Kuhn's theory of paradigm reveals a pattern of scientific progress, in which normal science alternates with scientific revolution. But Kuhn underrated too much the function of scientific test in his pattern, because he focuses all his attention on the hypothetico-deductive schema instead of Bayesian schema. This paper employs Bayesian schema to re-examine Kuhn's theory of paradigm, to uncover its logical and rational components, and to illustrate the tensional structure of logic and belief, rationality and irrationality, in the process of scientific (...) revolution. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...) emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

Legal probabilism is the view that juridical fact-finding should be modeled using Bayesian methods. One of the alternatives to it is the narration view, according to which instead we should conceptualize the process in terms of competing narrations of what happened. The goal of this paper is to develop a reconciliatory account, on which the narration view is construed from the Bayesian perspective within the framework of formal Bayesian epistemology.

James Maffie claims that weak continuity reliabilism is compatible with the principles, as well as the insights, of the Strong Programme in the Sociology of Knowledge (SPSK). There are three possible readings of weak continuity reliabilism: I argue that the first two are unsound, while the third is actually inconsistent with the principles of SPSK. SPSK is instead compatible with an identicist epistemology, one that does not aim to distinguish scientific epistemology from our everyday epistemic practice.

Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: it opens the door to the influence of values and biases, evidence judgments can vary substantially between scientists, it is not suited for informing policy decisions. My paper rebuts these concerns by connecting the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference with null hypothesis significance tests. Second, (...) the criticisms are based on specific senses of objectivity with unclear epistemic value. Third, I show that Subjective Bayesianism promotes other, epistemically relevant senses of scientific objectivity—most notably by increasing the transparency of scientific reasoning. (shrink)

What thesis is Hume trying to establish in his essay “On Miracles” and does he succeed? John Earman’s answer to the latter question is clearly conveyed by the title of his new book. Earman uses a Bayesian representation of the problem to make his case. For Earman, this mode of analysis is both perspicuous and nonanachronistic, in that probability reasoning was central to the 18th century debate about miracles in particular and testimony in general. Indeed, one of Hume’s most interesting (...) antagonists, Richard Price, was the person to whom Thomas Bayes entrusted his now-famous essay for posthumous publication. For Earman, Price is the proper Bayesian, while Hume’s essay provides only “rhetoric and schein geld”. Earman’s tone is consistently prosecutorial and sometimes snide; he says that his animus is not so much against Hume himself as against those who smugly invoke Hume’s essay as definitively settling the matter. This tone should not deter potential readers who are convinced that Hume’s essay contains something of value. Earman’s book is interesting and provocative in multiple ways—it places Hume’s essay in its historical setting, it offers an insightful close reading of the text, and it shows how the resources of Bayesianism can be powerfully put to work. Besides Earman’s own essay, the volume also contains Hume’s essay and relevant work by others, including Locke, Spinoza, Samuel Clarke, Price, Laplace, and Babbage. The book would be an excellent choice for an advanced undergraduate or graduate seminar. (shrink)

“Absence of evidence isn’t evidence of absence” is a slogan that is popular among scientists and nonscientists alike. This article assesses its truth by using a probabilistic tool, the Law of Likelihood. Qualitative questions (“Is E evidence about H ?”) and quantitative questions (“How much evidence does E provide about H ?”) are both considered. The article discusses the example of fossil intermediates. If finding a fossil that is phenotypically intermediate between two extant species provides evidence that those species have (...) a common ancestor, does failing to find such a fossil constitute evidence that there was no common ancestor? Or should the failure merely be chalked up to the imperfection of the fossil record? The transitivity of the evidence relation in simple causal chains provides a broader context, which leads to discussion of the fine-tuning argument, the anthropic principle, and observation selection effects. (shrink)

Formal epistemologists often claim that our credences should be representable by a probability function. Complete probabilistic coherence, however, is only possible for ideal agents, raising the question of how this requirement relates to our everyday judgments concerning rationality. One possible answer is that being rational is a contextual matter, that the standards for rationality change along with the situation. Just like who counts as tall changes depending on whether we are considering toddlers or basketball players, perhaps what counts as rational (...) shifts according to whether we are considering ideal agents or creatures more like ourselves. Even though a number of formal epistemologists have endorsed this type of solution, I will argue that there is no way to spell out this contextual account that can make sense of our everyday judgments about rationality. Those who defend probabilistic coherence requirements will need an alternative account of the relationship between real and ideal rationality. (shrink)

