This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (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)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

*This work is no longer under development* Two major themes in the literature on indicative conditionals are that the content of indicative conditionals 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 indicative conditionals, with indicatives whose antecedents are epistemically impossible being vacuously true: and indeed, the modal account of indicative conditionals 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 indicative conditionals 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)

The following four assumptions plausibly describe the ideal rational agent. (1) She knows what her beliefs are. (2) She desires to believe only truths. (3) Whenever she desires that P → Q and knows that P, she desires that Q. (4) She does not both desire that P and desire that ~P, for any P. Although the assumptions are plausible, they have an implausible consequence. They imply that the ideal rational agent does not believe and desire contradictory propositions. She neither (...) desires the world to be any different than she thinks it is, nor thinks it is any different than she desires it to be. The problem of preserving our intuitions about desire, without embracing the implausible conclusion, is what I call “the Wishful Thinking Puzzle.” In this paper, I examine how this puzzle arises, and I argue that it is surprisingly difficult to solve. Even the decision theoretic conception of desire is not immune to the puzzle. One approach, the contrastive conception of desire, does avoid the puzzle without being ad hoc, but it remains too inchoate to win our full confidence. (shrink)

Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present a probabilist account of antirealist truth in some formal detail, and we assess its ability to deal with the problems that are standardly taken to beset antirealism.

In this paper I argue against previous approaches to the semantics of generics which involved the notions of prototype, stereotype and relevant quantification. I assume that the logical form of generics includes a generic operator which, as Heim (1992) has suggested, can be construed as the modal operator of necessity. After demonstrating that the presence of the generic operator in a semantic representation, as well as its domain of quantification, are pragmatically supplied, I go on to show how the various (...) interpretations generics may receive can be successfully accounted for within a relevance-theoretic framework. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (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)

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The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version (...) of CP canthus be maintained. (shrink)

Suppose an agent has made a judgement of the form, 'all things considered, it would be better for me to do a rather than b (or any range of alternatives to doing a)' where a and b stand for particular actions. If she does not act upon her judgement in these circumstances would that be a failure of rationality on her part? In this paper I consider two different interpretations of all things considered judgements which give different answers to this (...) question, one suggested by Donald Davidson, the other by Paul Grice and Judith Baker. I argue that neither interpretation is adequate. However, a third interpretation that combines features of the Grice/Baker view with the Davidsonian view is possible. In the final section of the paper I defend this interpretation against two objections. (shrink)

This paper presents a unified theory of the truth conditions and probability of indicative conditionals and their compounds in a trivalent framework. The semantics validates a Reduction Theorem: any compound of conditionals is semantically equivalent to a simple conditional. This allows us to validate Stalnaker's Thesis in full generality and to use Adams's notion of $p$-validity as a criterion for valid inference. Finally, this gives us an elegant account of Bayesian update with indicative conditionals, establishing that despite differences in meaning, (...) it is tantamount to learning a material conditional. (shrink)

This paper is intended to show that, at least in a considerably wide class of cases, indicative conditionals are adequately formalized as strict conditionals. The first part of the paper outlines three arguments that support the strict conditional view, that is, three reasons for thinking that an indicative conditional is true just in case it is impossible that its antecedent is true and its consequent is false. The second part of the paper develops the strict conditional view and defends it (...) from some foreseeable objections. (shrink)

The classic formulation of causal decision theory (CDT) appeals to counterfactuals. It says that you should aim to choose an option that would have a good outcome, were you to choose it. However, this version of CDT faces trouble if the laws of nature are deterministic. After all, the standard theory of counterfactuals says that, if the laws are deterministic, then if anything—including the choice you make—were different in the present, either the laws would be violated or the distant past (...) would be changed. And as several authors have shown, it's easy to transform this upshot of the standard theory of counterfactuals into full-blown counterexamples to CDT. In response to these counterexamples, I argue here that the problem lies, not so much with CDT's guiding idea—that it's the expected causal consequences of your actions that matter for rational decision-making—but with the fact that the classic formulation of CDT doesn't pay sufficient attention to the context-sensitivity of counterfactuals. I develop a contextualist version of CDT which better accounts for this context-sensitivity. And I show that my theory avoids the problems faced by the classic formulation of CDT in determinstic worlds. (shrink)

