This is a textbook on quantum mechanics. It is addressed to graduates and advanced undergraduates. The book presents quantum theory as a logically coherent system, placing stronger emphasis on the theory' s probabilistic structure and on the role of symmetries. It makes students aware of foundational problems from the very beginning, but at the same time, it urges them to adopt a pragmatic attitude towards the quantum formalism. The book consists of five parts. Part I is a review of classical (...) physics, including probability theory, and a historical introduction to quantum theory. Part II presents quantum theory in terms of six fundamental principles. The principles are presented together with the necessary mathematical background and with applications to simple systems. Part III analyses the properties of quantum particles. It starts with the description of symmetries, continues to non-relativistic particles, the introduction of spin, and particle statistics. It concludes with a symmetries-based introduction to relativistic quantum systems and with the first steps towards relativistic quantum field theory. Part IV presents techniques adapted to specific problems: the structure and spectra of composite systems, decays and transitions, particle scattering, and open quantum systems. Finally, Part V revisits quantum foundations: quantum measurement theory, the major interpretations of quantum theory, and the frontiers of quantum theory in contemporary research. (shrink)

This thesis modifies the wording of William Clifford’s 1877 evidence principle (that ‘it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence’) to propose an explicitly moral principle, restricted to descriptive beliefs (about what is or is not the case) and excluding prescriptive beliefs (about what ought or ought not to be the case). It considers potential counter-examples, particularly William James’s 1896 defence of religious belief; and concludes that the modified principle survives unscathed. It then searches (...) for suitable criteria for ‘sufficient’ and ‘insufficient’ evidence, first within a Bayesian framework enriched by pragmatic considerations, and finally by returning to Clifford’s conception of our shared responsibilities to our shared epistemic asset. Combined with elements of Edward Craig’s (1990, 1999) ‘state-of-nature’ theory of knowledge this gets us to a minimum threshold to avoid insufficient evidence and an aspirational criterion of sufficient evidence. (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)

This volume bridges contemporary philosophical conceptions of risk and responsibility and offers an extensive examination of the topic. It shows that risk and responsibility combine in ways that give rise to new philosophical questions and problems. Philosophical interest in the relationship between risk and responsibility continues to rise, due in no small part due to environmental crises, emerging technologies, legal developments, and new medical advances. Despite such interest, scholars are just now working out how to conceive of the links between (...) risk and responsibility, the implications that risks may have to conceptions of responsibility (and vice versa), as well as how such theorizing might play out in applied cases. With contributions from leading scholars, this volume brings together new work examining the interplay between risk and responsibility, exploring its varied philosophical aspects and applications to contemporary issues in law, bioethics, technology, and environmental ethics. Risk and Responsibility in Context will be of interest to philosophers working in ethics, bioethics, philosophy of law, and philosophy of technology, as well as scholars and practitioners in law, health and science management, public policy, and environmental studies. (shrink)

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)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Eyewitness testimony is both an important and a notoriously unreliable type of criminal evidence. How should investigators, lawyers and decision-makers evaluate eyewitness reliability? In this article, I argue that Testimonial Inference to the Best Explanation is a promising, but underdeveloped prescriptive account of eyewitness evaluation. On this account, we assess the reliability of eyewitnesses by comparing different explanations of how their testimony came about. This account is compatible with, and complementary to both the Bayesian framework of rational eyewitness evaluation and (...) with prescriptive methods for eyewitness assessment developed by psychologists. Compared to these frameworks, the distinctive value of thinking in terms of competing explanations is that it helps us select, interpret and draw conclusions from the available evidence about the witness’s reliability. (shrink)

This essay offers a revisionist defense of classical utilitarianism from an infamous objection to it, which is derived from American science fiction writer, Ursula Le Guin’s, short story, “The Ones Who Walk Away from Omelas.” To that effect, the reply takes inspiration from Le Guin and John Stuart Mill in appealing to the natural law theoretical concept of conscience. I argue that a conscientious utilitarian ethic can escape Le Guin’s objection more satisfactorily than other popular utilitarian ethics. Along the way, (...) this essay discusses at length conscience and its place in moral epistemology, both as it occurs in the natural law tradition and in Mill. The natural law account of conscience is defended and Mill’s account is critiqued. Consequently, this paper also provides an interesting synthesis of utilitarianism with natural law ethics. (shrink)

