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 circumstances where one proposition A is propositional evidence for another proposition B, my believing A can confer warrant upon B. I use the term “epistemic probability” to refer to the relationship between a pair of propositions A and B when A is propositional evidence for B; more precisely, in those cases, I shall say that the epistemic conditional probability of B on A is high. In this chapter and the next, I concern myself with an (...) analysis of epistemic conditional probability. The first thing to see, in trying to get a general grasp of this topic, is to note the divide between epistemic probability and objective probability. In this chapter, I distinguish the former from the latter and point out some debilitating problems with the three main accounts of the former ; in the next chapter, I propose what I hope is a better substitute. (shrink)

Epistemic probability theories of luck come in two versions. They are easiest to distinguish by the epistemic property they claim eliminates luck. One view says that the property is knowledge. The other view says that the property is being guaranteed by a subject’s evidence. Asbjørn Steglich-Petersen defends the Knowledge Account (KA). He has recently argued that his view is preferable to my Epistemic Analysis of Luck (EAL), which defines luck in terms of evidential probability. In (...) this paper, I defend EAL against Steglich-Petersen’s arguments, clarify the view, and argue for the explanatory significance of EAL with respect to some core epistemological issues. My overall goal is to show that an epistemic probability account of luck rooted in the concepts of evidence and evidential support remains a viable and fruitful overall account of luck. (shrink)

Philosophers have often attempted to use counterfactual conditionals to analyze probability. This article focuses on counterfactual analyzes of epistemic probability by Alvin Plantinga and Peter van Inwagen. I argue that a certain type of counterfactual situation creates problems for these analyses. I then argue that Plantinga's intuition about the role of warrant in epistemic probability is mistaken. Both van Inwagen's and Plantinga's intuitions about epistemic probability are flawed.

Many philosophers think that part of what makes an event lucky concerns how probable that event is. In this paper, I argue that an epistemic probability account of luck successfully resists recent arguments that all theories of luck, including probability theories, are subject to counterexample (Hales 2016). I argue that an event is lucky if and only if it is significant and sufficiently improbable. An event is significant when, given some reflection, the subject would regard the event (...) as significant, and the event’s epistemic probability, determined by the subject’s evidence, is the only kind of probability that directly bears on whether or not the event is lucky. I conclude with some lessons that are applicable to probability theorists of luck generally, including those defending non-epistemic probability theories. (shrink)

The epistemic probability of A given B is the degree to which B evidentially supports A, or makes A plausible. This paper is a first step in answering the question of what determines the values of epistemic probabilities. I break this question into two parts: the structural question and the substantive question. Just as an object’s weight is determined by its mass and gravitational acceleration, some probabilities are determined by other, more basic ones. The structural question asks (...) what probabilities are not determined in this way—these are the basic probabilities which determine values for all other probabilities. The substantive question asks how the values of these basic probabilities are determined. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. I defend this against the view, implicit in orthodox mathematical treatments of probability, that basic probabilities are the unconditional probabilities of complete worlds. I then apply my answer to the structural question to clear up common confusions in expositions of Bayesianism and shed light on the “problem of the priors.”. (shrink)

Is consistency always epistemically virtuous? In this paper, I examine one threat to the traditional view that consistency is a minimum requirement for rational belief. Central to the argument is the notion of epistemic probability, understood as the degree of support or confirmation provided by the total available evidence. My strategy in examining this argument is to apply analogous reasoning to carefully tailored examples. The conclusions which emerge are substantive, informative and utterly implausible. I conclude, first, that the (...) argument for inconsistency fails and, second, that it fails because epistemic probability does not conform to the axioms of the probability calculus. A plausible alternate model for determining degree of support is briefly considered. (shrink)