This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

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 this paper, we will present an analysis of the Oswald example that takes a closer look at the antecedents of the Oswald minimal pair. We will argue that diverging foci in the antecedents of the Oswald example result in different truth conditions of the conditionals, explaining the difference in truth values between the two sentences. Although the explanation will incorporate aspects of Stalnaker’s theory of conditionals, it will go beyond Stalnaker’s analysis of the Oswald example on one crucial point. (...) The difference in focus assignments between the two sentences will not be explained by a difference in appropriateness conditions between indicative and subjunctive mood. Instead, the diverging foci will stem from pragmatic requirements imposed on the presuppositions of indicative and subjunctive antecedents. This analysis will be further confirmed by extending it to similar examples with ascriptions of hopes and wishes, pointing towards a more clear-cut separation of and the effect of the Oswald example conditionality. (shrink)

The Identity principle says that conditionals with the form 'If p, then p' are logical truths. Identity is overwhelmingly plausible, and has rarely been explicitly challenged. But a wide range of conditionals nonetheless invalidate it. I explain the problem, and argue that the culprit is the principle known as Import-Export, which we must thus reject. I then explore how we can reject Import-Export in a way that still makes sense of the intuitions that support it, arguing that the differences between (...) indicative and subjunctive conditionals play a key role in solving this puzzle. (shrink)

There is strong disagreement about whether indicative conditionals have truth values. In this paper, I present a new argument for the conclusion that indicative conditionals have truth values based on the claim that some true statements entail indicative conditionals. I then address four arguments that conclude that indicative conditionals 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 indicative conditionals. I conclude (...) that certain types of account of indicative conditionals, which have been ignored in the literature partly on the basis of assigning truth values to indicative conditionals, deserve consideration. (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.

A probability distribution is regular if it does not assign probability zero to any possible event. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson and Benci et al. have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

KK is the thesis that if you can know p, you can know that you can know p. Though it’s unpopular, a flurry of considerations has recently emerged in its favour. Here we add fuel to the fire: standard resources allow us to show that any failure of KK will lead to the knowability and assertability of abominable indicative conditionals of the form ‘If I don’t know it, p’. Such conditionals are manifestly not assertable—a fact that KK defenders can easily (...) explain. I survey a variety of KK-denying responses and find them wanting. Those who object to the knowability of such conditionals must either deny the possibility of harmony between knowledge and belief, or deny well-supported connections between conditional and unconditional attitudes. Meanwhile, those who grant knowability owe us an explanation of such conditionals’ unassertability—yet no successful explanations are on offer. Upshot: we have new evidence for KK. (shrink)

Assume that it is your evidence that determines what opinions you should have. I argue that since you should take peer disagreement seriously, evidence must have two features. (1) It must sometimes warrant being modest: uncertain what your evidence warrants, and (thus) uncertain whether you’re rational. (2) But it must always warrant being guided: disposed to treat your evidence as a guide. Surprisingly, it is very difficult to vindicate both (1) and (2). But diagnosing why this is so leads to (...) a proposal—Trust—that is weak enough to allow modesty but strong enough to yield many guiding features. In fact, I claim that Trust is the Goldilocks principle—for it is necessary and sufficient to vindicate the claim that you should always prefer to use free evidence. Upshot: Trust lays the foundations for a theory of disagreement and, more generally, an epistemology that permits self-doubt—a modest epistemology. (shrink)

