This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to (...) the introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. We propose application of the language of relative analysis (a type of non-standard analysis) to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (shrink)

This paper offers and account of the "system" of probable reasoning presented in Hume's Treatise and first Enquiry. The system is sceptical because it takes our beliefs to be the product of naturally occurring psychological mechanisms rather than logically sound judgment, and because it declares those beliefs to be ultimately unjustifiable. This paper explains how Hume was nonetheless able to provide for a logic of probable reasoning, grounded on natural, but unjustifiable beliefs.

The epistemology of essence is a topic that has received relatively little attention, although there are signs that this is changing. The lack of literature engaging directly with the topic is probably partly due to the mystery surrounding the notion of essence itself, and partly due to the sheer difficulty of developing a plausible epistemology. The need for such an account is clear especially for those, like E.J. Lowe, who are committed to a broadly Aristotelian conception of essence, (...) whereby essence plays an important theoretical role. In this chapter, our epistemic access to essence is examined in terms of the a posteriori vs. a priori distinction. The two main accounts to be contrasted are those of David S. Oderberg and E.J. Lowe. (shrink)

The near-miss has been considered an important factor of reinforcement in gambling behavior, and previous research has focused more on its industry-related causes and effects and less on the gaming phenomenon itself. The near-miss has usually been associated with the games of slots and scratch cards, due to the special characteristics of these games, which include the possibility of pre-manipulation of award symbols in order to increase the frequency of these “engineered” near-misses. In this paper, we argue that starting from (...) an elementary mathematical description of the classical (by pure chance) near-miss, generalizable to any game, and focusing equally on the epistemology of its constitutive concepts and their mathematical description, we can identify more precisely the fallacious elements of the near-miss cognitive effects and the inadequate perception and representation of the observational-intentional “I was that close.” This approach further suggests a strategy of using non-standard mathematical knowledge of an epistemological type in problem-gambling prevention and cognitive therapies. (shrink)

The epistemology of risk examines how risks bear on epistemic properties. A common framework for examining the epistemology of risk holds that strength of evidential support is best modelled as numerical probability given the available evidence. In this essay I develop and motivate a rival ‘relevant alternatives’ framework for theorising about the epistemology of risk. I describe three loci for thinking about the epistemology of risk. The first locus concerns consequences of relying on a belief (...) for action, where those consequences are significant if the belief is false. The second locus concerns whether beliefs themselves—regardless of action—can be risky, costly, or harmful. The third locus concerns epistemic risks we confront as social epistemic agents. I aim to motivate the relevant alternatives framework as a fruitful approach to the epistemology of risk. I first articulate a ‘relevant alternatives’ model of the relationship between stakes, evidence, and action. I then employ the relevant alternatives framework to undermine the motivation for moral encroachment. Finally, I argue the relevant alternatives framework illuminates epistemic phenomena such as gaslighting, conspiracy theories, and crying wolf, and I draw on the framework to diagnose the undue skepticism endemic to rape accusations. (shrink)

In a recent paper in this journal, Carter and Peterson raise two distinctly epistemological puzzles that arise for anyone aspiring to defend the precautionary principle. The first puzzle trades on an application of epistemic contextualism to the precautionary principle; the second puzzle concerns the compatibility of the precautionary principle with the de minimis rule. In this note, I argue that neither puzzle should worry defenders of the precautionary principle. The first puzzle can be shown to be an instance of the (...) familiar but conceptually harmless challenge of adjudicating between relevant interests to reach assessments of threats when applying the precautionary principle. The second puzzle can be shown to rely on a subtle but crucial misrepresentation of the relevant probabilities at play when applying the precautionary principle. (shrink)

When people disagree about what is moral, we face an epistemological challenge—when the answer to a moral question is not obvious, how do we determine who is right? What if, under the circumstances, we do not have the means to show one party or the other is right? In recent years, a number of epistemologists have turned their attention to the general epistemic problem of how to respond reasonably to disagreement, and we can look to their work for guidance. While (...) there remains significant disagreement about how to respond to disagreement, I will focus on what I take to be the best position in the debate, known as the “Conciliatory” position (or “Conciliation” for short), which holds that parties to a disagreement should become less confident of their initial opinions to some degree, according to the credibility of the parties involved. Conciliation, if interpreted straightforwardly, has some counter-intuitive implications for unpopular opinions, including unpopular moral judgments. If a moral non-conformist becomes somewhat less confident of her view in response to each disagreement with a presumed epistemic peer, she will eventually have such a low degree of confidence in her initial view that she will effectively have switched positions. This result is troubling because almost everyone accepts moral views that were non-conforming views at some point in time, and these views probably would not have become widespread if non-conformists had changed their positions. I propose a modified version of Conciliation which would enable moral non-conformists to engage in cautious “experiments in living.” This modified view, I argue, is reasonable for those who are concerned, not only with correcting their own mistaken moral views, but with promoting moral progress in general. (shrink)

I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.