Some recent work in philosophy of religion addresses what can be called the “axiological question,” i.e., regardless of whether God exists, would it be good or bad if God exists? Would the existence of God make the world a better or a worse place? Call the view that the existence of God would make the world a better place “Pro-Theism.” We argue that Pro-Theism is not implausible, and moreover, many Theists, at least, (often implicitly) think that it is true. That (...) is, many Theists think that various good outcomes would arise if Theism is true. We then discuss work in cognitive science concerning human cognitive bias, before discussing two noteworthy attempts to show that at least some religious beliefs arise because of cognitive bias: Hume’s, and Draper’s and Nichols’s. We then argue that, as a result of certain cognitive biases that result when good outcomes might be at stake, Pro-Theism causes many Theists to inflate the epistemic probability that God exists, and as a result, Theists should lower the probability they assign to God’s existence. Finally, based our arguments, we develop a novel objection to Pascal’s wager. (shrink)

Epistemology in modern times has been much influenced by the growth of the mathematical theory of probability. The reverse influence is less obvious, but perhaps equally important. This interrelation affords, moreover, an excellent example of the way philosophic ideas, while directing attention in one fruitful line of inquiry, at the same time may inhibit other discoveries until long overdue.

In Ch. 8, I distinguished epistemic probability from objective probability and then pointed out some debilitating problems with the three main accounts of epistemic probability. In this chapter, I propose my own account of epistemic probability. I first distinguish between two sides to epistemic probability, which I call the objective component and the normative component. In typical cases where we assert that some proposition is epistemically probable, two things get asserted: that (...) the proposition is objectively probable with respect to the evidence, and that it is rational to place a high degree of confidence in the proposition, given the circumstances of having as evidence what in fact we do have as evidence. Attempting to unpack these two components, I sketch the view that the normative component of the epistemic conditional probability of A on B is the interval containing the degrees of belief a rational person could have in A, provided she believed B and was aware that she believed B, considered the evidential bearing of B on A, had no other source of warrant for B or its denial, and had no defeater for the warrant, if any, accruing to A or its denial by virtue of being thus believed on the basis of B. (shrink)

This paper develops an information-sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional If A, then C equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that (...) rational agents update their credences via conditionalization. We offer a new rule of update, Hyperconditionalization, which agrees with Conditionalization whenever nonmodal statements are at stake but differs for modal and conditional sentences. (shrink)

This paper contributes to the investigation of the nature of the relation between probability theory and ranking theory. The paper aims at explaining the structural harmony between the laws of probability theory and those of ranking theory in a way that respects the foundational dualistic attitude developed by Spohn in The Laws of Belief. The paper argues that the so called atomic translation family satisfies the desiderata and does so in the ‘best’ possible way. On the one hand, (...) the atomic translation can be seen as ensuring maximal order agreement between rankings and probability—more would lead to trivialising dualism. On the other hand, the atomic translation also is assumption minimal, i.e., a minimal set of justifiable correspondences or translation principles suffice to derive the translation family, and this result is relatively robust. (shrink)

The representational epistemic approach to the design of visual displays and notation systems advocates encoding the fundamental conceptual structure of a knowledge domain directly in the structure of a representational system. It is claimed that representations so designed will benefit from greater semantic transparency, which enhances comprehension and ease of learning, and plastic generativity, which makes the meaningful manipulation of the representation easier and less error prone. Epistemic principles for encoding fundamental conceptual structures directly in representational schemes are (...) described. The diagrammatic recodification of probability theory is undertaken to demonstrate how the fundamental conceptual structure of a knowledge domain can be analyzed, how the identified conceptual structure may be encoded in a representational system, and the cognitive benefits that follow. An experiment shows the new probability space diagrams are superior to the conventional approach for learning this conceptually challenging topic. (shrink)

