Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be made on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the data deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is non-demonstrative, or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

We consider a confidence parametrization of binary information sources in terms of appropriate likelihood ratios. This parametrization is used for Bayesian belief updates and for the equivalent comparison of binary experiments. In contrast to the standard parametrization of a binary information source in terms of its specificity and its sensitivity, one of the two confidence parameters is sufficient for a Bayesian belief update conditional on a signal realization. We introduce a confidence-augmented receiver operating characteristic for comparisons of binary experiments for (...) a class of “balanced” decision problems, relative to which the confidence order offers a higher resolution than Blackwell’s informativeness order. Where observation is concerned, Chance favors only the prepared mind.—Louis Pasteur (1822–1895). (shrink)

In this paper I argue that de Finetti provided compelling reasons for rejecting countable additivity. It is ironical therefore that the main argument advanced by Bayesians against following his recommendation is based on the consistency criterion, coherence, he himself developed. I will show that this argument is mistaken. Nevertheless, there remain some counter-intuitive consequences of rejecting countable additivity, and one in particular has all the appearances of a full-blown paradox. I will end by arguing that in fact it is no (...) paradox, and that what it shows is that conditionalisation, often claimed to be integral to the Bayesian canon, has to be rejected as a general rule in a finitely additive environment. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

Explanations of cognitive processes provided by traditional artificial intelligence were based on the notion of the knowledge level. This perspective has been challenged by new AI that proposes an approach based on embodied systems that interact with the real‐world. We demonstrate that these two views can be unified. Our argument is based on the assumption that knowledge level explanations can be defined in the context of Bayesian theory while the goals of new AI are captured by using a well established (...) robot based model of learning and problem solving, called Distributed Adaptive Control (DAC). In our analysis we consider random foraging and we prove that minor modifications of the DAC architecture renders a model that is equivalent to a Bayesian analysis of this task. Subsequently, we compare this enhanced, “rational,” model to its “non‐rational” predecessor and a further control condition using both simulated and real robots, in a variety of environments. Our results show that the changes made to the DAC architecture, in order to unify the perspectives of old and new AI, also lead to a significant improvement in random foraging. (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)

Relevant to, and drawing from, a range of disciplines, the chapters in this collection show the diversity, and applicability, of research in Bayesian argumentation.

‘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)

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)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

A central problem facing a probabilistic approach to the problem of induction is the difficulty of sufficiently constraining prior probabilities so as to yield the conclusion that induction is cogent. The Principle of Indifference, according to which alternatives are equiprobable when one has no grounds for preferring one over another, represents one way of addressing this problem; however, the Principle faces the well-known problem that multiple interpretations of it are possible, leading to incompatible conclusions. I propose a partial solution to (...) the latter problem, drawing on the notion of explanatory priority. The resulting synthesis of Bayesian and inference-to-best-explanation approaches affords a principled defense of prior probability distributions that support induction. (shrink)

Arguably no concept is more fundamental to science than that of causality, for investigations into cases of existence, persistence, and change in the natural world are largely investigations into the causes of these phenomena. Yet the metaphysics and epistemology of causality remain unclear. For example, the ontological categories of the causal relata have been taken to be objects (Hume 1739), events (Davidson 1967), properties (Armstrong 1978), processes (Salmon 1984), variables (Hitchcock 1993), and facts (Mellor 1995). (For convenience, causes and effects (...) will usually be understood as events in what follows.) Complicating matters, causal relations may be singular (Socrates’s drinking hemlock caused Socrates’s death) or general (Drinking hemlock causes death); hence the relata might be tokens (e.g., instances of properties) or types (e.g., types of events) of the category in question. Other questions up for grabs are: Are singular causes metaphysically and/or epistemologically prior to general causes or vice versa (or neither)? What grounds the intuitive asymmetry of the causal relation? Are macro-causal relations reducible to micro-causal relations? And perhaps most importantly: Are causal facts (e.g., the holding of causal relations) reducible to non-causal facts (e.g., the holding of certain spatiotemporal relations)? (shrink)

