The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We (...) show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis. (shrink)

In this paper, we analyse actual causation in terms of production. The latter concept is made precise by a strengthened Ramsey Test semantics of conditionals: \ iff, after suspending judgement about A and C, C is believed in the course of assuming A. This test allows us to verify or falsify that an event brings about another event. Complementing the concept of production by a weak condition of difference-making gives rise to a full-fledged analysis of causation.

Suppositional theories of conditionals take apparent similarities between supposition and conditionals as a starting point, appealing to features of the former to provide an account of the latter. This paper develops a novel form of suppositional theory, one which characterizes the relationship at the level of semantics rather than at the level of speech acts. In the course of doing so, it considers a range of novel data which shed additional light on how conditionals and supposition interact.

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed (...) in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. (shrink)

In this paper, a critical discussion is made of the role of entailments in the so-called New Paradigm of psychology of reasoning based on Bayesian models of rationality (Elqayam & Over, 2013). It is argued that assessments of probabilistic coherence cannot stand on their own, but that they need to be integrated with empirical studies of intuitive entailment judgments. This need is motivated not just by the requirements of probability theory itself, but also by a need to enhance the interdisciplinary (...) integration of the psychology of reasoning with formal semantics in linguistics. The constructive goal of the paper is to introduce a new experimental paradigm, called the Dialogical Entailment task, to supplement current trends in the psychology of reasoning towards investigating knowledge-rich, social reasoning under uncertainty (Oaksford and Chater, 2019). As a case study, this experimental paradigm is applied to reasoning with conditionals and negation operators (e.g. CEM, wide and narrow negation). As part of the investigation, participants’ entailment judgments are evaluated against their probability evaluations to assess participants’ cross-task consistency over two experimental sessions. (shrink)

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a subset (...) of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

Suppose you’re certain that a claim—say, ‘Frida is tall’—does not have a determinate truth value. What attitude should you take towards it? This is the question of the cognitive role of indeterminacy. This paper presents a puzzle for theories of cognitive role. Many of these theories vindicate a seemingly plausible principle: if you are fully certain that A, you are rationally required to be fully certain that A is determinate. Call this principle ‘Certainty’. We show that Certainty, in combination with (...) some minimal side premises, entails a very implausible claim: whenever you’re certain that it’s indeterminate whether A, it is rationally required that you reject A. This is a surprising result, which requires abandoning at least some intuitive views about indeterminacy and cognitive role. (shrink)

On an influential line of thinking tracing back to Ramsey, conditionals are closely linked to the attitude of supposition. When applied to counterfactuals, this view suggests a subjunctive version of the so-called Ramsey test: the probability of a counterfactual If A, would B ought to be equivalent to the probability of B, under the subjunctive supposition that A. I present a collapse result for any view that endorses the subjunctive version of the Ramsey test. Starting from plausible assumptions, the result (...) shows that one’s rational credence in a would-counterfactual and in the corresponding might-counterfactual have to be identical. (shrink)

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

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that (...) Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals. (shrink)

Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied (...) in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions. (shrink)

This article explores conditionals expressing that the antecedent makes a difference for the consequent. A ‘relevantised’ version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case the consequent is accepted if the belief state is revised by the antecedent and the consequent fails to be accepted if (...) the belief state is revised by the antecedent’s negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. The article also gives the logic of an alternative version, the ‘Dependent Ramsey Test,’ according to which a conditional is accepted just in case the consequent is accepted if the belief state is revised by the antecedent and the consequent is rejected if the belief state is revised by the antecedent’s negation. This conditional is closely related to David Lewis’s counterfactual analysis of causation. (shrink)

Toni Rønnow-Rasmussen | : This paper explores a novel metaethical theory according to which value judgments express conditional beliefs held by those who make them. Each value judgment expresses the belief that something is the case on condition that something else is the case. The paper aims to reach a better understanding of this view and to highlight some of the challenges that lie ahead. The most pressing of these revolves around the correct understanding of the nature of the relevant (...) cognitive attitudes. It is suggested that the distinction between “dormant attitudes” and “occurrent attitudes” helps us to understand these conditional beliefs. | : Cet article explore une nouvelle théorie méta-éthique selon laquelle les jugements de valeur expriment les croyances conditionnelles des sujets qui les font. Chaque jugement de valeur exprimerait la croyance selon laquelle quelque chose est le cas à la condition que quelque chose d’autre le soit. L’objectif de cet article est de parvenir à une meilleure compréhension de ce point de vue et de souligner certaines de ses difficultés. La plus urgente d’entre elles concerne la compréhension adéquate de la nature des attitudes cognitives pertinentes. Nous suggérons que la distinction entre « attitudes dormantes » et « attitudes occurrentes » permettrait de mieux comprendre les croyances conditionnelles. (shrink)

According to Stalnaker’s Thesis, the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does still lead to triviality, if the probability function in is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as (...) other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: Adams’ thesis, where the probability function on the left in is replaced by a probability-like function, abandoning conditionalisation, where probability conditionalisation on the right in is replaced by another propositional update procedure and the approximation thesis, where equality in is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. (shrink)