In this article, the epistemological interpretation of the relationship between concepts of relativism, beliefs, and probability ensures a defense of two theses, namely, (i) epistemic relativism refers to attitudes that depend on the repetition and anchoring of probabilistic beliefs, and (ii) Popper’s propensity interpretation of probability discloses the connections between relativity, probability, and collective subjectivity. The propensity interpretation brings a framework for describing the role of collective subjectivity in epistemic systems. This approach, as an acceptable (...) epistemological stance, is related to the variability of anchored collective beliefs. The repetition and anchoring of subjective probabilistic beliefs becomes a relative reference frame for evaluating the elements of knowledge. With this in mind, each particular way of considering probability indicates a manner of distinguishing epistemic systems. In epistemic systems, the statements are collective points of view expressed in the form ‘p is justified when belief in p is probably reliable.’ The statements can be accurate in a particular epistemic system but inaccurate in other systems. As a result, by avoiding the ‘all statements must be true or false’ requirement, each proponent of a certain epistemic system can build a probabilistic picture of the world. In this picture, not every statement needs to be ‘true’ when and if the statement expresses a collective point of view that has a propensity to be reliable and justified. (shrink)

A pluralistic scientific method is one that incorporates a variety of points of view in scientific inquiry. This paper investigates one example of pluralistic method: the use of weighted averaging in probability estimation. I consider two methods of weight determination, one based on disjoint evidence possession and the other on track record. I argue that weighted averaging provides a rational procedure for probability estimation under certain conditions. I consider a strategy for calculating ‘mixed weights’ which incorporate mixed information (...) about agent credibility. I address various objections to the weighted averaging technique and conclude that the technique is a promising one in various respects. (shrink)

Second or higher order probabilities have commonly been viewed with scepticism by those working within the realm of probability and decision theory. The aim of the present note is to show how the notion of second order probabilities can add to our understanding of judgmental and decision processes and how the traditional framework of Bayesian decision theory can be extended in a fruitful way by taking such entities into account. Section one consists of a brief account of arguments put (...) forth against higher order probabilities as well as of counterarguments. In order to provide an example of the applicability of second order probabilities a decision theory encompassing such probabilities will be presented in section two. In section three I will try to emphasize the value of second order probabilities for a deeper and more complete understanding of the notion of risk. (shrink)

This paper puts forward a novel pluralist theory of epistemic justification that brings together two competing views in the literature—probabilistic and non-probabilistic accounts of justification. The first part of the paper motivates the new theory by arguing that neither probabilistic nor non-probabilistic accounts alone are wholly satisfactory. The second part puts forward what I call the Functional Theory of Justification. The key merit of the new theory is that it combines the most attractive features of both probabilistic and non-probabilistic (...) accounts of justification while avoiding their most serious shortcomings. The paper also provides a blueprint for future pluralist projects in epistemology. (shrink)

This item was published as 'Appendix 3: An Implication of the k-option Condorcet jury mechanism for the probability of cycles' in List and Goodin (2001) http://eprints.lse.ac.uk/705/. Standard results suggest that the probability of cycles should increase as the number of options increases and also as the number of individuals increases. These results are, however, premised on a so-called "impartial culture" assumption: any logically possible preference ordering is assumed to be as likely to be held by an individual as (...) any other. The present chapter shows, in the three-option case, that given suitably systematic, however slight, deviations from an impartial culture situation, the probability of a cycle converges either to zero (more typically) or to one (less typically) as the number of individuals increases. (shrink)

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief (...) change is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

According to a standard view, quantum mechanics is a contextual theory and quantum probability does not satisfy Kolmogorov’s axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts underlying them, that one can interpret quantum probability as epistemic, despite its non-Kolmogorovian structure. To attain this result we introduce a predicate language L, a classical probability measure on it and a family of classical probability measures on sets of μ-contexts, each (...) element of the family corresponding to a measurement procedure. By using only Kolmogorovian probability measures we can thus define mean conditional probabilities on the set of properties of any quantum system that admit an epistemic interpretation but are not bound to satisfy Kolmogorov’s axioms. The generalized probability measures associated with states in QM can then be seen as special cases of these mean probabilities, which explains how they can be non-classical and provides them with an epistemic interpretation. Moreover, the distinction between compatible and incompatible properties is explained in a natural way, and purely theoretical classical conditional probabilities coexist with empirically testable quantum conditional probabilities. (shrink)