Disjunctive antecedent conditionals —conditionals of the form if A or B, C—sometimes seem to entail both of their simplifications and sometimes seem not to. I argue that this behavior reveals a genuine ambiguity in DACs. Along the way, I discuss a new observation about the role of focal stress in distinguishing the two interpretations of DACs. I propose a new theory, according to which the surface form of a DAC underdetermines its logical form: on one possible logical form, if A (...) or B, C does entail both of its simplifications, while on the other, it does not. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is speaking (...) of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)

This paper proposes a new model of graded modal judgment. It begins by problematizing the phenomenon: given plausible constraints on the logic of epistemic modality, it is impossible to model graded attitudes toward modal claims as judgments of probability targeting epistemically modal propositions. This paper considers two alternative models, on which modal operators are non-proposition-forming: (1) Moss (2015), in which graded attitudes toward modal claims are represented as judgments of probability targeting a “proxy” proposition, belief in which would underwrite belief (...) in the modal claim. (2) A model on which graded attitudes toward modal claims are represented as judgments of credence taking as their objects (non-propositional) modal representations (rather than proxy propositions). The second model, like Moss’ model, is shown to be semantically and mathematically tractable. The second model, however, can be straightforwardly integrated into a plausible model of the role of graded attitudes toward modal claims in cognition and normative epistemology. (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)

In recent years, a number of theorists have claimed that beliefs about probability are transparent. To believe probably p is simply to have a high credence that p. In this paper, I prove a variety of triviality results for theses like the above. I show that such claims are inconsistent with the thesis that probabilistic modal sentences have propositions or sets of worlds as their meaning. Then I consider the extent to which a dynamic semantics for probabilistic modals can capture (...) theses connecting belief, certainty, credence, and probability. I show that although a dynamic semantics for probabilistic modals does allow one to validate such theses, it can only do so at a cost. I prove that such theses can only be valid if probabilistic modals do not satisfy the axioms of the probability calculus. (shrink)

to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) -/- L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Dougherty, et al. 2015, Harman (...) 2015) — I call our argument the Fine-Graining Response. Paul has her own reply to this response, which we might call the Authenticity Reply. But Sarah Moss has recently offered an alternative reply to the Fine-Graining Response on Paul’s behalf (Moss 2017) — we’ll call it the No Knowledge Reply. This appeals to the knowledge norm of action, together with Moss’ novel and intriguing account of probabilistic knowledge. In this paper, I consider Moss’ reply and argue that it fails. I argue first that it fails as a reply made on Paul’s behalf, since it forces us to abandon many of the features of Paul’s challenge that make it distinctive and with which Paul herself is particularly concerned. Then I argue that it fails as a reply independent of its fidelity to Paul’s intentions. (shrink)

According to the so-called ‘deliberation crowds out prediction’ thesis, while deliberating about what you’ll do, you cannot rationally have credences for what you’ll do – you cannot rationally have option-credences. Versions of the thesis have been defended by authors such as Spohn, Levi, Gilboa, Price, Louise, and others. After registering a number of concerns about the thesis, I rehearse and rebut many of the main arguments for it, grouped according to their main themes: agency, vacuity, betting, and decision-theoretical considerations. I (...) go on to suggest many possible theoretical roles for option-credences. -/- I locate the debate about the thesis in a broader discussion: Are there rational credence gaps – propositions to which one cannot rationally assign credences? If there are, they spell trouble for various foundations of Bayesian epistemology, including the usual ratio formula for conditional probability, conditionalization, decision theory, and independence. According to the thesis, credence gaps are completely mundane; they arise every time someone rationally deliberates. But these foundations are safe from any threat here, I contend, since the thesis is false. Deliberation welcomes prediction. (shrink)

A common view among nontheists combines the de jure objection that theism is epistemically unacceptable with agnosticism about the de facto objection that theism is false. Following Plantinga, we can call this a “proper” de jure objection—a de jure objection that does not depend on any de facto objection. In his Warranted Christian Belief, Plantinga has produced a general argument against all proper de jure objections. Here I first show that this argument is logically fallacious (it makes subtle probabilistic fallacies (...) disguised by scope ambiguities), and proceed to lay the groundwork for the construction of actual proper de jure objections. (shrink)

My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.