Williamson proposes that a "suppositional procedure" is a central heuristic we use to evaluate the truth of conditionals, though he also argues that this method often leads us astray. An alternative approach to the link between supposition and conditionals is to claim that we are guided by our antecedent conditional judgements in our supposing, and in particular in our determining which things follow from an initial supposition. This alternative explanation of the close link between conditionals and supposition is developed and (...) compared to Williamson's proposal. (shrink)

ABSTRACT A trivalent theory of indicative conditionals automatically enforces Stalnaker's thesis – the equation between probabilities of conditionals and conditional probabilities. This result holds because the trivalent semantics requires, for principled reasons, a modification of the ratio definition of conditional probability in order to accommodate the possibility of undefinedness. I explain how this modification is motivated and how it allows the trivalent semantics to avoid a number of well-known triviality results, in the process clarifying why these results hold for many (...) bivalent theories. In short, the slew of triviality results published in the last 40-odd years need not be viewed as an argument against Stalnaker's thesis: it can be construed instead as an argument for abandoning the bivalent requirement that indicative conditionals somehow be assigned a truth-value in worlds in which their antecedents are false. (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)

Inquiry into the meaning of logical terms in natural language (‘and’, ‘or’, ‘not’, ‘if’) has generally proceeded along two dimensions. On the one hand, semantic theories aim to predict native speaker intuitions about the natural language sentences involving those logical terms. On the other hand, logical theories explore the formal properties of the translations of those terms into formal languages. Sometimes, these two lines of inquiry appear to be in tension: for instance, our best logical investigation into conditional connectives may (...) show that there is no conditional operator that has all the properties native speaker intuitions suggest if has. Indicative conditionals have famously been the source of one such tension, ever since the triviality proofs of both Lewis (1976) and Gibbard (1981) established conclusions which are in prima facie tension with ordinary judgments about natural language indicative conditionals. In a recent series of papers, Branden Fitelson has strengthened both triviality results (Fitelson 2013, 2015, 2016), revealing a common culprit: a logical schema known as IMPORT-EXPORT. Fitelson’s results focus the tension between the logical results and ordinary judgments, since IMPORT-EXPORT seems to be supported by intuitions about natural language. In this paper, we argue that the intuitions which have been taken to support IMPORT-EXPORT are really evidence for a closely related, but subtly different, principle. We show that the two principles are independent by showing how, given a standard assumption about the conditional operator in the formal language in which IMPORT-EXPORT is stated, many existing theories of indicative conditionals validate one, but not the other. Moreover, we argue that once we clearly distinguish these principles, we can use propositional anaphora to show that IMPORT-EXPORT is in fact not valid for natural language indicative conditionals (given this assumption about the formal conditional operator). This gives us a principled and independently motivated way of rejecting a crucial premise in many triviality results, while still making sense of the speaker intuitions which appeared to motivate that premise. We suggest that this strategy has broad application and an important lesson: in theorizing about the logic of natural language, we must pay careful attention to the translation between the formal languages in which logical results are typically proved, and natural languages which are the subject matter of semantic theory. (shrink)

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)

In ‘A Defence of the Ramsey Test’, Richard Bradley makes a case for not concluding from the famous impossibility results regarding the Ramsey Test — the thesis that a rational agent believes a conditional if he would believe the consequent upon learning the antecedent — that the thesis is false. He lays the blame instead on one of the other premisses in these results, namely the Preservation condition. In this paper, we explore how this condition can be weakened by strengthening (...) the notion of consistency which appears in it. After considering the effects of such weakenings for Bradley's argument, we propose a refinement of the Preservation condition which does not fall prey to Bradley's argument nor to Gärdenfors's impossibility theorem. We briefly compare it to Bradley's suggested restriction of Preservation. (shrink)

In trusting a speaker we adopt a credulous attitude, and this attitude is basic: it cannot be reduced to the belief that the speaker is trustworthy or reliable. However, like this belief, the attitude of trust provides a reason for accepting what a speaker says. Similarly, this reason can be good or bad; it is likewise epistemically evaluable. This paper aims to present these claims and offer a genealogical justification of them.

The logic of indicative conditionals remains the topic of deep and intractable philosophical disagreement. I show that two influential epistemic norms—the Lockean theory of belief and the Ramsey test for conditional belief—are jointly sufficient to ground a powerful new argument for a particular conception of the logic of indicative conditionals. Specifically, the argument demonstrates, contrary to the received historical narrative, that there is a real sense in which Stalnaker’s semantics for the indicative did succeed in capturing the logic of the (...) Ramseyan indicative conditional. (shrink)

A spectre haunts the semantics of natural language — the spectre of Triviality. Semanticists (in particular Rothschild 2013; Khoo and Mandelkern 2018a,b) have entered into a holy alliance to exorcise this spectre. None, I will argue, have yet succeeded.

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.

