This paper begins with a problem stemming from Hume regarding credences about credences. Suppose one has a credence of .95 in p, and suppose one assesses the credence to be such. But suppose one’s second-order credence in this assessment is less than 1. Then, by a standard conditionalization rule, one’s credence in p becomes less than .95. Moreover, such “erosion” can iterate by considering one’s, third-, fourth-, fifth-order credences, etc. (In light of this, some have rejected higher-order credences; however, it (...) is argued that Lewis’ “Principal Principle” forbids this.) The paper then offers a partial solution by describing circumstances under which a person has reason to assign credence 1 to a first-order credence. The solution takes the form of a “transparency” view of self-knowledge from Parent (2017, chapter 8). Briefly, it is argued that when one “reflex-like” utters a sentence “The probability of p is n”, then as a matter of psychological law, the utterance is an expression of one’s own judgment. The Principal Principle then necessitates that one’s credence in p is n, assuming one is being rational. Roughly, upon perceiving such an utterance, one can thereby have a reason to assign a second-order credence of 1. (shrink)

According to comparativism, degrees of belief are reducible to a system of purely ordinal comparisons of relative confidence. (For example, being more confident that P than that Q, or being equally confident that P and that Q.) In this paper, I raise several general challenges for comparativism, relating to (i) its capacity to illuminate apparently meaningful claims regarding intervals and ratios of strengths of belief, (ii) its capacity to draw enough intuitively meaningful and theoretically relevant distinctions (...) between doxastic states, and (iii) its capacity to handle common instances of irrationality. (shrink)

Beliefs come in degrees, and we often represent those degrees with numbers. We might say, for example, that we are 90% confident in the truth of some scientific hypothesis, or only 30% confident in the success of some risky endeavour. But what do these numbers mean? What, in other words, is the underlying psychological reality to which the numbers correspond? And what constitutes a meaningful difference between numerically distinct representations of belief? In this Element, we discuss the (...) main approaches to the measurement of belief. These fall into two broad categories—epistemic and decision-theoretic—with divergent foundations in the theory of measurement. Epistemic approaches explain the measurement of belief by appeal to relations between belief states themselves, whereas decision-theoretic approaches appeal to relations between beliefs and desires in the production of choice and preferences. -/- (This book is part of the Cambridge Elements in Decision Theory and Philosophy series.). (shrink)

There is a duality in our everyday view of belief. On the one hand, we sometimes speak of credence as a matter of degree. We talk of having some level of confidence in a claim (that a certain course of action is safe, for example, or that a desired event will occur) and explain our actions by reference to these degrees of confidence – tacitly appealing, it seems, to a probabilistic calculus such as that formalized in (...) Bayesian decision theory. On the other hand, we also speak of belief as an unqualified, or flat-out, state (‘plain belief’ as it is sometimes called), which is either categorically present or categorically absent. We talk of simply believing or thinking that something is the case, and we cite these flat-out attitudes in explanation of our actions – appealing to classical practical reasoning of the sort formalized in the so-called ‘practical syllogism’.1 This tension in everyday discourse is reflected in the theoretical literature on belief. In formal epistemology there is a division between those in the Bayesian tradition, who treat credence as graded, and those who think of it as a categorical attitude of some kind. The Bayesian perspective also contrasts with the dominant view in philosophy of mind, where belief is widely regarded as a categorical state (a token sentence of a mental language, inscribed in a functionally defined ‘belief box’, according to one popular account). A parallel duality is present in our everyday view of desire. Sometimes we talk of having degrees of preference or desirability; sometimes we speak simply of wanting or desiring something tout court, and, again, this tension is reflected in the theoretical literature. What should we make of these dualities? Are there two different types of belief and desire – partial and flat-out, as they are sometimes called? If so, how are they related? And how could both have a role in guiding rational action, as the everyday view has it? The last question poses a particular challenge in relation to flat-out belief and desire.. (shrink)

According to the recent Perceptual Confidence view, perceptual experiences possess not only a representational content, but also a degree of confidence in that content. The motivations for this view are partly phenomenological and partly epistemic. We discuss both the phenomenological and epistemic motivations for the view, and the resulting account of the interface between perceptual experiences and degrees of belief. We conclude that, in their present state of development, orthodox accounts of perceptual experience are still to (...) be favoured over the perceptual confidence view. (shrink)

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and (...) concludes with general lessons from the debate thus far. (shrink)

