When people want to identify the causes of an event, assign credit or blame, or learn from their mistakes, they often reflect on how things could have gone differently. In this kind of reasoning, one considers a counterfactual world in which some events are different from their real-world counterparts and considers what else would have changed. Researchers have recently proposed several probabilistic models that aim to capture how people do (or should) reason about counterfactuals. We present a new model and (...) show that it accounts better for human inferences than several alternative models. Our model builds on the work of Pearl (2000), and extends his approach in a way that accommodates backtracking inferences and that acknowledges the difference between counterfactual interventions and counterfactual observations. We present six new experiments and analyze data from four experiments carried out by Rips (2010), and the results suggest that the new model provides an accurate account of both mean human judgments and the judgments of individuals. (shrink)

Import-Export says that a conditional 'If p, if q, r' is always equivalent to the conditional 'If p and q, r'. I argue that Import-Export does not sit well with a classical approach to conjunction: given some plausible and widely accepted principles about conditionals, Import-Export together with classical conjunction leads to absurd consequences. My main goal is to draw out these surprising connections. In concluding I argue that the right response is to reject Import-Export and adopt instead a limited version (...) which better fits natural language data; accounts for all the intuitions that motivate Import-Export in the first place; and fits better with a classical conjunction. (shrink)

According to the Bayesian paradigm in the psychology of reasoning, the norms by which everyday human cognition is best evaluated are probabilistic rather than logical in character. Recently, the Bayesian paradigm has been applied to the domain of argumentation, where the fundamental norms are traditionally assumed to be logical. Here, we present a major generalisation of extant Bayesian approaches to argumentation that utilizes a new class of Bayesian learning methods that are better suited to modelling dynamic and conditional inferences than (...) standard Bayesian conditionalization, is able to characterise the special value of logically valid argument schemes in uncertain reasoning contexts, greatly extends the range of inferences and argumentative phenomena that can be adequately described in a Bayesian framework, and undermines some influential theoretical motivations for dual function models of human cognition. We conclude that the probabilistic norms given by the Bayesian approach to rationality are not necessarily at odds with the norms given by classical logic. Rather, the Bayesian theory of argumentation can be seen as justifying and enriching the argumentative norms of classical logic. (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)

This paper is about conjunctions and disjunctions in the scope of non-doxastic atti- tude verbs. These constructions generate a certain type of ignorance implicature. I argue that the best way to account for these implicatures is by appealing to a notion of contex- tual redundancy (Schlenker, 2008; Fox, 2008; Mayr and Romoli, 2016). This pragmatic approach to ignorance implicatures is contrasted with a semantic account of disjunctions under `wonder' that appeals to exhausti cation (Roelofsen and Uegaki, 2016). I argue that (...) exhausti cation-based theories cannot handle embedded conjunctions, so a pragmatic account of ignorance implicatures is superior. (shrink)

We propose a method of learning indicative conditional information. An agent learns conditional information by Jeffrey imaging on the minimally informative proposition expressed by a Stalnaker conditional. We show that the predictions of the proposed method align with the intuitions in Douven, 239–263 2012)’s benchmark examples. Jeffrey imaging on Stalnaker conditionals can also capture the learning of uncertain conditional information, which we illustrate by generating predictions for the Judy Benjamin Problem.

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)

Why should we believe that perceptions justify beliefs? One argument starts with the premise that sentences of the form “a looks F” may be used to justify conclusions of the form “a is F”. I will argue that this argument for the claim that perceptions justify beliefs founders on the following dilemma: Either “a looks F” does not report the content of a perception or, if it does, then it does not justify the conclusion “a is F”.

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...) popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

It has recently been argued that indeterminacy and indeterminism make most ordinary counterfactuals false. I argue that a plausible way to avoid such counterfactual skepticism is to postulate the existence of primitive modal facts that serve as truth-makers for counterfactual claims. Moreover, I defend a new theory of ‘might’ counterfactuals, and develop assertability and knowledge criteria to suit such unobservable ‘counterfacts’.

Edgington has proposed a solution to the sorites paradox in terms of ‘verities’, which she defines as degrees of closeness to clear truth. Central to her solution is the assumption that verities are formally probabilities. She is silent on what verities might derive from and on why they should be probabilities. This paper places Edgington’s solution in the framework of a spatial approach to conceptualization, arguing that verities may be conceived of as deriving from how our concepts relate to each (...) other. Building on work by Kamp and Partee, this paper further shows how verities, thus conceived of, may plausibly be assumed to have probabilistic structure. The new interpretation of verities is argued to also help answer the question of what the verities of indicative conditionals are, a question which Edgington leaves open. Finally, the question of how to accommodate higher-order vagueness, given this interpretation, is addressed. (shrink)

In this paper it is shown that Lewis' MWD (might/would duality) and imaging principles lead to wildly implausible probability assignments for would counterfactuals.