Whereas many philosophers accept the validity of 'probability' and confine themselves to interpreting it, this paper challenges its conceptual coherence by critically examining its use in the empirical world. While measure theory provides a rigorous mathematical framework for manipulating probability functions, we argue that applying precise probability measures to empirically uncertain outcomes introduces a fundamental contradiction. Probability measures claim to quantify uncertainty while simultaneously implying a degree of understanding about events that we do not fully possess. (...) This inconsistency undermines the idea that probability offers objective or reliable insights into reality. Moreover, we argue that it is impossible to assign a correct probability in the empirical world—neither deduction nor induction provides a justifiable basis for doing so. Therefore, despite probability appearing to work as a practical tool for managing uncertainty, its theoretical foundation collapses under scrutiny in empirical applications. (shrink)

This paper defends David Hume's "Of Miracles" from John Earman's (2000) Bayesian attack by showing that Earman misrepresents Hume's argument against believing in miracles and misunderstands Hume's epistemology of probable belief. It argues, moreover, that Hume's account of evidence is fundamentally non-mathematical and thus cannot be properly represented in a Bayesian framework. Hume's account of probability is show to be consistent with a long and laudable tradition of evidential reasoning going back to ancient Roman law.

This paper tries to develop an epistemological analysis on the notion of responsibility. After pointing out a peculiar kind of uncertainties concerning the notion of responsibility, I focus upon the issue of criminal responsibility, taking the case of mentally disordered offenders into account, and propose the distinction of the phases between sentence and practice with applying Slobogin's idea of integrationism. Finally, I propose a probabilistic approach to the problem of responsibility through considering the idea of relevance ratio, leading to my (...) final proposal concerning the concept of the degrees of responsibility. (shrink)

Evaluative studies of inductive inferences have been pursued extensively with mathematical rigor in many disciplines, such as statistics, econometrics, computer science, and formal epistemology. Attempts have been made in those disciplines to justify many different kinds of inductive inferences, to varying extents. But somehow those disciplines have said almost nothing to justify a most familiar kind of induction, an example of which is this: “We’ve seen this many ravens and they all are black, so all ravens are black.” This (...) is enumerative induction in itsfullstrength. For it does not settle with a weaker conclusion (such as “the ravens observed in the future will all be black”); nor does it proceed with any additional premise (such as the statistical IID assumption). The goal of this paper is to take some initial steps toward a justification for the full version of enumerative induction, against counterinduction, and against the skeptical policy. The idea is to explore various epistemic ideals, mathematically defined as different modes of convergence to the truth, and look for one that is weak enough to be achievable and strong enough to justify a norm that governs both the long run and the short run. So the proposal is learning-theoretic in essence, but a Bayesian version is developed as well. (shrink)

To understand something involves some sort of commitment to a set of propositions comprising an account of the understood phenomenon. Some take this commitment to be a species of belief; others, such as Elgin and I, take it to be a kind of cognitive policy. This paper takes a step back from debates about the nature of understanding and asks when this commitment involved in understanding is epistemically appropriate, or ‘acceptable’ in Elgin’s terminology. In particular, appealing to lessons from the (...) lottery and preface paradoxes, it is argued that this type of commitment is sometimes acceptable even when it would be rational to assign arbitrarily low probabilities to the relevant propositions. This strongly suggests that the relevant type of commitment is sometimes acceptable in the absence of epistemic justification for belief, which in turn implies that understanding does not require justification in the traditional sense. The paper goes on to develop a new probabilistic model of acceptability, based on the idea that the maximally informative accounts of the understood phenomenon should be optimally probable. Interestingly, this probabilistic model ends up being similar in important ways to Elgin’s proposal to analyze the acceptability of such commitments in terms of ‘reflective equilibrium’. (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)

An examination of the role played by general rules in Hume's positive (nonskeptical) epistemology. General rules for Hume are roughly just general beliefs. The difference between justified and unjustified belief is a matter of the influence of good versus bad general rules, the good general rules being the "extensive" and "constant" ones.

