According to a standard assumption in epistemology, if one only partially believes that p , then one cannot thereby have knowledge that p. For example, if one only partially believes that that it is raining outside, one cannot know that it is raining outside; and if one only partially believes that it is likely that it will rain outside, one cannot know that it is likely that it will rain outside. Many epistemologists will agree that epistemic agents are capable of (...) partial beliefs in addition to full beliefs and that partial beliefs can be epistemically assessed along some dimensions. However, it has been generally assumed that such doxastic attitudes cannot possibly amount to knowledge. In Probabilistic Knowledge, Moss challenges this standard assumption and provides a formidable defense of the claim that probabilistic beliefs—a class of doxastic attitudes including credences and degrees of beliefs—can amount to knowledge too. Call this the probabilistic knowledge claim . Throughout the book, Moss goes to great lengths to show that probabilistic knowledge can be fruitfully applied to a variety of debates in epistemology and beyond. My goal in this essay is to explore a further application for probabilistic knowledge. I want to look at the role of probabilistic knowledge within a “knowledge-centered” psychology—a kind of psychology that assigns knowledge a central stage in explanations of intentional behavior. My suggestion is that Moss’s notion of probabilistic knowledge considerably helps further both a knowledge-centered psychology and a broadly intellectualist picture of action and know-how that naturally goes along with it. At the same time, though, it raises some interesting issues about the notion of explanation afforded by the resulting psychology. (shrink)

The Adams Thesis holds for a conditional → and a probability assignment P if and only if P=P whenever P>0. The restriction ensures that P is well defined by the classical formula P=P/P. Drawing on deep results of Maharam on measure algebras, it is shown that, notwithstanding well-known triviality results, any probability space can be extended to a probability space with a new conditional satisfying the Adams Thesis and satisfying a number of axioms for conditionals. This puts significant limits on (...) how far triviality results can go. (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)

The Fallibility Norm—the claim that we ought to take our fallibility into account when managing our beliefs—appears to conflict with several other compelling epistemic norms. To shed light on these apparent conflicts, I distinguish two kinds of norms: norms of perfection and norms of compensation. Roughly, norms of perfection tell us how agents ought to behave if they’re to be perfect; norms of compensation tell us how imperfect agents ought to behave in order to compensate for their imperfections. I argue (...) that the Fallibility Norm is a norm of compensation, and that thinking of it like this helps us make progress in debates surrounding disagreement, higher-order evidence, and coherence. (shrink)

Gentzen’s approach to deductive systems, and Carnap’s and Popper’s treatment of probability in logic were two fruitful ideas that appeared in logic of the mid-twentieth century. By combining these two concepts, the notion of sentence probability, and the deduction relation formalized in the sequent calculus, we introduce the notion of ’probabilized sequent’ \ with the intended meaning that “the probability of truthfulness of \ belongs to the interval [a, b]”. This method makes it possible to define a system of derivations (...) based on ’axioms’ of the form \, obtained as a result of empirical research, and then infer conclusions of the form \. We discuss the consistency, define the models, and prove the soundness and completeness for the defined probabilized sequent calculus. (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)

There is a renewed debate about modus ponens. Strikingly, the recent counterexamples in Cantwell, Dreier and MacFarlane and Kolodny are generated by restricted readings of the ‘if’-clause. Moreover, it can be argued on general grounds that the restrictor view of conditionals developed in Kratzer and Lewis leads to counterexamples to modus ponens. This paper provides a careful analysis of modus ponens within the framework of the restrictor view. Despite appearances to the contrary, there is a robust sense in which modus (...) ponens is valid, owing to the fact that conditionals do not only allow for restricted readings but have bare interpretations, too. (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)

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)

We are fallible, and knowledge of our fallibility has normative implications. But these normative implications appear to conflict with other compelling epistemic norms. We therefore appear to face a choice: reject fallibility-based norms or reject these other epistemic norms. I argue that there is a plausible third option: reconcile these two sets of norms. Once we properly understand the nature of each of these norms, we aren’t forced to reject either.