We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...) disjunction. (shrink)

There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order beliefs. (...) This makes it possible for a subject to use probabilistic decision theory to manage in a rational way cases of potential failure of this self-knowledge, as we find in implicit bias. Through such cases I argue that it is possible for uncertainty about what our beliefs are to be not only rationally permissible but advantageous. (shrink)

An experiment was conducted to test the effectiveness of brief instruction in information structuring (i.e., representing and integrating information) for improving the coherence of probability judgments and binary choices among intelligence analysts. Forty-three analysts were presented with comparable sets of Bayesian judgment problems before and immediately after instruction. After instruction, analysts’ probability judgments were more coherent (i.e., more additive and compliant with Bayes theorem). Instruction also improved the coherence of binary choices regarding category membership: after instruction, subjects were more likely (...) to invariably choose the category to which they assigned the higher probability of a target’s membership. The research provides a rare example of evidence-based validation of effectiveness in instruction to improve the statistical assessment skills of intelligence analysts. Such instruction could also be used to improve the assessment quality of other types of experts who are required to integrate statistical information or make probabilistic assessments. (shrink)

The sentence ‘x is square’ might have had different truth conditions from those it in fact has. It might have had no truth conditions at all. Its having truth conditions and its having the ones it has rest on empirical facts about our use of ‘x is square’. What empirical facts? Any answer that goes into detail is inevitably highly controversial, but we think that there is a rough answer that is, by philosophers’ standards, relatively uncontroversial. It goes back to (...) Locke 1689 and beyond, and is best known to contemporary philosophers through the work of Grice 1957 and Lewis 1969. It is that we (usually implicitly) agreed, as a matter of contingent fact, to use ‘x is square’ as a way of conveying our taking it to be the case that x is square. (shrink)

The Desire-as-Belief thesis (DAB) states that any rational person desires a proposition exactly to the degree that she believes or expects the proposition to be good. Many people take David Lewis to have shown the thesis to be inconsistent with Bayesian decision theory. However, as we show, Lewis's argument was based on an Invariance condition that itself is inconsistent with the (standard formulation of the) version of Bayesian decision theory that he assumed in his arguments against DAB. The aim of (...) this paper is to explore what impact the rejection of Invariance has on the DAB thesis. Without assuming Invariance, we first refute all versions of DAB that entail that there are only two levels of goodness. We next consider two theses according to which rational desires are intimately connected to expectations of (multi-levelled) goodness, and show that these are consistent with Bayesian decision theory as long as we assume that the contents of 'value propositions' are not fixed. We explain why this conclusion is independently plausible, and show how to construct such propositions. (shrink)

Advocates of Expressivism about basically any kind of language are best-served by abandoning a traditional content-centric approach to semantic theorizing, in favor of an update-centric or dynamic approach (or so this paper argues). The type of dynamic approach developed here — in contrast to the content-centric approach — is argued to yield canonical, if not strictly classical, "explanations" of the core semantic properties of the connectives. (The cases on which I focus most here are negation and disjunction.) I end the (...) paper by describing a distinctive sense in which mental states might play a fundamental role in the practice of semantic theorizing (as I understand it), and I connect this to a distinctive account of the pragmatic function of, e.g., a normatively laden claim in discourse. (shrink)

This document presents a Gentzen-style deductive calculus and proves that it is complete with respect to a 3-valued semantics for a language with quantifiers. The semantics resembles the strong Kleene semantics with respect to conjunction, disjunction and negation. The completeness proof for the sentential fragment fills in the details of a proof sketched in Arnon Avron (2003). The extension to quantifiers is original but uses standard techniques.