Is it possible to give an explicit definition of belief in terms of subjective probability, such that believed propositions are guaranteed to have a sufficiently high probability, and yet it is neither the case that belief is stripped of any of its usual logical properties, nor is it the case that believed propositions are bound to have probability 1? We prove the answer is ‘yes’, and that given some plausible logical postulates on belief that involve a (...) contextual “cautiousness” threshold, there is but one way of determining the extension of the concept of belief that does the job. The qualitative concept of belief is not to be eliminated from scientific or philosophical discourse, rather, by reducing qualitative belief to assignments of resiliently high degrees of belief and a “cautiousness” threshold, qualitative and quantitative belief turn out to be governed by one unified theory that offers the prospects of a huge range of applications. Within that theory, logic and probability theory are not opposed to each other but go hand in hand. (shrink)

This paper begins with a problem stemming from Hume regarding credences about credences. Suppose one has a credence of .95 in p, and suppose one assesses the credence to be such. But suppose one’s second-order credence in this assessment is less than 1. Then, by a standard conditionalization rule, one’s credence in p becomes less than .95. Moreover, such “erosion” can iterate by considering one’s, third-, fourth-, fifth-order credences, etc. (In light of this, some have rejected higher-order credences; however, it (...) is argued that Lewis’ “Principal Principle” forbids this.) The paper then offers a partial solution by describing circumstances under which a person has reason to assign credence 1 to a first-order credence. The solution takes the form of a “transparency” view of self-knowledge from Parent (2017, chapter 8). Briefly, it is argued that when one “reflex-like” utters a sentence “The probability of p is n”, then as a matter of psychological law, the utterance is an expression of one’s own judgment. The Principal Principle then necessitates that one’s credence in p is n, assuming one is being rational. Thus, upon perceiving such an utterance, one can thereby have a reason to assign a second-order credence of 1. (shrink)

A number of authors have noted that vagueness engenders degrees of belief, but that these degrees of belief do not behave like subjective probabilities. So should we countenance two different kinds of degree of belief: the kind arising from vagueness, and the familiar kind arising from uncertainty, which obey the laws of probability? I argue that we cannot coherently countenance two different kinds of degree of belief. Instead, I present a framework in which (...) there is a single notion of degree of belief, which in certain circumstances behaves like a subjective probability assignment and in other circumstances does not. The core idea is that one’s degree of belief in a proposition P is one’s expectation of P’s degree of truth. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In (...) this paper, we seek to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

In this dissertation I aim to clarify the concept of probability. There are three kinds of interpretation of probability: the objective interpretation, the logical interpretation, and the subjective interpretation. The objective interpretation understands probability as a natural property that exists independently of our minds. I will clarify and defend one version of objective probability---the propensity interpretation of probability. I reject the logical interpretation of probability that treats probability as a logical relation between evidence and hypothesis, and maintain that probability (...) is an empirical relation. The subjective interpretation of probability, which is quite influential in recent literature, understands probability as the subject's degree of confidence that is only concerned with the states of one's mind. There are two arguments to support the claim that partial beliefs satisfy the probability measure, the Dutch Book Argument and the Representation Theorem . I argue that the subjective probability derived from both arguments is in fact the subjective estimate of objective chance, rather than subjective uncertainty of the mind assumed by subjective interpretation. The clarification of the concept of probability, I think, is of crucial importance to the studies in the philosophy of science, epistemology, and statistics. (shrink)

If we think, as Ramsey did, that a degree of belief that P is a stronger or weaker tendency to act as if P, then it is clear that not only uncertainty, but also vagueness, gives rise to degrees of belief. If I like hot coffee and do not know whether the coffee is hot or cold, I will have some tendency to reach for a cup; if I like hot coffee and know that the coffee is (...) borderline hot, I will have some tendency to reach for a cup. Suppose that we take degrees of belief arising from uncertainty to obey the laws of probability and that we model vagueness using degrees of truth. We then encounter a problem: it does not look as though degrees of belief arising from vagueness should obey the laws of probability. One response would be to countenance two different sorts of degrees of belief: degrees of belief arising from uncertainty, which obey the laws of probability; and degrees of belief arising from vagueness, which obey a different set of laws. I argue, however, that if a degree of belief that P is a stronger or weaker tendency to act as if P, then this option is not open. Instead, I propose an account of the behaviour of degrees of belief that integrates subjective probabilities and degrees of truth. On this account, degrees of belief are expectations of degrees of truth. The account explains why degrees of belief behave in accordance with the laws of probability in cases involving only uncertainty, while also allowing degrees of belief to behave differently in cases involving only vagueness, and in mixed cases involving both uncertainty and vagueness. Justifications of the account are given both via Dutch books and in terms of epistemic accuracy. (shrink)

This note is a postscript to Ramsey's 'Truth and Probability'. It replaces that article's psychological reading of subjective probability with a reading of it as a consistency condition on the theory that we act to maximise expected utility.