A major difficulty for currently existing theories of inductive inference involves the question of what to do when novel, unknown, or previously unsuspected phenomena occur. In this paper one particular instance of this difficulty is considered, the so-called sampling of species problem.The classical probabilistic theories of inductive inference due to Laplace, Johnson, de Finetti, and Carnap adopt a model of simple enumerative induction in which there are a prespecified number of types or species which may be observed. But, realistically, this (...) is often not the case. In 1838 the English mathematician Augustus De Morgan proposed a modification of the Laplacian model to accommodate situations where the possible types or species to be observed are not assumed to be known in advance; but he did not advance a justification for his solution. (shrink)

There is a substantial literature on the Bayesian approach, and the application of Bayes'' theorem, to legal matters. However, I have found no discussion that explores fully the issue of how a Bayesian juror might be led from an initial "presumption of innocence" to the judgment (required for conviction in criminal cases) that the suspect is "guilty beyond a reasonable doubt". I shall argue here that a Bayesian juror, if she acts in accord with what the law prescribes, will virtually (...) never reach such a judgment. In section I, I discuss Bayesianism, Bayes'' rule and the relation between them. Section II addresses the two legal notions key to my worries about Bayesian jurors: the presumption of innocence and the reasonable doubt criterion. Section III explores what a Bayesian is to make of these notions, and how the legal system requires her to reason in their light. If I am right, there emerges a conflict between current legal prescriptions and the Bayesian approach. Section IV explores the import of this conflict and how it might be resolved. (shrink)

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...) short presentation of Carnap''s theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti''s theorem Carnap''s inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald''s decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments. (shrink)

This paper consists of three main parts. First, we give an introduction to Hill’s assumption A (n) and to theory of interval probability, and an overview of recently developed theory and methods for nonparametric predictive inference (NPI), which is based on A (n) and uses interval probability to quantify uncertainty. Thereafter, we illustrate NPI by introducing a variation to the assumption A (n), suitable for inference based on circular data, with applications to several data sets from the literature. This includes (...) attention to comparison of two groups of circular data, and to grouped data. We briefly discuss such inference for multiple future observations. We end the paper with a discussion of NPI and objective Bayesianism. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

Bernoulli’s 1713 golden theorem is viewed retrospectively in the context of modern model-based frequentist inference that revolves around the concept of a prespecified statistical model Mθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}_{{{\varvec{\uptheta}}}} \left( {\mathbf{x}} \right)$$\end{document}, defining the inductive premises of inference. It is argued that several widely-accepted claims relating to the golden theorem and frequentist inference are either misleading or erroneous: (a) Bernoulli solved the problem of inference ‘from probability to frequency’, and thus (b) the golden theorem (...) cannot justify an approximate Confidence Interval (CI) for the unknown parameter θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta$$\end{document}, (c) Bernoulli identified the probability PA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P\left( A \right)$$\end{document} with the relative frequency 1n∑k=1nxk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{n}\sum\nolimits_{k = 1}^{n} {x_{k} }$$\end{document} of event A as a result of conflating f(x0|θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f({\mathbf{x}}_{0} |\theta )$$\end{document} with f(θ|x0),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(\theta |{\mathbf{x}}_{0} ),$$\end{document} where x0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{x}}_{0}$$\end{document} denotes the observed data, and (d) the same ‘swindle’ is currently perpetrated by the p value testers. In interrogating the claims (a)–(d), the paper raises several foundational issues that are particularly relevant for statistical induction as it relates to the current discussions on the replication crises and the trustworthiness of empirical evidence, arguing that: [i] The alleged Bernoulli swindle is grounded in the unwarranted claim θ^nx0≃θ∗,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\theta }_{n} \left( {{\mathbf{x}}_{0} } \right) \simeq \theta^{*},$$\end{document} for a large enough n, where θ^nX\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{\theta }_{n} \left( {\mathbf{X}} \right)$$\end{document} is an optimal estimator of the true value θ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta^{*}$$\end{document} of θ. [ii] Frequentist error probabilities are not conditional on hypotheses (H0 and H1) framed in terms of an unknown parameter θ since θ is neither a random variable nor an event. [iii] The direct versus inverse inference problem is a contrived and misplaced charge since neither conditional distribution f(x0|θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f({\mathbf{x}}_{0} |\theta )$$\end{document} and f(θ|x0)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(\theta |{\mathbf{x}}_{0} )$$\end{document} exists (formally or logically) in model-based (Mθx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{M}}_{{{\varvec{\uptheta}}}} \left( {\mathbf{x}} \right)$$\end{document}) frequentist inference. (shrink)