Various sexist and racist beliefs ascribe certain negative qualities to people of a given sex or race. Epistemic allies are people who think that in normal circumstances rationality requires the rejection of such sexist and racist beliefs upon learning of many counter-instances, i.e. members of these groups who lack the target negative quality. Accordingly, epistemic allies think that those who give up their sexist or racist beliefs in such circumstances are rationally responding to their evidence, while those who do not (...) are irrational in failing to respond to their evidence by giving up their belief. This is a common view among philosophers and non-philosophers. But epistemic allies face three problems. First, sexist and racist beliefs often involve generic propositions. These sorts of propositions are notoriously resilient in the face of counter-instances since the truth of generic propositions is typically compatible with the existence of many counter-instances. Second, background beliefs can enable one to explain away counter-instances to one’s beliefs. So even when counter-instances might otherwise constitute strong evidence against the truth of the generic, the ability to explain the counter-instances away with relevant background beliefs can make it rational to retain one’s belief in the generic despite the existence of many counter-instances. The final problem is that the kinds of judgements epistemic allies want to make about the irrationality of sexist and racist beliefs upon encountering many counter-instances is at odds with the judgements that we are inclined to make in seemingly parallel cases about the rationality of non-sexist and non-racist generic beliefs. Thus epistemic allies may end up having to give up on plausible normative supervenience principles. All together, these problems pose a significant prima facie challenge to epistemic allies. In what follows I explain how a Bayesian approach to the relation between evidence and belief can neatly untie these knots. The basic story is one of defeat: Bayesianism explains when one is required to become increasingly confident in chance propositions, and confidence in chance propositions can make belief in corresponding generics irrational. (shrink)

This paper describes the corner-stones of a means-ends approach to the philosophy of inductive inference. I begin with a fallibilist ideal of convergence to the truth in the long run, or in the 'limit of inquiry'. I determine which methods are optimal for attaining additional epistemic aims (notably fast and steady convergence to the truth). Means-ends vindications of (a version of) Occam's Razor and the natural generalizations in a Goodmanian Riddle of Induction illustrate the power of this approach. The paper (...) establishes a hierarchy of means-ends notions of empirical success, and discusses a number of issues, results and applications of means-ends epistemology. (shrink)

It is widely thought that Bayesian confirmation theory has provided a solution to Hempel's Paradox (the Ravens Paradox). I discuss one well‐known example of this approach, by John Mackie, and argue that it is unconvincing. I then suggest an alternative solution, which shows that the Bayesian approach is altogether mistaken. Nicod's Condition should be rejected because a generalisation is not confirmed by any of its instances if it is not law‐like. And even law‐like non‐basic empirical generalisations, which are expressions of (...) assumed underlying causal regularities, are not so confirmed if they are absurd in the light of our causal background knowledge or if their instances are not also possible instances of the relevant causal claim. (shrink)

In 1983, in an open letter to the journal Nature, Karl Popper and David Miller set forth a particularly strong critical argument which sought to demonstrate the impossibility of inductive probability. Since its publication the argument has faced many criticisms and we argue in this article that they do not reach their objectives. We will first reconstruct the demonstration made by Popper and Miller in their initial article and then try to evaluate the main arguments against it. Although it is (...) possible to conceptualize logically the idea of induction, it is shown that it is not possible on traditional Bayesian grounds. (shrink)

In 1983, in an open letter to the journal Nature, Karl Popper and David Miller set forth a particularly strong critical argument which sought to demonstrate the impossibility of inductive probability. Since its publication the argument has faced many criticisms and we argue in this article that they do not reach their objectives. We will first reconstruct the demonstration made by Popper and Miller in their initial article and then try to evaluate the main arguments against it. Although it is (...) possible to conceptualize logically the idea of induction, it is shown that it is not possible on traditional Bayesian grounds. (shrink)