In this paper I am concerned with the question of whether degrees of belief can figure in reasoning processes that are executed by humans. It is generally accepted that outright beliefs and intentions can be part of reasoning processes, but the role of degrees of belief remains unclear. The literature on subjective Bayesianism, which seems to be the natural place to look for discussions of the role of degrees of belief in reasoning, does (...) not address the question of whether degrees of belief play a role in real agents’ reasoning processes. On the other hand, the philosophical literature on reasoning, which relies much less heavily on idealizing assumptions about reasoners than Bayesianism, is almost exclusively concerned with outright belief. One possible explanation for why no philosopher has yet developed an account of reasoning with degrees of belief is that reasoning with degrees of belief is not possible for humans. In this paper, I will consider three arguments for this claim. I will show why these arguments are flawed, and conclude that, at least as far as these arguments are concerned, it seems like there is no good reason why the topic of reasoning with degrees of belief has received so little attention. (shrink)

In this article, I present some new group level interpretations of probability, and champion one in particular: a consensus-based variant where group degrees of belief are construed as agreed upon betting quotients rather than shared personal degrees of belief. One notable feature of the account is that it allows us to treat consensus between experts on some matter as being on the union of their relevant background information. In the course of the discussion, I also introduce (...) a novel distinction between intersubjective and interobjective interpretations of probability. (shrink)

Epistemology has always been concerned with mental states, especially doxastic states such as belief, suspension of judgment, and the like. A significant part of epistemology is the attempt to evaluate, appraise, or criticize alternative procedures for the formation of belief and other doxastic attitudes. In addressing itself to doxastic states, epistemology has usually employed our everyday mental concepts and language. Occasionally it has tried to systematize or precise these mental categories, e.g., by introducing the notion of subjective (...) probabilities. But this is a minor refinement in our intuitive notion of degrees of confidence. What epistemology has not done—at least 20th century analytic epistemology hasn’t done it—is to seek help from experimental psychology in choosing its doxastic categories. Analytic epistemology has generally assumed that doxastic descriptions generated by casual and introspective thought are adequate for its purposes. (shrink)

What is the relation between ‘full’ or ‘outright’ belief and the various levels of confidence that agents can have in the propositions that concern them? This paper argues for a new answer to this question. Decision theory implies that in making decisions, rational agents must treat certain propositions as though they were completely certain; but on most forms of decision theory, these propositions are not ones for which any finite agent could have maximal justification – the agent will (...) clearly have less justification for these propositions than for elementary logical truths. Thus, every adequate model of a finite rational agent's belief‐system must involve two set of credences – theoretical credences and practical credences . A full or outright belief in p can be defined as the state of being stably disposed to assign a practical credence of 1 to p, for all normal practical purposes. This definition allows for a kind of reconciliation between the pragmatist and intellectualist approaches in epistemology. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism (...) can be defended on the basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

In a penetrating investigation of the relationship between belief and quantitative degrees of confidence (or degrees of belief) Richard Foley (1992) suggests the following thesis: ... it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have a sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief. Foley goes on to suggest that rational (...) class='Hi'>belief may be just rational degree of confidence above some threshold level that the agent deems sufficient for belief. He finds hints of this view in Locke’s discussion of probability and degrees of assent, so he calls it the Lockean Thesis.1 The Lockean Thesis has important implications for the logic of belief. Most prominently, it implies that even a logically ideal agent whose degrees of confidence satisfy the axioms of probability theory may quite rationally believe each of a large body of propositions that are jointly inconsistent. For example, an agent may legitimately believe that on each given occasion her well-maintained car will start, but nevertheless believe that she will eventually encounter a.. (shrink)