Multiple epistemological programs make use of intuitive judgments pertaining to an individual’s ability to gain knowledge from exclusively probabilistic/statistical information. This paper argues that these judgments likely form without deference to such information, instead being a function of the degree to which having knowledge is representative of an agent. Thus, these judgments fit the pattern of formation via a representativeness heuristic, like that famously described by Kahneman and Tversky to explain similar probabilistic judgments. Given this broad insensitivity to probabilistic/statistical information, (...) it directly follows that these epistemic judgments are insensitive to a given agent’s epistemic status. From this, the paper concludes that, breaking with common epistemological practice, we cannot assume that such judgments are reliable. (shrink)

I present a straightforward objection to the view that what we know has epistemic probability 1: when combined with Bayesian decision theory, the view seems to entail implausible conclusions concerning rational choice. I consider and reject three responses. The first holds that the fault is with decision theory, rather than the view that knowledge has probability 1. The second two try to reconcile the claim that knowledge has probability 1 with decision theory by appealing to contextualism (...) and sensitive invariantism, respectively. I argue that each response fails, and that we can hold on to much of what was attractive in the responses while denying that what we know has probability 1. (shrink)

This article discusses Mesoudi et al.’s suggestion to synthesise the social sciences based on a theory of cultural evolution. In view of their proposal, I shall discuss two key questions. (I) Is their theory of cultural evolution a promising candidate to synthesise the social sciences? (II) What is the added value of evolutionary approaches for the social sciences? My aim is to highlight some hitherto underestimated challenges for transformative evolutionary approaches to the social sciences that come into view when one (...) looks at these questions against the backdrop of actual scientific practice in the social sciences. (shrink)

By “epistemic modals,” I mean epistemic uses of modal words: adverbs like “necessarily,” “possibly,” and “probably,” adjectives like “necessary,” “possible,” and “probable,” and auxiliaries like “might,” “may,” “must,” and “could.” It is hard to say exactly what makes a word modal, or what makes a use of a modal epistemic, without begging the questions that will be our concern below, but some examples should get the idea across. If I say “Goldbach’s conjecture might be true, and it (...) might be false,” I am not endorsing the Cartesian view that God could have made the truths of arithmetic come out differently. I make the claim not because I believe in the metaphysical contingency of mathematics, but because I know that Goldbach’s conjecture has not yet been proved or refuted. Similarly, if I say “Joe can’t be running,” I am not saying that Joe’s constitution prohibits him from running, or that Joe is essentially a non-runner, or that Joe isn’t allowed to run. My basis for making the claim may be nothing more than that I see Joe’s running shoes hanging on a hook. (shrink)

Subjective Probability: The Real Thing is the last book written by the late Richard Jeffrey, a key proponent of the Bayesian interpretation of probability.Bayesians hold that probability is a mental notion: saying that the probability of rain is 0.7 is just saying that you believe it will rain to degree 0.7. Degrees of belief are themselves cashed out in terms of bets—in this case you consider 7:3 to be fair odds for a bet on rain. There (...) are two extreme Bayesian positions. Strict subjectivists think that an agent can adopt whatever degrees of belief she likes, as long as they satisfy the axioms of probability. Thus your degree of belief in rain and degree of belief in no rain must sum to one but are otherwise unconstrained. At the other extreme, objectivists claim that an agent's background knowledge considerably narrows down the choice of appropriate degrees of belief. In particular, if you know only that the frequency of rain is 0.7 then you should believe it will rain to degree 0.7; if you know absolutely nothing about the weather then you should set your degree of belief in rain to be 0.5; in neither of these cases is there room for subjective choice of degree of belief. In this book, Jeffrey advocates what is sometimes called empirically-based subjectivism, a position that lies between the two extremes of strict subjectivism and objectivism. According to this position, knowledge of frequencies constrains degree of belief, but lack of knowledge does not impose any constraints, so that if you know nothing about the weather you may adopt any degree of belief in rain you like.1The aim of the book is not so much to justify this point of view as to provide a comprehensive exposition of probability theory from the …. (shrink)