Politics, Philosophy & Economics, Volume 21, Issue 2, Page 165-189, May 2022. It is generally acknowledged that a certain amount of state intervention in health and health care is needed to address the significant market failures in these sectors; however, it is also thought that the primary rationale for state involvement in health must lie elsewhere, for example in an egalitarian commitment to equalizing access to health care for all citizens. This paper argues that a complete theory of justice in (...) health can be derived from a commitment to correcting market failure, or in other words promoting Pareto-efficiency, in the domain of health. This approach can address familiar problems around access to care, as well as problems related to resource allocation and rationing, the control of health care costs, and the foundations of public health. Egalitarian theories of justice in health cannot make sense of the depth and pervasiveness of state involvement in health and health care; only a theory rooted in the need to correct market failure can. (shrink)

Abstract: The article presents and critically discusses Walton's (and Reed's and Macagno's) argument scheme approach to a theory of good argumentation. In particular, four characteristics of Walton's approach are presented: 1. It presents normative requirements for argumentation in the form of argument schemes, i.e. relatively concrete type descriptions. 2. These schemata are enthymematic, i.e. they omit some of the premises required by other approaches. 3. The actual argument schemes are usually supplemented by critical questions. 4. The method is inductive, bottom-up, (...) gaining the normative schemata by abstraction from empirically collected groups of similar arguments. These characteristics, among others, are then discussed on the basis of four adequacy conditions: AC1: effectiveness in achieving the epistemic goal of obtaining and communicating justified acceptable opinions; AC2: completeness in capturing the good argument types; AC3: efficiency in achieving the goals; AC4: justification of the argument schemes. The discussion then reveals a number of weaknesses in Walton's argument schemes; among other things, they are neither effective (in the defined sense) nor truly justified. Contributing factors to these problems include the schema approach, i.e. not looking at the form of arguments, and the lack of epistemological foundations in the development of good types of arguments. However, the critical analyses reveal a better alternative: an epistemological approach based on epistemological principles. The article concludes with a detailed analysis of the scheme Practical Inference, which confirms the general criticism in detail. (shrink)

Ian Hacking (born in 1936, Vancouver, British Columbia) is most well-known for his work in the philosophy of the natural and social sciences, but his contributions to philosophy are broad, spanning many areas and traditions. In his detailed case studies of the development of probabilistic and statistical reasoning, Hacking pioneered the naturalistic approach in the philosophy of science. Hacking’s research on social constructionism, transient mental illnesses, and the looping effect of the human kinds make use of historical materials to shed (...) light on how developments in the social, medical, and behavioural sciences have shaped our contemporary conceptions of identity and agency. Hacking’s other contributions to philosophy include his work on the philosophy of mathematics (Hacking, 2014), philosophy of statistics, philosophy of logic, inductive logic (Hacking, 1965, 1979, 2001) and natural kinds (Hacking, 1991, 2007a). (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)

What meaning does epidemiological evidence have for the individual? In evidence-based medicine, epidemiological evidence measures the patient’s risk of the outcome or the change in risk due to an intervention. The patient’s risk is commonly understood as an individual probability. The problem of understanding epidemiological evidence and risk thus becomes the challenge of interpreting individual patient probabilities. I argue that the patient’s risk is interpreted ontically, as a propensity. After exploring formidable problems with this interpretation in the medical context, I (...) propose an epistemic reinterpretation of individual patient probabilities as credences. On this view, epidemiological evidence informs medical uncertainty. (shrink)

I offer an explicit account of the underdetermination thesis as well as of the many challenges it poses to scientific realism; a way to answer to these challenges is explored and outlined, by shifting attention to the content of theories. I argue that, even if we have solid grounds (as I contend we do) to support that some varieties of the underdetermination thesis are true, scientific realism can still offer an adequate picture of the aims and achievements of science.

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)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

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)

This is book l of three philosophy books in international language; formal academic philosophy source in Kurdish language Given overall view on classic epistemology for university student in non English language philosophy departments and philosophy schools .