Causal reasoning is one of our most central cognitive competencies, enabling us to adapt to our world. Causal knowledge allows us to predict future events, or diagnose the causes of observed facts. We plan actions and solve problems using knowledge about cause-effect relations. Without our ability to discover and empirically test causal theories, we would not have made progress in various empirical sciences. In the past decades, the important role of causal knowledge has been discovered in many areas of cognitive (...) psychology. Despite the ubiquity of causal reasoning, textbooks of cognitive psychology have neglected this growing field. The goal of The Oxford Handbook of Causal Reasoning is to fill this gap. The handbook brings together the leading researchers in the field of causal reasoning and offers state-of-the-art presentations of theories and research. It provides introductions of competing theories of causal reasoning, and discusses its role in various cognitive functions and domains. The final section presents research from neighboring fields. 1. Causal Reasoning: An Introduction Michael R. Waldmann Part I: Theories of Causal Cognition 2. Associative Accounts of Causal Cognition Mike E. Le Pelley, Oren Griffiths, and Tom Beesley 3. Rules of Causal Judgment: Mapping Statistical Information Onto Causal Beliefs José C. Perales, Andrés Catena, Antonio Cándido, and Antonio Maldonado 4. The Inferential Reasoning Theory of Causal Learning: Toward a Multi- Process Propositional Account Yannick Boddez, Jan De Houwer, and Tom Beckers 5. Causal Invariance as an Essential Constraint for Creating a Causal Representation of the World: Generalizing the Invariance of Causal Power Patricia W. Cheng and Hongjing Lu 6. The Acquisition and Use of Causal Structure Knowledge Benjamin Margolin Rottman 7. Formalizing Prior Knowledge in Causal Induction Thomas L. Griffiths 8. Causal Mechanisms Samuel G. B. Johnson and Woo-kyoung Ahn 9. Force Dynamics and Causation Phillip Wolff and Robert Thorstad 10. Mental Models and Causation P. N. Johnson- Laird and Sangeet S. Khemlani 11. Pseudocontingencies Klaus Fiedler and Florian Kutzner 12. Singular Causation David Danks 13. Cognitive Neuroscience of Causal Reasoning Joachim T. Operskalski and Aron K. Barbey Part II: Basic Cognitive Functions 14. Visual Impressions of Causality Peter White 15. Goal-Directed Actions Bernhard Hommel 16. Planning and Control Magda Osman 17. Reinforcement Learning and Causal Models Samuel J. Gershman 18. Causation and the Probability of Causal Conditionals David E. Over 19. Causal Models and Conditional Reasoning Mike Oaksford and Nick Chater 20. Concepts as Causal Models: Categorization Bob Rehder 21. Concepts as Causal Models: Induction Bob Rehder 22. Causal Explanation Tania Lombrozo and Nadya Vasilyeva 23. Diagnostic Reasoning Björn Meder and Ralf Mayrhofer 24. Inferring Causal Relations by Analogy Keith J. Holyoak and Hee-Seung Lee 25. Causal Argument Ulrike Hahn, Roland Bluhm, and Frank Zenker 26. Causality in Decision- Making York Hagmayer and Philip M. Fernbach Part III: Domains of Causal Reasoning 27. Intuitive Theories Tobias Gerstenberg and Joshua B. Tenenbaum 28. Space, Time, and Causality Marc J. Buehner 29. Causation in Legal and Moral Reasoning David A. Lagnado and Tobias Gerstenberg 30. The Role of Causal Knowledge in Reasoning About Mental Disorders Woo-kyoung Ahn, Nancy S. Kim, and Matthew S. Lebowitz 31. Causality and Causal Reasoning in Natural Language Torgrim Solstad and Oliver Bott 32. Social Attribution and Explanation Denis Hilton Part IV: Development, Phylogeny, and Culture 33. The Development of Causal Reasoning Paul Muentener and Elizabeth Bonawitz 34. Causal Reasoning in Non-Human Animals Christian Schloegl and Julia Fischer 35. Causal Cognition and Culture Andrea Bender, Sieghard Beller, and Douglas L. Medin. (shrink)