This critical essay evaluates the potential integration of distinct kinds of expertise in policymaking, especially during situations of critical emergencies, such as the COVID-19 pandemic. This article relies on two case studies: herd immunity and restricted access to ventilators for disabled people. These case studies are discussed as examples of experts’ recommendations that have not been widely accepted, though they were made within the boundaries of expert epistemic authority. While the fundamental contribution of biomedical experts in devising public health (...) policies during the COVID-19 pandemic is fully recognized, this paper intends to discuss potential issues and limitations that may arise when adopting a strict expert-based approach. By drawing attention to the interests of minorities, the paper also claims a broader notion of “relevant expertise.” This critical essay thus calls for the necessity of wider inclusiveness and representativeness in the process underlying public health policymaking. (shrink)

Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett’s seminal idea is that all possible definite futures on the pointer basis exist as components of a macroscopic linear superposition. I demonstrate that these two conceptions of what is involved in quantum processes are linked via two alternative interpretations of the mind-body relation. This leads to a fission, rather than divergence, interpretation of Everettian theory (...) and to a novel explanation of why a principle of indifference does not apply to self-location uncertainty for a post-measurement, pre-observation subject, just as Sebens and Carroll claim. Their Epistemic Separability Principle is shown to arise out of this explanation and the derivation of the Born rule for Everettian theory is thereby put on a firmer footing. (shrink)

This chapter will review selected aspects of the terrain of discussions about probabilities in statistical mechanics (with no pretensions to exhaustiveness, though the major issues will be touched upon), and will argue for a number of claims. None of the claims to be defended is entirely original, but all deserve emphasis. The first, and least controversial, is that probabilistic notions are needed to make sense of statistical mechanics. The reason for this is the same reason that convinced Maxwell, Gibbs, and (...) Boltzmann that probabilities would be needed, namely, that the second law of thermodynamics, which in its original formulation says that certain processes are impossible, must, on the kinetic theory, be replaced by a weaker formulation according to which what the original version deems impossible is merely improbable. Second is that we ought not take the standard measures invoked in equilibrium statistical mechanics as giving, in any sense, the correct probabilities about microstates of the system. We can settle for a much weaker claim: that the probabilities for outcomes of experiments yielded by the standard distributions are effectively the same as those yielded by any distribution that we should take as a representing probabilities over microstates. Lastly, (and most controversially): in asking about the status of probabilities in statistical mechanics, the familiar dichotomy between epistemic probabilities (credences, or degrees of belief) and ontic (physical) probabilities is insufficient; the concept of probability that is best suited to the needs of statistical mechanics is one that combines epistemic and physical considerations. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context (...) are explored. (shrink)

_Probability: A Philosophical Introduction_ introduces and explains the principal concepts and applications of probability. It is intended for philosophers and others who want to understand probability as we all apply it in our working and everyday lives. The book is not a course in mathematical probability, of which it uses only the simplest results, and avoids all needless technicality. The role of probability in modern theories of knowledge, inference, induction, causation, laws of nature, action and decision-making (...) makes an understanding of it especially important to philosophers and students of philosophy, to whom this book will be invaluable both as a textbook and a work of reference. In this book D. H. Mellor discusses the three basic kinds of probability – physical, epistemic, and subjective – and introduces and assesses the main theories and interpretations of them. The topics and concepts covered include: * chance * frequency * possibility * propensity * credence * confirmation * Bayesianism. _Probability: A Philosophical Introduction_ is essential reading for all philosophy students and others who encounter or need to apply ideas of probability. (shrink)

Most Probably: Epistemic Modality in Old Babylonian by Nathan Wasserman is the first attempt to provide a description of the domain of epistemic modality in Old Babylonian Akkadian. This attempt is not entirely successful, for several reasons. Methodological inconsistency often impairs the author’s ability to convince the reader of his solutions. Both primary data and existing secondary literature are used only selectively, which renders the proposed description problematic. Finally, the lack of cross-referencing between the chapters evokes the feeling (...) that the different particles do not quite constitute a system. (shrink)