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)

This work explores the hypothesis that natural language is a tool for changing a language user's state of mind and, more specifically, the hypothesis that a sentence's meaning is constituted by its characteristic role in fulfilling this purpose. This view contrasts with the dominant approach to semantics due to Frege, Tarski and others' work on artificial languages: language is first and foremost a tool for representing the world. Adapted to natural language by Davidson, Lewis, Montague, et. al. this dominant approach (...) has crystalized as truth-conditional semantics: to know the meaning of a sentence is to know the conditions under which that sentence is true. Chapter 1 details the animating ideas of my alternative approach and shows that the representational function of language can be understood in terms of the more general function of changing representational mental states. Chapters 2-4 argue that the additional resources of this more general conception of meaning allow us to explain certain phenomena involving conditionals and grammatical mood that truth-conditional semantics does not. In the analysis of these specific phenomena and the articulation of the general approach on offer, it emerges that this approach combines insights and benefits from both use-theoretic and truth-theoretic work on meaning. (shrink)

What distinguishes indicative conditionals from subjunctive conditionals, according to one popular view, is that the so-called Adams’ thesis holds for the former kind of conditionals but the so-called Skyrms’ thesis for the latter. According to a plausible metaphysical view, both conditionals and chances supervene on non-modal facts. But since chances do not supervene on facts about particular events but facts about event-types, the past as well as the future is chancy. Some philosophers have worried that this metaphysical view is incompatible (...) with the aforementioned view on the probability of conditionals. This paper however shows that there is no need to worry, as these views can all be simultaneously satisfied within the so-called Multidimensional Possible World Semantics for conditionals. (shrink)

I argue that taking the Practical Conditionals Thesis seriously demands a new understanding of the semantics of such conditionals. Practical Conditionals Thesis: A practical conditional [if A][ought] expresses B’s conditional preferability given A Paul Weirich has argued that the conditional utility of a state of affairs B on A is to be identified as the degree to which it is desired under indicative supposition that A. Similarly, exploiting the PCT, I will argue that the proper analysis of indicative practical conditionals (...) is in terms of what is planned, desired, or preferred, given suppositional changes to an agent’s information. Implementing such a conception of conditional preference in a semantic analysis of indicative practical conditionals turns out to be incompatible with any approach which treats the indicative conditional as expressing non-vacuous universal quantification over some domain of relevant antecedent-possibilities. Such analyses, I argue, encode a fundamental misunderstanding of what it is to be best, given some condition. The analysis that does the best vis-à-vis the PCT is, instead, one that blends a Context-Shifty account of indicative antecedents with an Expressivistic, or non-propositional, treatment of their practical consequents. (shrink)

Most meanings we express belong to large families of variant meanings, among which it would be implausible to suppose that some are much more apt for being expressed than others. This abundance of candidate meanings creates pressure to think that the proposition attributing any particular meaning to an expression is modally plastic: its truth depends very sensitively on the exact microphysical state of the world. However, such plasticity seems to threaten ordinary counterfactuals whose consequents contain speech reports, since it is (...) hard to see how we could reasonably be confident in a counterfactual whose consequent can be true only if a certain very finely tuned microphysical configuration obtains. This essay develops the foregoing puzzle and explores several possible solutions. (shrink)

In this paper we consider conditional random quantities (c.r.q.’s) in the setting of coherence. Based on betting scheme, a c.r.q. X|H is not looked at as a restriction but, in a more extended way, as \({XH + \mathbb{P}(X|H)H^c}\) ; in particular (the indicator of) a conditional event E|H is looked at as EH + P(E|H)H c . This extended notion of c.r.q. allows algebraic developments among c.r.q.’s even if the conditioning events are different; then, for instance, we can give a (...) meaning to the sum X|H + Y|K and we can define the iterated c.r.q. (X|H)|K. We analyze the conjunction of two conditional events, introduced by the authors in a recent work, in the setting of coherence. We show that the conjoined conditional is a conditional random quantity, which may be a conditional event when there are logical dependencies. Moreover, we introduce the negation of the conjunction and by applying De Morgan’s Law we obtain the disjoined conditional. Finally, we give the lower and upper bounds for the conjunction and disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold. (shrink)

This paper discusses and relates two puzzles for indicative conditionals: a puzzle about indeterminacy and a puzzle about triviality. Both puzzles arise because of Ramsey's Observation, which states that the probability of a conditional is equal to the conditional probability of its consequent given its antecedent. The puzzle of indeterminacy is the problem of reconciling this fact about conditionals with the fact that they seem to lack truth values at worlds where their antecedents are false. The puzzle of triviality is (...) the problem of reconciling Ramsey's Observation with various triviality proofs which establish that Ramsey's Observation cannot hold in full generality. In the paper, I argue for a solution to the indeterminacy puzzle and then apply the resulting theory to the triviality puzzle. On the theory I defend, the truth conditions of indicative conditionals are highly context dependent and such that an indicative conditional may be indeterminate in truth value at each possible world throughout some region of logical space and yet still have a nonzero probability throughout that region. (shrink)