In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...) rigorously and two models are provided that demonstrate that the new thesis is indeed tenable within a standard possible world semantics based on selection functions. Unlike the Stalnaker-Lewis semantics the selection functions cannot be understood in terms of similarity. A probabilistic account of selection is defended in its place. -/- I end the paper by suggesting that this approach overcomes some of the objections often leveled at accounts of indicatives based on the notion of similarity. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...) binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

Philosophers typically rely on intuitions when providing a semantics for counterfactual conditionals. However, intuitions regarding counterfactual conditionals are notoriously shaky. The aim of this paper is to provide a principled account of the semantics of counterfactual conditionals. This principled account is provided by what I dub the Royal Rule, a deterministic analogue of the Principal Principle relating chance and credence. The Royal Rule says that an ideal doxastic agent’s initial grade of disbelief in a proposition \(A\) , given that the (...) counterfactual distance in a given context to the closest \(A\) -worlds equals \(n\) , and no further information that is not admissible in this context, should equal \(n\) . Under the two assumptions that the presuppositions of a given context are admissible in this context, and that the theory of deterministic alethic or metaphysical modality is admissible in any context, it follows that the counterfactual distance distribution in a given context has the structure of a ranking function. The basic conditional logic V is shown to be sound and complete with respect to the resulting rank-theoretic semantics of counterfactuals. (shrink)

According to what is now commonly referred to as “the Equation” in the literature on indicative conditionals, the probability of any indicative conditional equals the probability of its consequent of the conditional given the antecedent of the conditional. Philosophers widely agree in their assessment that the triviality arguments of Lewis and others have conclusively shown the Equation to be tenable only at the expense of the view that indicative conditionals express propositions. This study challenges the correctness of that assessment by (...) presenting data that cast doubt on an assumption underlying all triviality arguments. (shrink)

Adams’s Thesis, the claim that the probabilities of indicative conditionals equal the conditional probabilities of their consequents given their antecedents, has proven impossible to accommodate within orthodox possible-world semantics. This essay proposes a modification to the orthodoxy that removes this impossibility. The starting point is a proposal by Jeffrey and Stalnaker that conditionals take semantic values in the unit interval, interpreting these (à la McGee) as their expected truth-values at a world. Their theories imply a false principle, namely, that the (...) probability of a conditional is independent of any proposition inconsistent with its antecedent. But they also point to something important, namely, that our uncertainty about conditionals is not confined to uncertainty about the facts (what the actual world is like) but also expresses uncertainty about the counterfacts (what the world would be like if one or another supposition were true). To capture this observation, this essay proposes that the semantic contents of conditionals be treated as sets of vectors of possible worlds, not singleton worlds, with the coordinates of each specifying the world that is or would be true under the supposition that it represents. The probabilities of truth for conditionals will then depend on the joint probabilities of the facts and counterfacts, the latter in turn depending on the mode of supposition. The implication of this treatment is that the probabilities of conditionals are conditional probabilities whenever the mode of supposition is evidential. (shrink)

‘Probability logic’ might seem like an oxymoron. Logic traditionally concerns matters immutable, necessary and certain, while probability concerns the uncertain, the random, the capricious. Yet our subject has a distinguished pedigree. Ramsey begins his classic “Truth and Probability” with the words: “In this essay the Theory of Probability is taken as a branch of logic. … “speaks of “the logic of the probable.” And more recently, regards probabilities as estimates of truth values, and thus probability theory as a natural outgrowth (...) of two‐valued logic—what he calls “probability logic.” However the point is put, probability theory and logic are clearly intimately related. This chapter explores some of the multifarious connections between probability and logic, and focuses on various philosophical issues in the foundations of probability theory. (shrink)