Hope is an attitude with a distinctive epistemological dimension: it is incompatible with knowledge. This chapter examines hope as it relates to knowledge but also to probability and inductive considerations. Such epistemic constraints can make hope either impossible, or, when hope remains possible, they affect how one’s epistemic situation can make hope rational rather than irrational. Such issues are especially relevant to when hopefulness may permissibly figure in practical deliberation over a course of action. So I consider cases of (...) second-order inductive reflection on when one should, or should not, be hopeful for an outcome with which one has a long record of experience: in other words, what is the epistemology behind when one should, if ever, stop hoping for outcomes which have failed one many times in the past? (shrink)

Many philosophers argue that Keynes’s concept of the “weight of arguments” is an important aspect of argument appraisal. The weight of an argument is the quantity of relevant evidence cited in the premises. However, this dimension of argumentation does not have a received method for formalisation. Kyburg has suggested a measure of weight that uses the degree of imprecision in his system of “Evidential Probability” to quantify weight. I develop and defend this approach to measuring weight. I illustrate the (...) usefulness of this measure by employing it to develop an answer to Popper’s Paradox of Ideal Evidence. (shrink)

The aim of the paper is to develop general criteria of argumentative validity and adequacy for probabilistic arguments on the basis of the epistemological approach to argumentation. In this approach, as in most other approaches to argumentation, proabilistic arguments have been neglected somewhat. Nonetheless, criteria for several special types of probabilistic arguments have been developed, in particular by Richard Feldman and Christoph Lumer. In the first part (sects. 2-5) the epistemological basis of probabilistic arguments is discussed. With regard to the (...) philosophical interpretation of probabilities a new subjectivist, epistemic interpretation is proposed, which identifies probabilities with tendencies of evidence (sect. 2). After drawing the conclusions of this interpretation with respect to the syntactic features of the probability concept, e.g. one variable referring to the data base (sect. 3), the justification of basic probabilities (priors) by judgements of relative frequency (sect. 4) and the justification of derivative probabilities by means of the probability calculus are explained (sect. 5). The core of the paper is the definition of '(argumentatively) valid derivative probabilistic arguments', which provides exact conditions for epistemically good probabilistic arguments, together with conditions for the adequate use of such arguments for the aim of rationally convincing an addressee (sect. 6). Finally, some measures for improving the applicability of probabilistic reasoning are proposed (sect. 7). (shrink)

I examine what the mathematical theory of random structures can teach us about the probability of Plenitude, a thesis closely related to David Lewis's modal realism. Given some natural assumptions, Plenitude is reasonably probable a priori, but in principle it can be (and plausibly it has been) empirically disconfirmed—not by any general qualitative evidence, but rather by our de re evidence.

An aspect of Peirce’s thought that may still be underappreciated is his resistance to what Levi calls _pedigree epistemology_, to the idea that a central focus in epistemology should be the justification of current beliefs. Somewhat more widely appreciated is his rejection of the subjective view of probability. We argue that Peirce’s criticisms of subjectivism, to the extent they grant such a conception of probability is viable at all, revert back to pedigree epistemology. A thoroughgoing rejection (...) of pedigree in the context of probabilistic epistemology, however, _does_ challenge prominent subjectivist responses to the problem of the priors. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...) Staffel and compare it to a recent competitor put forth by Moss. (shrink)

When scientists come up with some incredible results, what should we believe? This paper discusses the role of probability and statistics in helping determine what science tells us about our knowledge of the world.

This paper shows that Hume was ultimately forced to conclude in The Treatise that all demonstrative and intuited claims can in fact, be imagined as otherwise. As a result, he was forced to conclude that all knowledge claims must, ultimately, reduce to probable claims, or in Hume’s own, and indisputably clear words: “all knowledge degenerates into probability." As a further result, it is suggested (briefly) that this anticipates Quine’s well-known attack on the analytic / synthetic distinction (Quine 1953).

