that p’. If it is more delicately formulated, we might be able to read as the epistemic modal ‘must’. (shrink)
In his interesting paper, Duca argues that even though people don't apply a logical rule of inference – contraposition- when they try to solve the Wason task, they may be using another kind of formal strategy in terms of probabilistic relations between the antecedent and the consequent. It is suggested that there are two ways of intepreting this task – one logical and apriori, the other hypothetical and data driven. Taking a probabilistic interpretation of the conditional rule for subjects' card (...) selections in the Wason task seems much more justified in this second reading. If this is true, new questions arise: how does a subject recognize which method is contextually appropriate, and what makes a solution contextually rational? (shrink)
This paper presents a new theory of the truth conditions for indicativeconditionals. 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 paper is a guide to the main ideas and innovations in Robert Stalnaker's "IndicativeConditionals". 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.
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)
This paper explores trivalent truth conditions for indicativeconditionals, examining the “defective” truth table proposed by de Finetti and Reichenbach. On their approach, a conditional takes the value of its consequent whenever its antecedent is true, and the value Indeterminate otherwise. Here we deal with the problem of selecting an adequate notion of validity for this conditional. We show that all standard validity schemes based on de Finetti’s table come with some problems, and highlight two ways out of (...) the predicament: one pairs de Finetti’s conditional with validity as the preservation of non-false values, but at the expense of Modus Ponens; the other modifies de Finetti’s table to restore Modus Ponens. In Part I of this paper, we present both alternatives, with specific attention to a variant of de Finetti’s table proposed by Cooper and Cantwell. In Part II, we give an in-depth treatment of the proof theory of the resulting logics, DF/TT and CC/TT: both are connexive logics, but with significantly different algebraic properties. (shrink)
In Part I of this paper, we identified and compared various schemes for trivalent truth conditions for indicativeconditionals, most notably the proposals by de Finetti and Reichenbach on the one hand, and by Cooper and Cantwell on the other. Here we provide the proof theory for the resulting logics DF/TT and CC/TT, using tableau calculi and sequent calculi, and proving soundness and completeness results. Then we turn to the algebraic semantics, where both logics have substantive limitations: DF/TT (...) allows for algebraic completeness, but not for the construction of a canonical model, while CC/TT fails the construction of a Lindenbaum-Tarski algebra. With these results in mind, we draw up the balance and sketch future research projects. (shrink)
Grice argues that indicativeconditionals ‘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)
Research into the cognition of conditionals has predominantly focused on conditional reasoning, producing a range of theories which explain associated phenomena with considerable success. However, such theories have been less successful in accommodating experimental data concerning how agents assess the probability of indicativeconditionals. Since an acceptable account of conditional reasoning should be compatible with evidence regarding how we evaluate conditionals’ likelihoods, this constitutes a failing of such theories. Section 1 introduces the most dominant established approach (...) to conditional reasoning: mental models theory. Surveying a range of experimental results, I show that mental models theory (along with competing theories) is incapable of fully accounting for findings regarding judgements about conditionals’ probabilities. Section 2 introduces an alternative account of deductive reasoning, the erotetic theory, recently proposed by Koralus and Mascarenhas (2013). Section 3 argues that, given a natural extension, this theory is able to explain the otherwise unaccounted for data. (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 (...) class='Hi'>indicativeconditionals. (shrink)
There is strong disagreement about whether indicativeconditionals have truth values. In this paper, I present a new argument for the conclusion that indicativeconditionals have truth values based on the claim that some true statements entail indicativeconditionals. I then address four arguments that conclude that indicativeconditionals lack truth values, showing them to be inadequate. Finally, I present further benefits to having a worldly view of conditionals, which supports the (...) assignment of truth values to indicativeconditionals. I conclude that certain types of account of indicativeconditionals, which have been ignored in the literature partly on the basis of assigning truth values to indicativeconditionals, deserve consideration. (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.