Karl Pearson is the leading figure of XX century statistics. He and his co-workers crafted the core of the theory, methods and language of frequentist or classical statistics – the prevalent inductive logic of contemporary science. However, before working in statistics, K. Pearson had other interests in life, namely, in this order, philosophy, physics, and biological heredity. Key concepts of his philosophical and epistemological system of anti-Spinozism (a form of transcendental idealism) are carried over to his subsequent works on the (...) logic of scientific discovery. This article’s main goal is to analyze K. Pearson early philosophical and theological ideas and to investigate how the same ideas came to influence contemporary science, either directly or indirectly – by the use of variant theories, methods and dialects of statistics, corresponding to variant statistical inference procedures and their specific belief calculi. (shrink)

Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematically explicating the relationships canonical representatives of each. Our representative qualitative accounts of indicative (...) and subjunctive supposition are based on the belief change operations provided by AGM revision and KM update respectively; our representative quantitative ones are offered by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as `provisional belief revision' wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we rely on a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update. (shrink)

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there (...) is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists (...) of a group of truth functions or membership functions. In comparison with likelihood functions, Bayesian posteriors, and Logistic functions used by popular methods, membership functions can be more conveniently used as learning functions without the above problem. In Logical Bayesian Inference (LBI), every label’s learning is independent. For Multilabel learning, we can directly obtain a group of optimized membership functions from a big enough sample with labels, without preparing different samples for different labels. A group of Channel Matching (CM) algorithms are developed for machine learning. For the Maximum Mutual Information (MMI) classification of three classes with Gaussian distributions on a two-dimensional feature space, 2-3 iterations can make mutual information between three classes and three labels surpass 99% of the MMI for most initial partitions. For mixture models, the Expectation-Maxmization (EM) algorithm is improved and becomes the CM-EM algorithm, which can outperform the EM algorithm when mixture ratios are imbalanced, or local convergence exists. The CM iteration algorithm needs to combine neural networks for MMI classifications on high-dimensional feature spaces. LBI needs further studies for the unification of statistics and logic. (shrink)

Justified by spectacular achievements facilitated through applied deep learning methodology, the “Everything is possible” view dominates this new hour in the “boom and bust” curve of AI performance. The optimistic view collides head on with the “It is not possible”—ascertainments often originating in a skewed understanding of both AI and medicine. The meaning of the conflicting views can be assessed only by addressing the nature of medicine. Specifically: Which part of medicine, if any, can and should be entrusted to AI—now (...) or at some moment in the future? AI or not, medicine should incorporate the anticipation perspective in providing care. (shrink)

Abstract : A measurement result is never absolutely accurate: it is affected by an unknown “measurement error” which characterizes the discrepancy between the obtained value and the “true value” of the quantity intended to be measured. As a consequence, to be acceptable a measurement result cannot take the form of a unique numerical value, but has to be accompanied by an indication of its “measurement uncertainty”, which enunciates a state of doubt. What, though, is the value of measurement uncertainty? What (...) is its numerical value: how does one calculate it? What is its epistemic value: how one should interpret a measurement result? Firstly, we describe the statistical models that scientists make use of in contemporary metrology to perform an uncertainty analysis, and we show that the issue of the interpretation of probabilities is vigorously debated. This debate brings out epistemological issues about the nature and function of physical measurements, metrologists insisting in particular on the subjective aspect of measurement. Secondly, we examine the philosophical elaboration of metrologists in their technical works, where they criticize the use of the notion of “true value” of a physical quantity. We then challenge this elaboration and defend such a notion. The third part turns to a specific use of measurement uncertainty in order to address our thematic from the perspective of precision physics, considering the activity of the adjustments of physical constants. In the course of this activity, physicists have developed a dynamic conception of the accuracy of their measurement results, oriented towards a future progress of knowledge, and underlining the epistemic virtues of a never-ending process of identification and correction of measurement errors. (shrink)