Recently there have been several attempts in formal epistemology to develop an adequate probabilistic measure of coherence. There is much to recommend probabilistic measures of coherence. They are quantitative and render formally precise a notion—coherence—notorious for its elusiveness. Further, some of them do very well, intuitively, on a variety of test cases. Siebel, however, argues that there can be no adequate probabilistic measure of coherence. Take some set of propositions A, some probabilistic measure of coherence, and a probability (...) distribution such that all the probabilities on which A’s degree of coherence depends (according to the measure in question) are defined. Then, the argument goes, the degree to which A is coherent depends solely on the details of the distribution in question and not at all on the explanatory relations, if any, standing between the propositions in A. This is problematic, the argument continues, because, first, explanation matters for coherence, and, second, explanation cannot be adequately captured solely in terms of probability. We argue that Siebel’s argument falls short. (shrink)

This article analyzes the role of entropy in Bayesian statistics, focusing on its use as a tool for detection, recognition and validation of eigen-solutions. “Objects as eigen-solutions” is a key metaphor of the cognitive constructivism epistemological framework developed by the philosopher Heinz von Foerster. Special attention is given to some objections to the concepts of probability, statistics and randomization posed by George Spencer-Brown, a figure of great influence in the field of radical constructivism.

Most of us are either philosophically naïve scientists or scientifically naïve philosophers, so we misjudged Schrödinger’s “very burlesque” portrait of Quantum Theory (QT) as a profound conundrum. The clear signs of a strawman argument were ignored. The Ontic Probability Interpretation (TOPI) is a metatheory: a theory about the meaning of QT. Ironically, equating Reality with Actuality cannot explain actual data, justifying the century-long philosophical struggle. The actual is real but not everything real is actual. The ontic character of the (...) Probable has been elusive for so long because it cannot be grasped directly from experiment; it can only be inferred from physical setups that do not morph it into the Actual. In this Part III, Born’s Rule and the quantum formalism for the microworld are intuitively surmised from instances in our macroworld. The posited reality of the quanton’s probable states and properties is probed and proved. After almost a century, TOPI aims at setting the record straight: the so-called ‘Basis’ and ‘Measurement’ problems are ill-advised. About the first, all bases are legitimate regardless of state and milieu. As for the second, its premise is false: there is no need for a physical ‘collapse’ process that would convert many states into a single state. Under TOPI, a more sensible variant of the ‘measurement problem’ can be reformulated in non-anthropic terms as a real problem. Yet, as such, it is not part of QT per se and will be tackled in future papers. As for the mythical cat, the ontic state of a radioactive nucleus is not pure, so its evolution is not governed by Schrödinger’s equation – let alone the rest of his “hellish machine”. Einstein was right: “The Lord is subtle but not malicious”. However, ‘The Lord’ turned out to be much subtler than what Einstein and Schrödinger could have ever accepted. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [1]. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work (...) in neuroscience and behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (shrink)

This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism about objects. Section wraps it all up with metametaphysical considerations regarding the epistemology of metaphysics of science.

In his entry on "Quantum Logic and Probability Theory" in the Stanford Encyclopedia of Philosophy, Alexander Wilce (2012) writes that "it is uncontroversial (though remarkable) the formal apparatus quantum mechanics reduces neatly to a generalization of classical probability in which the role played by a Boolean algebra of events in the latter is taken over the 'quantum logic' of projection operators on a Hilbert space." For a long time, Patrick Suppes has opposed this view (see, for example, the (...) paper collected in Suppes and Zanotti (1996). Instead of changing the logic and moving from a Boolean algebra to a non-Boolean algebra, one can also 'save the phenomena' by weakening the axioms of probability theory and work instead with upper and lower probabilities. However, it is fair to say that despite Suppes' efforts upper and lower probabilities are not particularly popular in physics as well as in the foundations of physics, at least so far. Instead, quantum logic is booming again, especially since quantum information and computation became hot topics. Interestingly, however, imprecise probabilities are becoming more and more popular in formal epistemology as recent work by authors such as James Joye (2010) and Roger White (2010) demonstrates. (shrink)

This paper is about teaching probability to students of philosophy who don’t aim to do primarily formal work in their research. These students are unlikely to seek out classes about probability or formal epistemology for various reasons, for example because they don’t realize that this knowledge would be useful for them or because they are intimidated by the material. However, most areas of philosophy now contain debates that incorporate probability, and basic knowledge of it is essential (...) even for philosophers whose work isn’t primarily formal. In this paper, I explain how to teach probability to students who are not already enthusiastic about formal philosophy, taking into account the common phenomena of math anxiety and the lack of reading skills for formal texts. I address course design, lesson design, and assignment design. Most of my recommendations also apply to teaching formal methods other than probability theory. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that (...) it is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