This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic confusion—one which some semantic theories, (...) but not others, are prone to making. On the interpretation proposed here, Triviality Results thus play a theoretically constructive role in the project of natural language semantics. (shrink)

In a recent pair of publications, Richard Bradley has offered two novel no-go theorems involving the principle of Preservation for conditionals, which guarantees that one’s prior conditional beliefs will exhibit a certain degree of inertia in the face of a change in one’s non-conditional beliefs. We first note that Bradley’s original discussions of these results—in which he finds motivation for rejecting Preservation, first in a principle of Commutativity, then in a doxastic analogue of the rule of modus ponens —are problematic (...) in a significant number of respects. We then turn to a recent U-turn on his part, in which he winds up rescinding his commitment to modus ponens, on the grounds of a tension with the rule of Import-Export for conditionals. Here we offer an important positive contribution to the literature, settling the following crucial question that Bradley leaves unanswered: assuming that one gives up on full-blown modus ponens on the grounds of its incompatibility with Import-Export, what weakened version of the principle should one be settling for instead? Our discussion of the issue turns out to unearth an interesting connection between epistemic undermining and the apparent failures of modus ponens in McGee’s famous counterexamples. (shrink)

Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.

Brian Hill argues for a restriction of the Preservation condition that is based on a notion of epistemic, as opposed to logical, consistency. In this reply I consider possible criteria for epistemic consistency and suggest that a natural candidate for one leads to a more severe restriction on the Preservation condition than Hill proposes. I also question whether his proposed restriction is either necessary or sufficient to avoid the impossibility results for the Preservation condition, suggesting that it is the way (...) in which belief expansion is characterized within the AGM framework that is the real source of the problem. Finally, I draw on the notion of belief undermining to support a different resolution of the problem. (shrink)

This is an essay on the understanding of disposition concepts, which exploits the Ramsey test semantics of conditionals for a refined conditional analysis of dispositions. I will show that this semantics allows for a more accurate account of disposition concepts than the standard semantics of conditionals by David Lewis. This includes dealing with the counterexamples to the conditional analysis, which are known as finks, antidotes, and mimics.

Habilitation thesis in psychology. The book consists of a collection of reasoning studies. The experimental investigations will take us from people’s reasoning about probabilities, entailments, pragmatic factors, argumentation, and causality to morality. An overarching theme of the book is norm pluralism and individual differences in rationality research.

This dissertation is devoted to empirically contrasting the Suppositional Theory of conditionals, which holds that indicative conditionals serve the purpose of engaging in hypothetical thought, and Inferentialism, which holds that indicative conditionals express reason relations. Throughout a series of experiments, probabilistic and truth-conditional variants of Inferentialism are investigated using new stimulus materials, which manipulate previously overlooked relevance conditions. These studies are some of the first published studies to directly investigate the central claims of Inferentialism empirically. In contrast, the Suppositional Theory (...) of conditionals has an impressive track record through more than a decade of intensive testing. The evidence for the Suppositional Theory encompasses three sources. Firstly, direct investigations of the probability of indicative conditionals, which substantiate “the Equation” (P(if A, then C) = P(C|A)). Secondly, the pattern of results known as “the defective truth table” effect, which corroborates the de Finetti truth table. And thirdly, indirect evidence from the uncertain and-to-if inference task. Through four studies each of these sources of evidence are scrutinized anew under the application of novel stimulus materials that factorially combine all permutations of prior and relevance levels of two conjoined sentences. The results indicate that the Equation only holds under positive relevance (P(C|A) – P(C|¬A) > 0) for indicative conditionals. In the case of irrelevance (P(C|A) – P(C|¬A) = 0), or negative relevance (P(C|A) – P(C|¬A) < 0), the strong relationship between P(if A, then C) and P(C|A) is disrupted. This finding suggests that participants tend to view natural language conditionals as defective under irrelevance and negative relevance (Chapter 2). Furthermore, most of the participants turn out only to be probabilistically coherent above chance levels for the uncertain and-to-if inference in the positive relevance condition, when applying the Equation (Chapter 3). Finally, the results on the truth table task indicate that the de Finetti truth table is at most descriptive for about a third of the participants (Chapter 4). Conversely, strong evidence for a probabilistic implementation of Inferentialism could be obtained from assessments of P(if A, then C) across relevance levels (Chapter 2) and the participants’ performance on the uncertain-and-to-if inference task (Chapter 3). Yet the results from the truth table task suggest that these findings could not be extended to truth-conditional Inferentialism (Chapter 4). On the contrary, strong dissociations could be found between the presence of an effect of the reason relation reading on the probability and acceptability evaluations of indicative conditionals (and connate sentences), and the lack of an effect of the reason relation reading on the truth evaluation of the same sentences. A bird’s eye view on these surprising results is taken in the final chapter and it is discussed which perspectives these results open up for future research. (shrink)

Drawing inspiration from Lakatos’s philosophy of science, the paper presents a notion of intertheory explanation that is suitable to explain, from the point of view of a successor theory, its predecessor theory’s success (where it is successful) as well as the latter’s failure (where it fails) at the same time. A variation of the Ramsey-test is used, together with a standard AGM belief revision model, to give a semantics for open and counterfactual conditionals and ’because’-sentences featuring in such intertheory explanations. (...) Pre-theoretically described idealizing assumptions play a crucial role in this model, especially when the predecessor theory and the successor theory contradict each other. (shrink)

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)