This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...) dominance principle. (shrink)

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)

The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...) deduction to induction, and I will critically discuss her argument for the thesis that we cannot justify the principles of deduction next. In concluding I will defend the thesis that we can justify induction deductively relative to one end, and deduction inductively relative to a different end, and that we can do so in a non-circular way. Along the way I will show how we can understand deductive and inductive logic as normative theories, and I will briefly sketch an argument to the effect that there are only hypothetical, but no categorical imperatives. (shrink)

There are two general conceptions on the relationship between probability and logic. In the first, these systems are viewed as complementary—having offsetting strengths and weaknesses—and there exists a fusion of the two that creates a reasoning system that improves upon each. In the second, probability is viewed as an instance of logic, given some sufficiently broad formulation of it, and it is this that should inform the development of more general reasoning systems. These two conceptions are in conflict with each (...) other, where the root issue of contention is the proper abstraction of the concept of logical consequence. In this work, we put forth a proposal on this abstraction based on an extension of the subset relation through the use of projections, which in turn, allows for the formalization of valid inferences to more general settings. Our proposal results in a formalism that encompasses probability and classical logic, and importantly, does so with minimal machinery. This formalism makes assertions about the relationship between these two systems that are explicit, and suggests a path forward in the development of alternatives to them. (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)

Statements about the future are central in everyday conversation and reasoning. How should we understand their meaning? The received view among philosophers treats will as a tense: in ‘Cynthia will pass her exam’, will shifts the reference time forward. Linguists, however, have produced substantial evidence for the view that will is a modal, on a par with must and would. The different accounts are designed to satisfy different theoretical constraints, apparently pulling in opposite directions. We show that these constraints are (...) jointly satisfied by a novel modal account of will. On this account, will is a modal but doesn't work as a quantifier over worlds. Rather, the meaning of will involves a selection function similar to the one used by Stalnaker in his semantics for conditionals. The resulting theory yields a plausible semantics and logic for will and vindicates our intuitive views about the attitudes that rational agents should have towards future-directed contents. (shrink)

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

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)

The strongest possible Lewisian triviality result for the indicative conditional is proven.

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)

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will (...) look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise. (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)

Suppose we wish to provide a naturalistic account of intentionality. Like several other philosophers, we focus on the intentionality of belief, hoping that we may later supplement our account to accommodate other intentional states like desires and fears. Now suppose that we also take partial beliefs or credences seriously. In cashing out our favoured theory of intentionality, we may for the sake of simplicity talk as if belief is merely binary or all-or-nothing. But we should be able to supplement or (...) modify our account to accommodate credences. I shall argue, however, that it is difficult to do so with respect to certain causal or teleological theories of intentionality-in particular, those advanced by the likes of Stalnaker (Inquiry, 1984) and Millikan (J Philos 86:281–297, 1989). I shall first show that such theories are tailor-made to account for the intentionality of binary beliefs. Then I shall argue that it is hard to extend or supplement such theories to accommodate credences. Finally, I shall offer some natural ways of modifying the theories that involve an appeal to objective probabilities. But unfortunately, such modifications face problems. (shrink)

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

Magnetism in meta-semantics is the view that the meaning of our words is determined in part by their use and in part by the objective naturalness of candidate meanings. This hypothesis is commonly attributed to David Lewis, and has been put to philosophical work by Brian Weatherson, Ted Sider and others. I argue that there is no evidence that Lewis ever endorsed the view, and that his actual account of language reveals good reasons against it.

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)

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)

Recent work on the interpretation of counterfactual conditionals has paid much attention to the role of causal independencies. One influential idea from the theory of Causal Bayesian Networks is that counterfactual assumptions are made by intervention on variables, leaving all of their causal non-descendants unaffected. But intervention is not applicable across the board. For instance, backtracking counterfactuals, which involve reasoning from effects to causes, cannot proceed by intervention in the strict sense, for otherwise they would be equivalent to their consequents. (...) We discuss these and similar cases, focusing on two factors which play a role in determining whether and which causal parents of the manipulated variable are affected: Speakers' need for an explanation of the hypothesized state of affairs, and differences in the ‘resilience’ of beliefs that are independent of degrees of certainty. We describe the relevant theoretical notions in some detail and provide experimental evidence that these factors do indeed affect speakers' interpretation of counterfactuals. (shrink)

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.

‘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)

This is a study in the meaning of natural language probability operators, sentential operators such as probably and likely. We ask what sort of formal structure is required to model the logic and semantics of these operators. Along the way we investigate their deep connections to indicative conditionals and epistemic modals, probe their scalar structure, observe their sensitivity to contex- tually salient contrasts, and explore some of their scopal idiosyncrasies.