I demonstrate that a "speech act" theory of meaning for imperatives is—contra a dominant position in philosophy and linguistics—theoretically desirable. A speech act-theoretic account of the meaning of an imperative !φ is characterized, broadly, by the following claims. -/- LINGUISTIC MEANING AS USE !φ’s meaning is a matter of the speech act an utterance of it conventionally functions to express—what a speaker conventionally uses it to do (its conventional discourse function, CDF). -/- IMPERATIVE USE AS PRACTICAL !φ's CDF is to (...) express a practical (non-representational) state of mind—one concerning an agent's preferences and plans, rather than her beliefs. -/- Opposed to speech act accounts is a preponderance of views which deny that a sentence's linguistic meaning is a matter of what speech act it is used to perform, or its CDF. On such accounts, meaning is, instead, a matter of "static" properties of the sentence—e.g., how it depicts the world as being (or, more neutrally, the properties of a model-theoretic object with which the semantic value of the sentence co-varies). On one version of a static account, an imperative 'shut the window!' might, for instance, depict the world as being such that the window must be shut. -/- Static accounts are traditionally motivated against speech act-theoretic accounts by appeal to supposedly irremediable explanatory deficiencies in the latter. Whatever a static account loses in saying (prima facie counterintuitively) that an imperative conventionally represents, or expresses a picture of the world, is said to be offset by its ability to explain a variety of phenomena for which speech act-theoretic accounts are said to lack good explanations (even, in many cases, the bare ability to offer something that might meet basic criteria on what a good explanation should be like). -/- I aim to turn the tables on static accounts. I do this by showing that speech act accounts are capable of giving explanations of phenomena which fans of static accounts have alleged them unable to give. Indeed, for a variety of absolutely fundamental phenomena having to do with the conventional meaning of imperatives (and other types of practical language), speech act accounts provide natural and theoretically satisfying explanations, where a representational account provides none. (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)

In this paper I will develop a view about the semantics of imperatives, which I term Modal Noncognitivism, on which imperatives might be said to have truth conditions (dispositionally, anyway), but on which it does not make sense to see them as expressing propositions (hence does not make sense to ascribe to them truth or falsity). This view stands against “Cognitivist” accounts of the semantics of imperatives, on which imperatives are claimed to express propositions, which are then enlisted in explanations (...) of the relevant logico-semantic phenomena. It also stands against the major competitors to Cognitivist accounts—all of which are non-truth-conditional and, as a result, fail to provide satisfying explanations of the fundamental semantic characteristics of imperatives (or so I argue). The view of imperatives I defend here improves on various treatments of imperatives on the market in giving an empirically and theoretically adequate account of their semantics and logic. It yields explanations of a wide range of semantic and logical phenomena about imperatives—explanations that are, I argue, at least as satisfying as the sorts of explanations of semantic and logical phenomena familiar from truth-conditional semantics. But it accomplishes this while defending the notion—which is, I argue, substantially correct—that imperatives could not have propositions, or truth conditions, as their meanings. (shrink)

I resolve the major challenge to an Expressivist theory of the meaning of normative discourse: the Frege–Geach Problem. Drawing on considerations from the semantics of directive language (e.g., imperatives), I argue that, although certain forms of Expressivism (like Gibbard’s) do run into at least one version of the Problem, it is reasonably clear that there is a version of Expressivism that does not.

In this paper I will present a puzzle about epistemic akrasia, and I will use that puzzle to motivate accepting some non-standard views about the nature of epistemological judgment. The puzzle is that while it seems obvious that epistemic akrasia must be irrational, the claim that epistemic akrasia is always irrational amounts to the claim that a certain sort of justified false belief—a justified false belief about what one ought to believe—is impossible. But justified false beliefs seem to be possible (...) in any domain, and it’s hard to see why beliefs about what one ought to believe should be an exception. I will argue that when we get clearer about what sort of psychological state epistemic akrasia is, we can resolve the puzzle in favor of the intuitive view that epistemic akrasia is always irrational. (shrink)

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)

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)