Despite the ubiquity of uncertainty, scientific attention has focused primarily on probabilistic approaches, which predominantly rely on the assumption that uncertainty can be measured and expressed numerically. At the same time, the increasing amount of research from a range of areas including psychology, economics, and sociology testify that in the real world, people’s understanding of risky and uncertain situations cannot be satisfactorily explained in probabilistic and decision-theoretical terms. In this article, we offer a theoretical overview of an alternative approach to (...) uncertainty developed in the framework of the ecological rationality research program. We first trace the origins of the ecological approach to uncertainty in Simon’s bounded rationality and Brunswik’s lens model framework and then proceed by outlining a theoretical view of uncertainty that ensues from the ecological rationality approach. We argue that the ecological concept of uncertainty relies on a systemic view of uncertainty that features it as a property of the organism–environment system. We also show how simple heuristics can deal with unmeasurable uncertainty and in what cases ignoring probabilities emerges as a proper response to uncertainty. (shrink)

The primary aim of this chapter is to explain the nature of evidential reasoning, the characteristic difficulties encountered, and the tools to address these difficulties. Our focus is on evidential reasoning in criminal cases. There is an extensive scholarly literature on these topics, and it is a secondary aim of the chapter to provide readers the means to find their way in historical and ongoing debates.

Citizens in wealthy liberal democracies are typically expected to see to basic needs like food, clothing, and shelter out of their own income, and those without the means to do so usually receive assistance in the form of cash transfers. Things are different with health care. Most liberal societies provide their citizens with health care or health care insurance in kind, either directly from the state or through private insurance companies that are regulated like public utilities. Except perhaps for small (...) co-pays or deductibles, citizens are not expected to see to their health needs out-of-pocket, at least for some basic level of care. Instead, when a citizen gets sick, the state or her insurance company foots the... (shrink)

This editorial offers new ways to ethically practice, evaluate, and use quantitative research. Our central claim is that ready-made formulas for QR, including ‘best practices’ and common notions of ‘validity’ or ‘objectivity,’ are often divorced from the ethical and practical implications of doing, evaluating, and using QR for specific purposes. To focus on these implications, we critique common theoretical foundations for QR and then recommend approaches to QR that are ‘built for purpose,’ by which we mean designed to ethically address (...) specific problems or situations on terms that are contextually relevant. For this, we propose a new tool for evaluating the quality of QR, which we call ‘relational validity.’ Studies, including their methods and results, are relationally valid when they ethically connect researchers’ purposes with the way that QR is oriented and the ways that it is done—including the concepts and units of analysis invoked, as well as what its ‘methods’ imply more generally. This new way of doing QR can provide the liberty required to address serious worldly problems on terms that are both practical and ethically informed in relation to the problems themselves rather than the confines of existing QR logics and practices. (shrink)

Uncertainty is a feeling of anxiety and a part of culture since the dawn of civilization. Civilizations have invented numerous ways to cope with uncertainty, statistics is one of those technologies. The rhetoric as the discourse of investment theory uncovers that the theory of statistics applied is a blind spot in the current conversation about investment theory and practice. Probability and prediction in investment theory look like a tying sale, since investment theory is founded on stochastical predictability. The proof of (...) unpredictability, however, lies outside the paradigm of statistics, because statistics assumes that the substrate, that produces probability outcomes, is stable. The theory of objective probabilities founds the Capital Asset Pricing Model but does not stochastically predict, and neither do Markowitz’s subjective probabilities for his portfolio theory. Statistical models for investing have a function, despite that they cannot predict: in essence, the models try to quantify statistically the equity, the fairness of the distribution of risk and return between parties involved. In the dissertation, a lot of ideas to change finance have had attention: the alternative statistical theory of Mandelbrot, bubble theory, political finance, the analysis of rhetoric, the analysis of culture, innovative practices, ethics in the form of virtue and value ethics, and the history of finance. How to make the culture of finance more heterogeneous? That starts with awareness of the current problems, the introduction of multiform metaphors for investment theory, and handling the ambiguity of theory uncertainty, by presenting, explaining and elaborating the alternatives. (shrink)

Many hold that distributing healthcare according to medical need is a requirement of equality. Most egalitarians believe, however, that people ought to be equal on the whole, by some overall measure of well-being or life-prospects; it would be a massive coincidence if distributing healthcare according to medical need turned out to be an effective way of promoting equality overall. I argue that distributing healthcare according to medical need is important for reducing individuals' uncertainty surrounding their future medical needs. In other (...) words, distributing healthcare according to medical need is a natural feature of healthcare insurance; it is about indemnity, not equality. (shrink)