Quantitative researchers often discuss research ethics as if specific ethical problems can be reduced to abstract normative logics (e.g., virtue ethics, utilitarianism, deontology). Such approaches overlook how values are embedded in every aspect of quantitative methods, including ‘observations,’ ‘facts,’ and notions of ‘objectivity.’ We describe how quantitative research practices, concepts, discourses, and their objects/subjects of study have always been value-laden, from the invention of statistics and probability in the 1600s to their subsequent adoption as a logic made to appear as (...) if it exists prior to, and separate from, ethics and values. This logic, which was embraced in the Academy of Management from the 1960s, casts management researchers as ethical agents who ought to know about a reality conceptualized as naturally existing in the image of statistics and probability (replete with ‘constructs’), while overlooking that S&P logic and practices, which researchers made for themselves, have an appreciable role in making the world appear this way. We introduce a different way to conceptualize reality and ethics, wherein the process of scientific inquiry itself requires an examination of its own practices and commitments. Instead of resorting to decontextualized notions of ‘rigor’ and its ‘best practices,’ quantitative researchers can adopt more purposeful ways to reason about the ethics and relevance of their methods and their science. We end by considering implications for addressing ‘post truth’ and ‘alternative facts’ problems as collective concerns, wherein it is actually the pluralistic nature of description that makes defending a collectively valuable version of reality so important and urgent. (shrink)

In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ. The deduction of those fees is the main result of Section 2. We then propose (...) a Bayesian approach to the problem. When the probability of heads is θ the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in, for in this case there is a paradox. (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 offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency. Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: change in the commitment to the reason, the reason’s sensitivity and selectivity to the claim, one’s prior commitment to the claim, and the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and (...) may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align. (shrink)

It has been just over 100 years since the birth of Alan Turing and more than 65 years since he published in Mind his seminal paper, Computing Machinery and Intelligence. In the Mind paper, Turing asked a number of questions, including whether computers could ever be said to have the power of “thinking”. Turing also set up a number of criteria—including his imitation game—under which a human could judge whether a computer could be said to be “intelligent”. Turing’s paper, as (...) well as his important mathematical and computational insights of the 1930s and 1940s led to his popular acclaim as the “Father of Artificial Intelligence”. In the years since his paper was published, however, no computational system has fully satisfied Turing’s challenge. In this paper we focus on a different question, ignored in, but inspired by Turing’s work: How might the Artificial Intelligence practitioner implement “intelligence” on a computational device? Over the past 60 years, although the AI community has not produced a general-purpose computational intelligence, it has constructed a large number of important artifacts, as well as taken several philosophical stances able to shed light on the nature and implementation of intelligence. This paper contends that the construction of any human artifact includes an implicit epistemic stance. In AI this stance is found in commitments to particular knowledge representations and search strategies that lead to a product’s successes as well as its limitations. Finally, we suggest that computational and human intelligence are two different natural kinds, in the philosophical sense, and elaborate on this point in the conclusion. (shrink)

Many theorists have proposed that we can use the principle of indifference to defeat the inductive sceptic. But any such theorist must confront the objection that different ways of applying the principle of indifference lead to incompatible probability assignments. Huemer offers the explanatory priority proviso as a strategy for overcoming this objection. With this proposal, Huemer claims that we can defend induction in a way that is not question-begging against the sceptic. But in this article, I argue that the opposite (...) is true: if anything, Huemer’s use of the principle of indifference supports the rationality of inductive scepticism. (shrink)

This addendum presents results that confound some commonly made claims about the sorts of environments in which the performance of TTB exceeds that of Franklin's rule, and vice versa.