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of belief are those representable (...) by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

This paper explores the possibility of supplementing the suppositional view of indicative conditionals with a corresponding view of epistemic modals. The most striking feature of the suppositional view consists in its claim that indicative conditionals are to be evaluated by conditional probabilities. On the basis of a natural link between indicative conditionals and epistemic modals, a corresponding thesis about the probabilities of statements governed by epistemic modals can be derived. The paper proceeds by deriving further consequences of this thesis, in (...) particular, the logic of epistemic modals and their logical interaction with indicative conditionals are studied. (shrink)

The ontology of decision theory has been subject to considerable debate in the past, and discussion of just how we ought to view decision problems has revealed more than one interesting problem, as well as suggested some novel modifications of classical decision theory. In this paper it will be argued that Bayesian, or evidential, decision-theoretic characterizations of decision situations fail to adequately account for knowledge concerning the causal connections between acts, states, and outcomes in decision situations, and so they are (...) incomplete. Second, it will be argues that when we attempt to incorporate the knowledge of such causal connections into Bayesian decision theory, a substantial technical problem arises for which there is no currently available solution that does not suffer from some damning objection or other. From a broader perspective, this then throws into question the use of decision theory as a model of human or machine planning. (shrink)

We establish a probabilized version of modus tollens, deriving from p(E|H)=a and p()=b the best possible bounds on p(). In particular, we show that p() 1 as a, b 1, and also as a, b 0. Introduction Probabilities of conditionals Conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities.

Kolmogorov''s axiomatization of probability includes the familiarratio formula for conditional probability: 0).$$ " align="middle" border="0">.

Two partition-theorems are proved for a particular causal decision theory. One is restricted to a certain kind of partition of circumstances, and analyzes the utility of an option in terms of its utilities in conjunction with circumstances in this partition. The other analyzes an option's utility in terms of its utilities conditional on circumstances and is quite unrestricted. While the first form seems more useful for applications, the second form may be of theoretical importance in foundational exercises. Comparisons are made (...) with theorems of Richard Jeffrey, Brad Armendt, and Peter Fishburn. (shrink)

Following Nancy Cartwright and others, I suggest that most (if not all) theories incorporate, or depend on, one or more idealizing assumptions. I then argue that such theories ought to be regimented as counterfactuals, the antecedents of which are simplifying assumptions. If this account of the logic form of theories is granted, then a serious problem arises for Bayesians concerning the prior probabilities of theories that have counterfactual form. If no such probabilities can be assigned, the the posterior probabilities will (...) be undefined, as the latter are defined in terms of the former. I argue here that the most plausible attempts to address the problem of probabilities of conditionals fail to help Bayesians, and, hence, that Bayesians are faced with a new problem. In so far as these proposed solutions fail, I argue that Bayesians must give up Bayesianism or accept the counterintuitive view that no theories that incorporate any idealizations have ever really been confirmed to any extent whatsoever. Moreover, as it appears that the latter horn of this dilemma is highly implausible, we are left with the conclusion that Bayesianism should be rejected, at least as it stands. (shrink)

This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. (...) The penultimate section explores some of the consequences of the resulting logic of conditional events while the last defends it. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

In The Logic of Decision Richard Jeffrey defends a version of expected utility theory that advises agents to choose acts with an eye to securing evidence for thinking that desirable results will ensue. Proponents of "causal" decision theory have argued that Jeffrey's account is inadequate because it fails to properly discriminate the causal features of acts from their merely evidential properties. Jeffrey's approach has also been criticized on the grounds that it makes it impossible to extract a unique probability/utility representation (...) from a sufficiently rich system of preferences (given a zero and unit for measuring utility). The existence of these problems should not blind us to the fact that Jeffrey's system has advantages that no other decision theory can match: it can be underwritten by a particularly compelling representation theorem proved by Ethan Bolker; and it has a property called partition invariance that every reasonable theory of rational choice must possess. I shall argue that the non-uniqueness problem can be finessed, and that it is impossible to adequately formulate causal decision theory, or any other, without using Jeffrey's theory as one's basic analysis of rational desire. (shrink)

Pascal’s Wager is simply too good to be true—or better, too good to be sound. There must be something wrong with Pascal’s argument that decision-theoretic reasoning shows that one must (resolve to) believe in God, if one is rational. No surprise, then, that critics of the argument are easily found, or that they have attacked it on many fronts. For Pascal has given them no dearth of targets.

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)

Thanks to David Kaplan (1989a, 1989b), we all know how to handle indexicals like ‘I’. ‘I’ doesn’t refer to an object simpliciter; rather, it refers to an object only relative to a context. In particular, relative to a context C, ‘I’ refers to the agent of C. Since different contexts can have different agents, ‘I’ can refer to different objects relative to different contexts. For example, relative to a context cwhose agent is Gottlob Frege, ‘I’ refers to Frege; relative to (...) a context 0* whose agent is Alexius.. (shrink)