The current state of inductive logic is puzzling. Survey presentations are recurrently offered and a very rich and extensive handbook was entirely dedicated to the topic just a few years ago [23]. Among the contributions to this very volume, however, one finds forceful arguments to the effect that inductive logic is not needed and that the belief in its existence is itself a misguided illusion , while other distinguished observers have eventually come to see at least the label as “slightly (...) antiquated” .What seems not to have lost any of its currency is the problem which inductive logic is meant to address. Inference from limited ascertained information to uncertain hypotheses is ubiquitous in learning, prediction and discovery. The logical insight that such kind of inference is fallible m .. (shrink)

Why conduct research concerning human genome or proving the existence of Higgs particle? What makes these problems significant or worthy of investigation? In recent epistemological discussions one can find at least two conceptions of the problem of epistemic significance: research question or cognitive problem can be practically significant or intrinsically epistemically significant, in a way that depends on the consideration whether reasons that support the significance of the problem are practical or epistemic. In this paper I am dealing with the (...) question of the possibility of determining the significance of the problem from the purely epistemic perspective. In that regard I argue that (under suitable interpretation of the problem of epistemic significance) there are no pure epistemic reasons that could determine the importance of the cognitive problem. The argument is based on three objections: (1) epistemic duty is unjustifiably identified with epistemic justification, (2) the dependence of epistemic reasons on conceputal schemes is not taken into consideration, and (3) the infinite justificatory potential of evidence is being disregarded. (shrink)

Medical diagnosis has been traditionally recognized as a privileged field of application for so called probabilistic induction. Consequently, the Bayesian theorem, which mathematically formalizes this form of inference, has been seen as the most adequate tool for quantifying the uncertainty surrounding the diagnosis by providing probabilities of different diagnostic hypotheses, given symptomatic or laboratory data. On the other side, it has also been remarked that differential diagnosis rather works by exclusion, e.g. by modus tollens, i.e. deductively. By drawing on a (...) case history, this paper aims at clarifying some points on the issue. Namely: 1) Medical diagnosis does not represent, strictly speaking, a form of induction, but a type, of what in Peircean terms should be called ‘abduction’ (identifying a case as the token of a specific type); 2) in performing the single diagnostic steps, however, different inferential methods are used for both inductive and deductive nature: modus tollens, hypothetical-deductive method, abduction; 3) Bayes’ theorem is a probabilized form of abduction which uses mathematics in order to justify the degree of confidence which can be entertained on a hypothesis given the available evidence; 4) although theoretically irreconcilable, in practice, both the hypothetical- deductive method and the Bayesian one, are used in the same diagnosis with no serious compromise for its correctness; 5) Medical diagnosis, especially differential diagnosis, also uses a kind of “probabilistic modus tollens”, in that, signs (symptoms or laboratory data) are taken as strong evidence for a given hypothesis not to be true: the focus is not on hypothesis confirmation, but instead on its refutation [Pr (¬ H/E1, E2, …, En)]. Especially at the beginning of a complicated case, odds are between the hypothesis that is potentially being excluded and a vague “other”. This procedure has the advantage of providing a clue of what evidence to look for and to eventually reduce the set of candidate hypotheses if conclusive negative evidence is found. 6) Bayes’ theorem in the hypothesis-confirmation form can more faithfully, although idealistically, represent the medical diagnosis when the diagnostic itinerary has come to a reduced set of plausible hypotheses after a process of progressive elimination of candidate hypotheses; 7) Bayes’ theorem is however indispensable in the case of litigation in order to assess doctor’s responsibility for medical error by taking into account the weight of the evidence at his disposal. (shrink)

In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...) to read it. That is what you have in front of you. The account of Laplace’s theory of probability in Chapter 4 is very different to what I said in my seminar lectures, and also very different to any other account I have seen; it is based on a reading of important texts by Laplace that appear not to have been read by other commentators. The discussion of von Mises’ theory in Chapter 7 is also new, though perhaps less revolutionary. And the final chapter is a new attempt to come to grips with the popular, but amorphous, subjective theory of probability. The material in the other chapters has mostly appeared in previous articles of mine but things are sometimes expressed differently here. I would like to say again that this is an incomplete draft of a book, not the book I would have written if I had decided to finish it. It no doubt contains poor expressions, it may contain some errors or inconsistencies, and it doesn’t cover all the theories that I originally intended to discuss. Apart from this preface, I have done no work on the book since October 2009. (shrink)