Enjoying great popularity in decision theory, epistemology, and philosophy of science, Bayesianism as understood here is fundamentally concerned with epistemically ideal rationality. It assumes a tight connection between evidential probability and ideally rational credence, and usually interprets evidential probability in terms of such credence. Timothy Williamson challenges Bayesianism by arguing that evidential probabilities cannot be adequately interpreted as the credences of an ideal agent. From this and his assumption that evidential probabilities cannot be interpreted as the actual (...) credences of human agents either, he concludes that no interpretation of evidential probabilities in terms of credence is adequate. I argue to the contrary. My overarching aim is to show on behalf of Bayesians how one can still interpret evidential probabilities in terms of ideally rational credence and how one can maintain a tight connection between evidential probabilities and ideally rational credence even if the former cannot be interpreted in terms of the latter. By achieving this aim I illuminate the limits and prospects of Bayesianism. (shrink)

Philosophers have long debated ‘substrate’ and ‘bundle’ theories as to how properties hold together in objects ― but have neglected to consider that every chemical entity is defined by closure of relationships among components ― here designated ‘Closure Louis de Broglie.’ That type of closure underlies the coherence of spectroscopic and chemical properties of chemical substances, and is importantly implicated in the stability and definition of entities of many other types, including those usually involved in philosophic discourse ― such as (...) roses, statues, and tennis balls. Characteristics of composites are often presumed to ‘supervene on’ properties of components. This assumption does not apply when cooperative interactions among components are significant. Once correlations dominate, then adequate descriptions must involve different entities and relationships than those that are involved in ‘fundamental-level’ description of similar but uncorrelated systems. That is to say, descriptions must involve different semantics than would be appropriate if cooperative interactions were insignificant. This is termed ‘Closure Henri Poincaré. Networks of chemical reactions that have certain types of closure of processes display properties that make other more-complex coherences possible. This is termed ‘Closure Jacques Cauvin.’ Each of these three modes of closure provides a sufficient basis for warranted recognition of causal interaction, thus each of them has epistemological significance. Other modes of epistemologically-important closure probably exist. It is important to recognize that causal efficacy generally depends on closure of relationships of constituents. (shrink)

How do agents with limited cognitive capacities flourish in informationally impoverished or unexpected circumstances? Aristotle argued that human flourishing emerged from knowing about the world and our place within it. If he is right, then the virtuous processes that produce knowledge, best explain flourishing. Influenced by Aristotle, virtue epistemology defends an analysis of knowledge where beliefs are evaluated for their truth and the intellectual virtue or competences relied on in their creation. However, human flourishing may emerge from how degrees (...) of ignorance are managed in an uncertain world. Perhaps decision-making in the shadow of knowledge best explains human wellbeing—a Bayesian approach? In this dissertation I argue that a hybrid of virtue and Bayesian epistemologies explains human flourishing—what I term homeostatic epistemology. Homeostatic epistemology supposes that an agent has a rational credence p when p is the product of reliable processes aligned with the norms of probability theory; whereas an agent knows that p when a rational credence p is the product of reliable processes such that: 1) p meets some relevant threshold for belief, 2) p coheres with a satisficing set of relevant beliefs and, 3) the relevant set of beliefs is coordinated appropriately to meet the integrated aims of the agent. Homeostatic epistemology recognizes that justificatory relationships between beliefs are constantly changing to combat uncertainties and to take advantage of predictable circumstances. Contrary to holism, justification is built up and broken down across limited sets like the anabolic and catabolic processes that maintain homeostasis in the cells, organs and systems of the body. It is the coordination of choristic sets of reliably produced beliefs that create the greatest flourishing given the limitations inherent in the situated agent. (shrink)

According to the so-called Lockean thesis, a rational agent believes a proposition just in case its probability is sufficiently high, i.e., greater than some suitably fixed threshold. The Preface paradox is usually taken to show that the Lockean thesis is untenable, if one also assumes that rational agents should believe the conjunction of their own beliefs: high probability and rational belief are in a sense incompatible. In this paper, we show that this is not the case in general. (...) More precisely, we consider two methods of computing how probable must each of a series of propositions be in order to rationally believe their conjunction under the Lockean thesis. The price one has to pay for the proposed solutions to the paradox is what we call “quasi-dogmatism”: the view that a rational agent should believe only those propositions which are “nearly certain” in a suitably defined sense. (shrink)

Dorothy Edgington’s work has been at the centre of a range of ongoing debates in philosophical logic, philosophy of mind and language, metaphysics, and epistemology. This work has focused, although by no means exclusively, on the overlapping areas of conditionals, probability, and paradox. In what follows, I briefly sketch some themes from these three areas relevant to Dorothy’s work, highlighting how some of Dorothy’s work and some of the contributions of this volume fit in to these debates.