The paper’s target is the historically influential betting interpretation of subjective probabilities due to Ramsey and de Finetti. While there are several classical and well-known objections to this interpretation, the paper focuses on just one fundamental problem: There is a sense in which degrees of belief cannot be interpreted as betting rates. The reasons differ in different cases, but there’s one crucial feature that all these cases have in common: The agent’s degree of belief in a (...) proposition A does not coincide with her degree of belief in a conditional that A would be the case if she were to bet on A, where the belief in this conditional itself is conditioned on the supposition that the agent will have an opportunity to make such a bet. Even though the two degrees of belief sometimes can coincide (they will coincide in those cases when the bet has no expected causal bearings on the proposition A and the opportunity to bet have no evidential bearings on that proposition), it is the latter belief rather than the former that guides the agent’s rational betting behaviour. The reason is that this latter belief takes into consideration potential interferences that bet opportunities and betting itself might create with regard to the proposition to be betted on. It is because of this interference problem that the agent’s degree of belief in A cannot be interpreted as her betting rate for A. (shrink)

What does it mean to have “strong beliefs”? My thesis is that it can mean two very different things. That is, there are two distinct psychological features to which “strong belief” can refer, and these often come apart. I call the first feature epistemic confidence and the second identity centrality. They are conceptually distinct and, if we take ethnographies of religion seriously, distinct in fact as well. If that’s true, it’s methodologically important for the psychological sciences to have (...) measures that tease them apart. In this paper, I critique some measures that are currently in use and propose some strategies for developing measurement tools that track the distinction in question. (shrink)

In this article, I present some new group level interpretations of probability, and champion one in particular: a consensus-based variant where group degrees of belief are construed as agreed upon betting quotients rather than shared personal degrees of belief. One notable feature of the account is that it allows us to treat consensus between experts on some matter as being on the union of their relevant background information. In the course of the discussion, I also introduce (...) a novel distinction between intersubjective and interobjective interpretations of probability. (shrink)

The Puzzle of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, (...) but ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable. (shrink)

One response to the problem of logical omniscience in standard possible worlds models of belief is to extend the space of worlds so as to include impossible worlds. It is natural to think that essentially the same strategy can be applied to probabilistic models of partial belief, for which parallel problems also arise. In this paper, I note a difficulty with the inclusion of impossible worlds into probabilistic models. Under weak assumptions about the space of worlds, most (...) of the propositions which can be constructed from possible and impossible worlds are in an important sense inexpressible; leaving the probabilistic model committed to saying that agents in general have at least as many attitudes towards inexpressible propositions as they do towards expressible propositions. If it is reasonable to think that our attitudes are generally expressible, then a model with such commitments looks problematic. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, which, it (...) is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim (...) that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent’s prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent’s prior beliefs. Quantum certainty is therefore always some agent’s certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [(1983). Quantum logic, realism, and value-definiteness. Philosophy of Science, 50, 578], which applies the Kochen–Specker theorem to an entangled bipartite system. (shrink)

(1976). PROBABILITY, LIKELIHOOD AND SUPPORT: A METAMATHEMATICAL APPROACH TO A SYSTEM OF AXIOMS FOR UPPER AND LOWER DEGREES OF BELIEF. Philosophical Papers: Vol. 5, No. 2, pp. 153-161.

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.

Bayesianism is the position that scientific reasoning is probabilistic and that probabilities are adequately interpreted as an agent's actual subjective degrees of belief, measured by her betting behaviour. Confirmation is one important aspect of scientific reasoning. The thesis of this paper is the following: if scientific reasoning is at all probabilistic, the subjective interpretation has to be given up in order to get right confirmation—and thus scientific reasoning in general. The Bayesian approach to scientific reasoning Bayesian (...) confirmation theory The example The less reliable the source of information, the higher the degree of Bayesian confirmation Measure sensitivity A more general version of the problem of old evidence Conditioning on the entailment relation The counterfactual strategy Generalizing the counterfactual strategy The desired result, and a necessary and sufficient condition for it Actual degrees of belief The common knock-down feature, or ‘anything goes’ The problem of prior probabilities. (shrink)

Subjective probability considered as a logic of partial belief succumbs to three fundamental fallacies. These concern the representation of preference via expectation, the measurability of partial belief, and the normalization of belief.