An early, very preliminary edition of this book was circulated in 1962 under the title Set-theoretical Structures in Science. There are many reasons for maintaining that such structures play a role in the philosophy of science. Perhaps the best is that they provide the right setting for investigating problems of representation and invariance in any systematic part of science, past or present. Examples are easy to cite. Sophisticated analysis of the nature of representation in perception is to be found already (...) in Plato and Aristotle. One of the great intellectual triumphs of the nineteenth century was the mechanical explanation of such familiar concepts as temperature and pressure by their representation in terms of the motion of particles. A more disturbing change of viewpoint was the realization at the beginning of the twentieth century that the separate invariant properties of space and time must be replaced by the space-time invariants of Einstein's special relativity. Another example, the focus of the longest chapter in this book, is controversy extending over several centuries on the proper representation of probability. The six major positions on this question are critically examined. Topics covered in other chapters include an unusually detailed treatment of theoretical and experimental work on visual space, the two senses of invariance represented by weak and strong reversibility of causal processes, and the representation of hidden variables in quantum mechanics. The final chapter concentrates on different kinds of representations of language, concluding with some empirical results on brain-wave representations of words and sentences. (shrink)

Does the formation of delusions involve abnormal reasoning? According to the prominent ‘two-factor’ theory of delusions (e.g. Coltheart, 2007), the answer is yes. The second factor in this theory is supposed to affect a deluded individual's ability to evaluate candidates for belief. However, most published accounts of the two-factor theory have not said much about the nature of this second factor. In an effort to remedy this shortcoming, Coltheart, Menzies and Sutton (2010) recently put forward a Bayesian account of inference (...) in delusions. I outline some criticisms of this important account, and sketch an alternative account of delusional inference that, I argue, avoids these criticisms. Specifically, I argue that the second factor in delusion formation involves a systematic deviation from Bayesian updating, a deviation that may be characterized as a bias towards ‘explanatory adequacy’. I present a numerical model of this idea and show that my alternative account is broadly consistent with prominent prediction error models of delusion formation (e.g. Corlett, Murray et al., 2007). (shrink)

After sketching the conflict between objectivists and subjectivists on the foundations of statistics, this paper discusses an issue facing statisticians of both schools, namely, model validation. Statistical models originate in the study of games of chance, and have been successfully applied in the physical and life sciences. However, there are basic problems in applying the models to social phenomena; some of the difficulties will be pointed out. Hooke's law will be contrasted with regression models for salary discrimination, the latter being (...) a fairly typical application in the social sciences. (shrink)

Different approaches analyze the strength of a natural language argument in different ways. This paper contrasts the dialectical, structural, probabilistic (or Bayesian), computational, and empirical approaches by exemplarily applying them to a single argumentative text (Epicureans on Squandering Life; Aikin & Talisse, 2019). Rather than pitching these approaches against one another, our main goal is to show the room for fruitful interaction. Our focus is on a dialectical analysis of the squandering argument as an argumentative response that voids an interlocutor’s (...) right to assertion. This analysis addresses the pragmatic dimensions of arguing and implies an argument structure that is consistent with empirical evidence of perceived argument strength. Results show that the squandering argument can be evaluated as a (non-fallacious) ad hominem argument, which however is not necessarily stronger than possible arguments attacking it. (shrink)

Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is (...) problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set. (shrink)

The state of computing science and, particularly, software engineering and knowledge engineering is generally considered immature. The best starting point for achieving a mature engineering discipline is a solid scientific theory, and the primary reason behind the immaturity in these fields is precisely that computing science still has no such agreed upon underlying theory. As theories in other fields of science do, this paper formally establishes the fundamental elements and postulates making up a first attempt at a theory in this (...) field, considering the features and peculiarities of computing science. The fundamental elements of this approach are informons and holons, and it is a general and comprehensive theory of software engineering and knowledge engineering that related disciplines (e.g., information systems) can particularise and/or extend to take benefit from it (Lakatos’ concepts of core theory and protective belt theories). (shrink)

There is a growing interest in the foundations as well as the application of imprecise probability in contemporary epistemology. This dissertation is concerned with the application. In particular, the research presented concerns ways in which imprecise probability, i.e. sets of probability measures, may helpfully address certain philosophical problems pertaining to rational belief. The issues I consider are disagreement among epistemic peers, complete ignorance, and inductive reasoning with imprecise priors. For each of these topics, it is assumed that belief can be (...) modeled with imprecise probability, and thus there is a non-classical solution to be given to each problem. I argue that this is the case for peer disagreement and complete ignorance. However, I discovered that the approach has its shortcomings, too, specifically in regard to inductive reasoning with imprecise priors. Nevertheless, the dissertation ultimately illustrates that imprecise probability as a model of rational belief has a lot of promise, but one should be aware of its limitations also. (shrink)