This paper explores the possibility that causal decision theory can be formulated in terms of probabilities of conditionals. It is argued that a generalized Stalnaker semantics in combination with an underlying branching time structure not only provides the basis for a plausible account of the semantics of indicative conditionals, but also that the resulting conditionals have properties that make them well-suited as a basis for formulating causal decision theory. Decision theory (at least if we omit the frills) is not an (...) esoteric science, however unfamiliar it may seem to an outsider. Rather it is a systematic exposition of the consequences of certain well-chosen platitudes about belief, desire, preference and choice. It is the very core of our common-sense theory of persons, dissected out and elegantly systematized. (David Lewis, Synthese 23:331–344, 1974, p. 337). A small distortion in the analysis of the conditional may create spurious problems with the analysis of other concepts. So if the facts about usage favor one among a number of subtly different theories, it may be important to determine which one it is. (Robert Stalnaker, A Defense of Conditional Excluded Middle, pp. 87–104, 1980, p. 87). (shrink)

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

What should we do when we won't do as we ought? Suppose it ought to be that the procrastinating professor accept the task of reviewing a book, and actually review the book. It seems clear that given he won't review it, he ought not to accept the task. That is a genuine moral obligation in light of less than perfect circumstances. I want to entertain the possibility that a set of such obligations form something like a 'practical morality'; that which (...) we ought to do given that we're unlikely or unwilling to do much of what ideal morality demands. If it is possible to give a coherent account of these kinds of obligations, then it is possible to entertain the idea that these obligations are in fact what morality demands. The conceptual truths about justice (good, right, fairness) that come from ideals are one thing; the actions that morality demands of people given their actual circumstances are quite another. In this paper I will ask about the kinds of facts that can be used to establish a more circumscribed set of obligations than we get from the orthodox view about moral obligation. (shrink)

In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...) at any given time be adequately described by a single subjective probability function. We show that monistic Bayesians cannot provide an adequate solution to the new Tweety puzzle, because this requires one to refer to a frequency-based probability function. We conclude that monistic Bayesianism cannot be a fully adequate theory of epistemic states. In the second part we describe an empirical study, which provides support for the thesis that monistic Bayesianism is also inadequate as a descriptive theory of cognitive states. In the final part of the paper we criticize Bayesian approaches in cognitive science, insofar as their monistic tendency cannot adequately address the new Tweety puzzle. We, further, argue against monistic Bayesianism in cognitive science by means of a case study. In this case study we show that Oaksford and Chater’s (2007, 2008) model of conditional inference—contrary to the authors’ theoretical position—has to refer also to a frequency-based probability function. (shrink)

In this paper, I explore a question about deductive reasoning: why am I in a position to immediately infer some deductive consequences of what I know, but not others? I show why the question cannot be answered in the most natural ways of answering it, in particular in Descartes’s way of answering it. I then go on to introduce a new approach to answering the question, an approach inspired by Hume’s view of inductive reasoning.

We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.

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

This paper argues that just as full beliefs can constitute knowledge, so can properties of your credence distribution. The resulting notion of probabilistic knowledge helps us give a natural account of knowledge ascriptions embedding language of subjective uncertainty, and a simple diagnosis of probabilistic analogs of Gettier cases. Just like propositional knowledge, probabilistic knowledge is factive, safe, and sensitive. And it helps us build knowledge-based norms of action without accepting implausible semantic assumptions or endorsing the claim that knowledge is interest-relative.

This book is a sustained defense of the compatibility of the presence of idealizations in the sciences and scientific realism. So, the book is essentially a detailed response to the infamous arguments raised by Nancy Cartwright to the effect that idealization and scientific realism are incompatible.

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (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)

Students often study logic on the assumption that it provides a normative guide to reasoning in English. In particular, they are taught to associate connectives like “and” with counterparts in Sentential Logic. English conditionals go over to formulas with → as principal connective. The well-known difficulties that arise from such translation are not emphasized. The result is the conviction that ordinary reasoning is faulty when discordant with the usual representation in standard logic. Psychologists are particularly susceptible to this attitude.

This paper argues that several leading theories of subjunctive conditionals are incompatible with ordinary intuitions about what credences we ought to have in subjunctive conditionals. In short, our theory of subjunctives should intuitively display semantic humility, i.e. our semantic theory should deliver the truth conditions of sentences without pronouncing on whether those conditions actually obtain. In addition to describing intuitions about subjunctive conditionals, I argue that we can derive these ordinary intuitions from justified premises, and I answer a possible worry (...) for my derivation by refuting a subjunctive triviality result modeled on (Lewis 1976). I conclude that the debate over the correct theory of subjunctive conditionals requires settling meta-philosophical questions about the relative value of various virtues of first-order theories of subjunctive conditionals. (shrink)