Scientists and policy‐makers have long understood that the products of research can often be used for good or evil. Nuclear fission research can be used to generate electricity or create a powerful bomb. Studies on the genetics of human populations can be used to understand relationships between different groups or to perpetuate racist ideologies. While the notion that scientific research often has beneficial and harmful uses has been discussed before, the threat of bioterrorism—a concern that has only grown since 2001—has (...) led to increased awareness about the need to prevent the misuse of biomedical research, particularly when it involves dangerous pathogens or toxins. In 2012, the concern was ratcheted up another notch by two papers reporting the results of research on genetically engineered strains of the H5N1 avian influenza virus. Although the H5N1 papers have potential scientific and social value, some scientists and policy‐makers opposed their publication because they feared that terrorists (or others with nefarious motives) could use the research to create a bioweapon that could trigger a global pandemic. The H5N1 papers raise difficult questions concerning the ethics of knowledge. Should scientific research with dangerous applications be published? Should some types of research be kept secret or not be conducted at all? What type of government oversight of dangerous research is appropriate? In this essay, I will develop a framework for thinking about the ethics of knowledge and apply it to the H5N1 controversy, focusing on issues related to publication. I will argue that redacted publication would have been a reasonable response to the dilemmas posed by the H5N1 papers if not for practical and legal problems with this option. Given these problems, full publication seems appropriate. (shrink)

Kantian philosophy of space, time and gravity is significantly affected in three ways by particle physics. First, particle physics deflects Schlick’s General Relativity-based critique of synthetic a priori knowledge. Schlick argued that since geometry was not synthetic a priori, nothing was—a key step toward logical empiricism. Particle physics suggests a Kant-friendlier theory of space-time and gravity presumably approximating General Relativity arbitrarily well, massive spin-2 gravity, while retaining a flat space-time geometry that is indirectly observable at large distances. The theory’s roots (...) include Seeliger and Neumann in the 1890s and Einstein in 1917 as well as 1920s–1930s physics. Such theories have seen renewed scientific attention since 2000 and especially since 2010 due to breakthroughs addressing early 1970s technical difficulties. Second, particle physics casts additional doubt on Friedman’s constitutive a priori role for the principle of equivalence. Massive spin-2 gravity presumably should have nearly the same empirical content as General Relativity while differing radically on foundational issues. Empirical content even in General Relativity resides in partial differential equations, not in an additional principle identifying gravity and inertia. Third, Kant’s apparent claim that Newton’s results could be known a priori is undermined by an alternate gravitational equation. The modified theory has a smaller symmetry group than does Newton’s. What Kant wanted from Newton’s gravity is impossible due its large symmetry group, but is closer to achievable given the alternative theory. (shrink)

In this article, I first give a short outline of the different interpretations of the concept of probability that emerged in the twentieth century. In what follows, I give an overview of the main problems and problematic concepts from the philosophy of probability and show how they relate to Bayesian inference. In this overview, I emphasise that the understanding of the main concepts related to different interpretations of probability influences the understanding and status of Bayesian inference. In the conclusion, I (...) express that, from a broad epistemological point of view, a kind of compatibilism between the two main lines of interpretations of probability is worth pursuing, as they represent different aspects of the epistemological process. (shrink)

In this essay, I aim to motivate and defend a pluralistic view of epistemic rationality. At the core of the view is the notion that epistemic rationality is essentially a species of practical rationality put in the service of various epistemic goals. I begin by sketching some closely related views that have appeared in the literature. I then present my preferred version of the view and sketch some of its benefits. Thomas Kelly has raised challenging objections to a part of (...) the view, which I then present and address. I then raise some distinct worries that might linger and sketch some possible ways one might address them. (shrink)

Reliabilism is an intuitive and attractive view about epistemic justification. However, it has many well-known problems. I offer a novel condition on reliabilist theories of justification. This method coherence condition requires that a method be appropriately tested by appeal to a subject’s other belief-forming methods. Adding this condition to reliabilism provides a solution to epistemic circularity worries, including the bootstrapping problem.

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the traditional Bayesian (...) epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment. (shrink)

An influential suggestion about the relationship between Bayesianism and inference to the best explanation holds that IBE functions as a heuristic to approximate Bayesian reasoning. While this view promises to unify Bayesianism and IBE in a very attractive manner, important elements of the view have not yet been spelled out in detail. I present and argue for a heuristic conception of IBE on which IBE serves primarily to locate the most probable available explanatory hypothesis to serve as a working hypothesis (...) in an agent’s further investigations. Along the way, I criticize what I consider to be an overly ambitious conception of the heuristic role of IBE, according to which IBE serves as a guide to absolute probability values. My own conception, by contrast, requires only that IBE can function as a guide to the comparative probability values of available hypotheses. This is shown to be a much more realistic role for IBE given the nature and limitations of the explanatory considerations with which IBE operates. (shrink)