This paper describes a formal measure of epistemic justification motivated by the dual goal of cognition, which is to increase true beliefs and reduce false beliefs. From this perspective the degree of epistemic justification should not be the conditional probability of the proposition given the evidence, as it is commonly thought. It should be determined instead by the combination of the conditional probability and the prior probability. This is also true of the degree of incremental confirmation, and I argue that (...) any measure of epistemic justification is also a measure of incremental confirmation. However, the degree of epistemic justification must meet an additional condition, and all known measures of incremental confirmation fail to meet it. I describe this additional condition as well as a measure that meets it. The paper then applies the measure to the conjunction fallacy and proposes an explanation of the fallacy. (shrink)

Philosophers commonly say that beliefs come in degrees. Drawing from the literature, I make precise three arguments for this claim: an argument from degrees of confidence, an argument from degrees of firmness, and an argument from natural language. I show that they all fail. I also advance three arguments that beliefs do not come in degrees: an argument from natural language, an argument from intuition, and an argument from the metaphysics of degrees. On the (...) basis of these arguments, I conclude that beliefs do not come in degrees. (shrink)

Credences are beliefs about evidential probabilities. We give the view an assessment-sensitive formulation, show how it evades the standard objections, and give several arguments in support.

We describe a dual-process theory of how individuals estimate the probabilities of unique events, such as Hillary Clinton becoming U.S. President. It postulates that uncertainty is a guide to improbability. In its computer implementation, an intuitive system 1 simulates evidence in mental models and forms analog non-numerical representations of the magnitude of degrees of belief. This system has minimal computational power and combines evidence using a small repertoire of primitive operations. It resolves the uncertainty of divergent evidence for (...) single events, for conjunctions of events, and for inclusive disjunctions of events, by taking a primitive average of non-numerical probabilities. It computes conditional probabilities in a tractable way, treating the given event as evidence that may be relevant to the probability of the dependent event. A deliberative system 2 maps the resulting representations into numerical probabilities. With access to working memory, it carries out arithmetical operations in combining numerical estimates. Experiments corroborated the theory's predictions. Participants concurred in estimates of real possibilities. They violated the complete joint probability distribution in the predicted ways, when they made estimates about conjunctions: P, P, P, disjunctions: P, P, P, and conditional probabilities P, P, P. They were faster to estimate the probabilities of compound propositions when they had already estimated the probabilities of each of their components. We discuss the implications of these results for theories of probabilistic reasoning. (shrink)

Comparativism is the view that comparative confidences (e.g., being more confident that P than that Q) are more fundamental than degrees of belief (e.g., believing that P with some strength x). In this paper, I outline the basis for a new, non-probabilistic version of comparativism inspired by a suggestion made by Frank Ramsey in `Probability and Partial Belief'. I show how, and to what extent, `Ramseyan comparativism' might be used to weaken the (unrealistically strong) probabilistic coherence (...) conditions that comparativism traditionally relies on. (shrink)

One very popular framework in contemporary epistemology is Bayesian. The central epistemic state is subjective confidence, or credence. Traditional epistemic states like belief and knowledge tend to be sidelined, or even dispensed with entirely. Credences are often introduced as familiar mental states, merely in need of a special label for the purposes of epistemology. But whether they are implicitly recognized by the folk or posits of a sophisticated scientific psychology, they do not appear to fit well with (...) perception, as is often noted. -/- This paper investigates the tension between probabilistic cognition and non-probabilistic perception. The tension is real, and the solution—to adapt a phrase from Quine and Goodman—is to renounce credences altogether. (shrink)

I applaud recent improvements upon previous guidelines for the assessment of pain in non-human species and the application of their framework towards decapod crustaceans. Rather than constituting a mere intermediate solution between the scientific difficulty of settling questions of animal consciousness and the need for a framework for the purposes of animal welfare legislation, I will argue that the longer lists of criteria for animal sentience should make us realize that animal sentience is a multi-dimensional phenomenon that must be studied (...) with a plethora of methods in order to assess its diversity across the tree of life. (shrink)

The logical treatment of the nature of religious belief (here I will concentrate on belief in Christianity) has been distorted by the acceptance of a false dilemma. On the one hand, many (e.g., Braithwaite, Hare) have placed the significance of religious belief entirely outside the realm of intellectual cognition. According to this view, religious statements do not express factual propositions: they are not made true or false by the ways things are. Religious belief consists in a (...) certain attitude toward the world, life, or other human beings, or in what sorts of things one values. On the other hand, others (such as Swinburne, 1981, Chapers 1 and 4) have taken religious belief to include (at least) being certain of the truth of particular factual religious propositions. The strength of a person's religious belief is identified with his degree of confidence in the truth of those propositions, measured by the "subjective probability" which those propositions have for that person. I propose a third alternative, according to which, (1) contrary to the first view, religious belief does involve a relation to factual religious propositions, such as that God exists, that Jesus was God and man, etc., -- propositions which are made true or false by the way things actually are -- but, (2) contrary to the second view, the strength of religious belief is measured, not by the degree of one's confidence1 in the truth of these propositions, but rather by the way in which the value or desirability to oneself of the various ways the world could be is affected by their including or not including the truth of these religious propositions. Thus, religious belief does consist in what one values or prizes, not in what.. (shrink)

Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this (...) analysis for Bayesian reasoning with idealized models in science. (shrink)

The purpose of this paper is to improve on the logical and measure-theoretic foundations for the notion of probability in the law of evidence, which were given in my contributions Åqvist [ (1990) Logical analysis of epistemic modality: an explication of the Bolding–Ekelöf degrees of evidential strength. In: Klami HT (ed) Rätt och Sanning (Law and Truth. A symposium on legal proof-theory in Uppsala May 1989). Iustus Förlag, Uppsala, pp 43–54; (1992) Towards a logical theory of legal evidence: semantic (...) analysis of the Bolding–Ekelöf degrees of evidential strength. In: Martino AA (ed) Expert systems in law. Elsevier Science Publishers BV, Amsterdam, North-Holland, pp 67–86]. The present approach agrees with the one adopted in those contributions in taking its main task to be that of providing a semantic analysis, or explication, of the so called Bolding–Ekelöf degrees of evidential strength (“proof-strength”) as applied to the establishment of matters of fact in law-courts. However, it differs from the one advocated in our earlier work on the subject in explicitly appealing to what is known as “Pro-et-Contra Argumentation”, after the famous Norwegian philosopher Arne Naess. It tries to bring out the logical form of that interesting kind of reasoning, at least in the context of the law of evidence. The formal techniques used here will be seen to be largely inspired by the important work done by Patrick Suppes, notably Suppes [(1957) Introduction to logic. van Nostrand, Princeton and (1972) Finite equal-interval measurement structures. Theoria 38:45–63]. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from (...) law to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the (...) agent’s evidence. (shrink)

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

What propositions are rational for one to believe? With what confidence is it rational for one to believe these propositions? Answering the first of these questions requires an epistemology of beliefs, answering the second an epistemology of degrees of belief.

I argue that when we use ‘probability’ language in epistemic contexts—e.g., when we ask how probable some hypothesis is, given the evidence available to us—we are talking about degrees of support, rather than degrees of belief. The epistemic probability of A given B is the mind-independent degree to which B supports A, not the degree to which someone with B as their evidence believes A, or the degree to which someone would or should believe A if they (...) had B as their evidence. My central argument is that the degree-of-support interpretation lets us better model good reasoning in certain cases involving old evidence. Degree-of-belief interpretations make the wrong predictions not only about whether old evidence confirms new hypotheses, but about the values of the probabilities that enter into Bayes’ Theorem when we calculate the probability of hypotheses conditional on old evidence and new background information. (shrink)

In this collection the authors have attempted to bring together a number of the essential papers in the subjective interpretation of probability theory; several of them—Borel's "Apropos of a theory on probability" and de Finetti's "Foresight: its logical laws, its subjective sources"—have never appeared before in English. Other articles include Venn's pioneering study as well as the more recent work of Ramsey, Koopman, and Savage. The editors provide an introduction which presents the three basic elements of any subjectivistic (...) theory: probability as degree of belief, the coherence of beliefs of an individual, and the notion of exchangeable events. A bibliography includes references to virtually all the more important works in subjective probability, with special emphasis on the development of the mathematical side of the theory. This anthology belongs on the shelf of any philosopher concerned with inductive logic, statistical inference, or the foundations of probability theory.—P. J. M. (shrink)

I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old evidence, (...) a problem that, we will see, is much more extensive than usually recognized. I will argue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief. (shrink)

Reports of the Intergovernmental Panel on Climate Change (IPCC) employ an evolving framework of calibrated language for assessing and communicating degrees of certainty in findings. A persistent challenge for this framework has been ambiguity in the relationship between multiple degree-of-certainty metrics. We aim to clarify the relationship between the likelihood and confidence metrics used in the Fifth Assessment Report (2013), with benefits for mathematical consistency among multiple findings and for usability in downstream modeling and decision analysis. We discuss (...) how our proposal meshes with current and proposed practice in IPCC uncertainty assessment. (shrink)