Contrary to common views that philosophy is extraneous to cognitive science, this paper argues that philosophy has a crucial role to play in cognitive science with respect to generality and normativity. General questions include the nature of theories and explanations, the role of computer simulation in cognitive theorizing, and the relations among the different fields of cognitive science. Normative questions include whether human thinking should be Bayesian, whether decision making should maximize expected utility, and how norms should be established. These (...) kinds of general and normative questions make philosophical reflection an important part of progress in cognitive science. Philosophy operates best, however, not with a priori reasoning or conceptual analysis, but rather with empirically informed reflection on a wide range of findings in cognitive science. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

A moral-pragmatic argument for a proposition is an argument intended to establish that believing the proposition would be morally beneficial. Since such arguments do not adduce epistemic reasons, i.e., reasons that support the truth of a proposition, they can seem at best to be irrelevant epistemically. At worst, believing on the basis of such reasoning can seem to involve wishful thinking and intellectual dishonesty of a sort that that precludes such beliefs from being epistemically unjustified. Inspired by an argument from (...) William James’ classic, “The Will to Believe”, I argue that there is a way of making sense of moral-pragmatic arguments such that they are epistemically relevant. I develop and argue for a theory of epistemic justification that I dub the “moral encroachment theory” (emphasizing its connection to recent pragmatic encroachment views). According to the theory, moral considerations can raise or lower epistemic standards from where they would be in morally neutral settings. The moral encroachment theory, I contend, denotes a normative property that is at once distinctively epistemic and valuable. The theory also allows a legitimate role for moral-pragmatic reasoning under certain conditions. The upshot is that moral-pragmatic reasoning can be epistemically as well as morally appropriate. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Interest in the Keynesian concept of evidential weight has led to divergent views concerning the burden of proof in adjudication. It is argued that Keynes's concept is properly engaged only in the context of one special kind of decision, the decision whether or not the evidence is ripe for a decision on the underlying merits, whether the latter decision is based on probability, relative plausibility, coherence or otherwise. As a general matter, this question of ripeness is appropriately assigned to the (...) judiciary for resolution as part of the burden of production, rather than to the jury or other factfinder as part of the burden of persuasion. (shrink)

Laurence BonJour has recently proposed a novel and interesting approach to the problem of induction. He grants that it is contingent, and so not a priori, that our patterns of inductive inference are reliable. Nevertheless, he claims, it is necessary and a priori that those patterns are highly likely to be reliable, and that is enough to ground an a priori justification induction. This paper examines an important defect in BonJour's proposal. Once we make sense of the claim that inductive (...) inference is "necessarily highly likely" to be reliable, we find that it is not knowable a priori after all. (shrink)

The inaugural title in the new, Open Access series BSPS Open, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single (...) formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it. Which that is, and its extent, is determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference. (shrink)

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective (...) Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made. (shrink)

The formal definition of species as explanatory hypotheses presented by Fitzhugh is emended. A species is an explanatory account of the occurrences of the same character among gonochoristic or cross-fertilizing hermaphroditic individuals by way of character origin and subsequent fixation during tokogeny. In addition to species, biological systematics also employs hypotheses that are ontogenetic, tokogenetic, intraspecific, and phylogenetic, each of which provides explanatory hypotheses for distinctly different classes of causal questions. It is suggested that species hypotheses can not be applied (...) to organisms with obligate asexual, parthenogenetic, and self-fertilizing modes of reproduction. Hypotheses explaining shared characters among such organisms are, instead, strictly phylogenetic. Several implications of this emended definition are examined, especially the relations between species, intraspecific, and phylogenetic hypotheses, as well as the limitations of species names to be applied to temporally different characters within populations. (shrink)