With the previous technical reports, we presented the main insights from the qualitative analysis of the reflection of the mathematical dimension of gambling in gambling-related sites, in its structural, linguistic, epistemic, and informative aspects. In this report we will focus on the factors responsible for the patterns that the content of the gambling-related sites exhibit and the way that the mathematical dimension of gambling is reflected in this content, namely the factors that influence the content policies of these sites. The (...) report will also point to further directions of research-for both this project and for other investigators-for finding the appropriate balance and relation between the commercial policies on the one hand, and the adequacy and ethics of the content on the other hand. (shrink)

The current study evaluates qualitatively how the mathematical dimension of gambling is reflected in the content of gambling websites. A number of gambling websites have been reviewed for their content in that respect. A statistical analysis recorded the presence of the mathematical dimension of gambling and its forms in the content of the participating websites, and a qualitative research study analyzed and assessed the quality of the content with respect to that dimension. The technical reports associated with this study describe (...) the methods used in the processes of review and content analysis, details of the processes, and the specific challenges and difficulties that they posed. (shrink)

The current technical report of the research project investigating how the mathematical dimension of gambling is reflected in the communication and texts associated with the gambling industry raises the problem of the adequacy of sampling and proposes a new approach in this respect. The qualitative analysis of the reviewed websites is extended to a deeper analysis of language and also to the organization and structure of websites’ content. Although not stated as a goal of the initial project, the research will (...) also try to identify relationships between the specificity of content relative to the mathematical dimension of gambling, and the management and marketing of the website. An overview of the results of the statistical analysis of the current sample is also presented. (shrink)

The enigma of the Emergence of Natural Languages, coupled or not with the closely related problem of their Evolution is perceived today as one of the most important scientific problems. The purpose of the present study is actually to outline such a solution to our problem which is epistemologically consonant with the Big Bang solution of the problem of the Emergence of the Universe}. Such an outline, however, becomes articulable, understandable, and workable only in a drastically extended epistemic and scientific (...) oecumene, where known and habitual approaches to the problem, both theoretical and experimental, become distant, isolated, even if to some degree still hospitable conceptual and methodological islands. The guiding light of our inquiry will be Eugene Paul Wigner's metaphor of ``the unreasonable effectiveness of mathematics in natural sciences'', i.e., the steadily evolving before our eyes, since at least XVIIth century, ``the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics''. Kurt Goedel's incompleteness and undecidability theory will be our guardian discerner against logical fallacies of otherwise apparently plausible explanations. John Bell's ``unspeakableness'' and the commonplace counterintuitive character of quantum phenomena will be our encouragers. And the radical novelty of the introduced here and adapted to our purposes Big Bang epistemological paradigm will be an appropriate, even if probably shocking response to our equally shocking discovery in the oldest among well preserved linguistic fossils of perfect mathematical structures outdoing the best artifactual Assemblers. (shrink)

If we add as an extra premise that the agent does know H, then it is possible for her to know E — H, we get the conclusion that the agent does not really know H. But even without that closure premise, or something like it, the conclusion seems quite dramatic. One possible response to the argument, floated by both Descartes and Hume, is to accept the conclusion and embrace scepticism. We cannot know anything that goes beyond our evidence, so (...) we do not know very much at all. This is a remarkably sceptical conclusion, so we should resist it if at all possible. A more modern response, associated with externalists like John McDowell and Timothy Williamson, is to accept the conclusion but deny it is as sceptical as it first appears. The Humean argument, even if it works, only shows that our evidence and our knowledge are more closely linked than we might have thought. Perhaps that’s true because we have a lot of evidence, not because we have very little knowledge. There’s something right about this response I think. We have more evidence than Descartes or Hume thought we had. But I think we still need the idea of ampliative knowledge. It stretches the concept of evidence to breaking point to suggest that all of our knowledge, including knowledge about the future, is part of our evidence. So the conclusion really is unacceptable. Or, at least, I think we should try to see what an epistemology that rejects the conclusion looks like. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, (...) indicated by an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