Bayesians defend norms of ideal rationality such as probabilism, which they claim should be approximated by non-ideal thinkers. Yet, it is not often discussed exactly in what sense it is beneficial for an agent’s credence function to approximate probabilistic coherence. Some existing research indicates that approximating coherence leads to improvements in accuracy, whereas other research suggests that it decreases Dutch book vulnerability. Yet, the existing results don’t settle whether there is a way of approximating coherence that delivers both benefits at (...) once. We show that there is. (shrink)

Diversity of evidence is widely claimed to be crucial for evidence amalgamation to have distinctive epistemic merits. Bayesian epistemologists capture this idea in the variety-of-evidence thesis: ceteris paribus, the strength of confirmation of a hypothesis by an evidential set increases with the diversity of the evidential elements in that set. Yet, formal exploration of this thesis has shown that it fails to be generally true. This article demonstrates that the thesis fails in even more circumstances than recent results would lead (...) us to expect. Most importantly, it can fail whatever the chance that the evidential sources are unreliable. Our results hold for two types of degrees of variety: reliability independence and testable aspect independence. We conclude that the variety-of-evidence thesis can, at best, be interpreted as an exception-prone rule of thumb. (shrink)

The theory-theory of human uniqueness posits that the capacity to theorize, in a way strongly analogous to theorizing in scientific practice, was a key innovation in the hominid lineage and was responsible for many of our unique cognitive traits. One of the central arguments that its proponents have used to support the claim that animals are not theorists, the logical problem, bears strong similarities to Hempel's theoretician's dilemma, which purports to show that theories are unnecessary. This similarity threatens to undermine (...) both the claim that theorizing serves a unique, adaptive role in human cognition and our ability to test for the presence of theories. I examine two historical responses to the theoretician's dilemma and argue that they open up strategies for experimentally testing for theoretical ability in other animals. (shrink)

The requirement of total evidence is a mainstay of Bayesian epistemology. Peter Fisher Epstein argues that the requirement generates mistaken conclusions about several examples that he devises. Here we examine the example of Epstein’s that we find most interesting and argue that Epstein’s analysis of it is flawed.

The paper discusses Bayesian convergence when the truth is excluded from the analysis by means of a simple coin-tossing example. In the fair-balance paradox a fair coin is tossed repeatedly. A Bayesian agent, however, holds the a priori view that the coin is either biased towards heads or towards tails. As a result the truth is ignored by the agent. In this scenario the Bayesian approach tends to confirm a false model as the data size goes to infinity. I argue (...) that the fair-balance paradox reveals an unattractive feature of the Bayesian approach to scientific inference and explore a modification of the paradox. (shrink)

Bayes’ rule shows how one might rationally change one’s beliefs in the light of evidence. It is the foundation of a statistical method called Bayesianism. In health care research, Bayesianism has its advocates but the dominant statistical method is frequentism. There are at least two important philosophical differences between these methods. First, Bayesianism takes a subjectivist view of probability (i.e. that probability scores are statements of subjective belief, not objective fact) whilst frequentism takes an objectivist view. Second, Bayesianism is explicitly (...) inductive (i.e. it shows how we may induce views about the world based on partial data from it) whereas frequentism is at least compatible with non-inductive views of scientific method, particularly the critical realism of Popper. Popper and others detail significant problems with induction. Frequentism’s apparent ability to avoid these, plus its ability to give a seemingly more scientific and objective take on probability, lies behind its philosophical appeal to health care researchers. However, there are also significant problems with frequentism, particularly its inability to assign probability scores to single events. Popper thus proposed an alternative objectivist view of probability, called propensity theory, which he allies to a theory of corroboration; but this too has significant problems, in particular, it may not successfully avoid induction. If this is so then Bayesianism might be philosophically the strongest of the statistical approaches. The article sets out a number of its philosophical and methodological attractions. Finally, it outlines a way in which critical realism and Bayesianism might work together. (shrink)

The Humean argument concerning miracles says that one should always think it more likely that anyone who testifies to a miracle is lying or deluded than that the alleged miracle actually occurred, and so should always reject any single report of it. A longstanding and widely accepted objection is that even if this is right, the concurring and non-collusive testimony of many witnesses should make it rational to believe in whatever miracle they all report. I argue that on the contrary, (...) even multiple reports from non-collusive witnesses lack the sort of independence that could make trouble for Hume. (shrink)