Three competing ‘methods’ have been endorsed for inferring phylogenetic hypotheses: parsimony, likelihood, and Bayesianism. The latter two have been claimed superior because they take into account rates of sequence substitution. Can rates of substitution be justified on its own accord in inferences of explanatory hypotheses? Answering this question requires addressing four issues: (1) the aim of scientific inquiry, (2) the nature of why-questions, (3) explanatory hypotheses as answers to why-questions, and (4) acknowledging that neither parsimony, likelihood, nor Bayesianism are inferential (...) actions leading to explanatory hypotheses. The aim of scientific inquiry is to acquire causal understanding of effects. Observation statements of organismal characters lead to implicit or explicit why-questions. Those questions, conveyed in data matrices, assume the truth of observation statements, which is contrary to subsequently invoking substitution rates within inferences to phylogenetic hypotheses. Inferences of explanatory hypotheses are abductive in form, such that some version of an evolutionary theory(ies) is/are included or implied. If rates of sequence evolution are to be considered, it must be done prior to, rather than within abduction, which requires renaming those putatively-shared nucleotides subject to substitution rates. There are, however, no epistemic grounds for renaming characters to accommodate rates, calling into question the legitimacy of causally accounting for sequence data. (shrink)

The aim of this contribution is to provide a rather general answer to Hume’s problem. To this end, induction is treated within a straightforward formal paradigm, i.e., several connected levels of abstraction. Within this setting, many concrete models are discussed. On the one hand, models from mathematics, statistics and information science demonstrate how induction might succeed. On the other hand, standard examples from philosophy highlight fundamental difficulties. Thus it transpires that the difference between unbounded and bounded inductive steps is crucial: (...) while unbounded leaps of faith are never justified, there may well be reasonable bounded inductive steps. In this endeavour, the twin concepts of information and probability prove to be indispensable, pinning down the crucial arguments, and, at times, reducing them to calculations. Essentially, a precise study of boundedness settles Goodman’s challenge. Hume’s more profound claim of seemingly inevitable circularity is answered by obviously non-circular hierarchical structures. (shrink)

The modal account of luck has become very popular and influential in the past decade. More recently, some of its proponents have also put forth a modal account of risk and argued that we ought to apply it to problems both in and out of philosophy. This paper tries to show that modal conceptions of luck and risk are mistaken.

The aim of this contribution is to provide a rather general answer to Hume's problem, the well-known problem of induction. To this end, it is very useful to apply his differentiation between ``relations of ideas'' and ``matters of fact'', and to reconsider earlier approaches. In so doing, we consider the problem formally, as well as empirically. Next, received attempts to solve the problem are discussed. The basic structure of inductive problems is exposed in chap. 6. Our final conclusions are to (...) the positive, i.e., Hume's problem can be dealt with - solved - in a constructive way. More specifically, bounded generalisations can be justified, and the key to the solution is the concept of information. (shrink)

I aim to provide some evidence that Husserl’s description of perceptual updating actually fits very nicely into the Bayesian Brain paradigm, articulated by Karl Friston and others, and that that paradigm, in turn, can be taken as an excellent example of “Neurophenomenology”. The apparently un-phenomenological Helmholtzian component of the Bayesian Brain paradigm, according to which what one consciously seems to see is a product of unconscious causal reasoning to the best explanation of one’s sensory stimulations, can be finessed, I claim, (...) in a way that makes it compatible with a phenomenological orientation. I begin by roughly characterizing the Bayesian Brain paradigm as it relates to perceptual cognition. I then show how Husserl’s descriptions of the conscious perceptual process relate to the paradigm. I conclude with some considerations about how to understand the relation between conscious and unconscious brain process in the present case and in relation to Neurophenomenology generally. (shrink)

This paper seeks to recover the function of universal history, which was to place particulars into relation with universals. By the 20th century universal history was largely discredited because of an idealism that served to lend epistemic coherence to the overwhelming complexity arising from universal history's comprehensive scope. Idealism also attempted to account for history's being "open"--for the human ability to transcend circumstance. The paper attempts to recover these virtues without the idealism by defining universal history not by its scope (...) but rather as a scientific method that provides an understanding of any kind of historical process, be it physical, biological or human. While this method is not new, it is in need of a development that offers a more robust historiography and warrant as a liberating historical consciousness. The first section constructs an ontology of process by defining matter as ontic probabilities rather than as closed entities. This is lent warrant in the next section through an appeal to contemporary physical science. The resulting conceptual frame and method is applied to the physical domain of existents, to the biological domain of social being and finally to the human domain of species being. It is then used to account for the emergence of human history's initial stage--the Archaic Socio-Economic Formation and for history' stadial trajectory--its alternation of evolution and revolution. (shrink)