Evidentialists say that a necessary condition of sound epistemic reasoning is that our beliefs reflect only our evidence. This thesis arguably conflicts with standard Bayesianism, due to the importance of prior probabilities in the latter. Some evidentialists have responded by modelling belief-states using imprecise probabilities (Joyce 2005). However, Roger White (2010) and Aron Vallinder (2018) argue that this Imprecise Bayesianism is incompatible with evidentialism due to “inertia”, where Imprecise Bayesian agents become stuck in a state of ambivalence towards hypotheses. Additionally, (...) escapes from inertia apparently only create further conflicts with evidentialism. This dilemma gives a reason for evidentialist imprecise probabilists to look for alternatives without inertia. I shall argue that Henry E. Kyburg’s approach offers an evidentialist-friendly imprecise probability theory without inertia, and that its relevant anti-inertia features are independently justified. I also connect the traditional epistemological debates concerning the “ethics of belief” more systematically with formal epistemology than has been hitherto done. (shrink)

Bayesianism is our leading theory of uncertainty. Epistemology is defined as the theory of knowledge. So “Bayesian Epistemology” may sound like an oxymoron. Bayesianism, after all, studies the properties and dynamics of degrees of belief, understood to be probabilities. Traditional epistemology, on the other hand, places the singularly non-probabilistic notion of knowledge at centre stage, and to the extent that it traffics in belief, that notion does not come in degrees. So how can there be a Bayesian (...) epistemology? (shrink)

The paper develops a classificatory system of basic argument types on the basis of the epis-temological approach to argumentation. This approach has provided strict rules for several kinds of argu-ments. These kinds may be brought into a system of basic irreducible types, which rely on different parts of epistemology: deductive logic, probability theory, utility theory. The system reduces a huge mass of differ-ent argument schemes to basic types and gives them an epistemological foundation.

This paper examines how accepting the simulation hypothesis as a serious philosophical proposition forces a fundamental reconsideration of epistemological certainty. While previous work has focused on the probability of living in a simulation or the nature of consciousness within simulations, we demonstrate that the mere possibility of simulated reality creates a unique crisis for knowledge hierarchies that differs fundamentally from traditional sceptical arguments. Unlike Cartesian doubt, which preserves the notion of an objective reality while questioning our access to it, (...) the simulation hypothesis suggests reality itself might be programmatically mutable. We argue this undermines traditional distinctions between scientific and religious epistemology, creates an insoluble verification paradox for scientific methodology, and requires a radical reimagining of knowledge and truth. While we suggest that complete epistemological scepticism might be avoided through appeal to necessary logical primitives, we conclude that accepting the possibility of simulated reality requires a fundamental reconstruction of how we understand knowledge, scientific practice, and the relationship between competing explanatory frameworks. (shrink)

This paper calls for a re-appraisal of McGee's analysis of the semantics, logic and probabilities of indicative conditionals presented in his 1989 paper Conditional probabilities and compounds of conditionals. The probabilistic measures introduced by McGee are given a new axiomatisation built on the principle that the antecedent of a conditional is probabilistically independent of the conditional and a more transparent method of constructing such measures is provided. McGee's Dutch book argument is restructured to more clearly reveal that it introduces a (...) novel contribution to the epistemology of semantic indeterminacy, and shows that its more controversial implications are unavoidable if we want to maintain the Ramsey Test along with the standard laws of probability. Importantly, it is shown that the counterexamples that have been levelled at McGee's analysis|generating a rather wide consensus that it yields `unintuitive' or `wrong' probabilities for compounds |fail to strike at their intended target; for to honour the intuitions of the counterexamples one must either give up the Ramsey Test or the standard laws of probability. It will be argued that we need to give up neither if we take the counterexamples as further evidence that the indicative conditional sometimes allows for a non-epistemic `causal' interpretation alongside its usual epistemic interpretation. (shrink)

It is often claimed that credences are not reducible to ordinary beliefs about probabilities. Such a reduction appears to be decisively ruled out by certain sorts of triviality results–analogous to those often discussed in the literature on conditionals. I show why these results do not, in fact, rule out the view. They merely give us a constraint on what such a reduction could look like. In particular they show that there is no single proposition belief in which suffices for having (...) a particular credence, regardless of one’s evidence. But if we allow such propositions to vary with evidence–as we should–then the results do not rule out a reduction. So, at least on this count, credences might very well just be beliefs about probabilities. (shrink)