Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does or should (...) make use of them in assigning probabilities to hypotheses. I argue that van Fraassen has not succeeded in establishing that IBE and Bayesianism are incompatible, but that the existing compatibilist response is also not satisfactory. I suggest that a more promising approach to the problem is to investigate whether explanatory considerations are taken into account by a Bayesian who assigns priors and likelihoods on his or her own terms. In this case, IBE would emerge from the Bayesian account, rather than being used to constrain priors and likelihoods. I provide a detailed discussion of the case of how the Copernican and Ptolemaic theories explain retrograde motion, and suggest that one of the key explanatory considerations is the extent to which the explanation a theory provides depends on its core elements rather than on auxiliary hypotheses. I then suggest that this type of consideration is reflected in the Bayesian likelihood, given priors that a Bayesian might be inclined to adopt even without explicit guidance by IBE. The aim is to show that IBE and Bayesianism may be compatible, not because they can be amalgamated, but rather because they capture substantially similar epistemic considerations. 1 Introduction2 Preliminaries3 Inference to the Best Explanation4 Bayesianism5 The Incompatibilist View : Inference to the Best Explanation Contradicts Bayesianism5. 1 Criticism of the incompatibilist view6 Constraint - Based Compatibilism6. 1 Criticism of constraint - based compatibilism7 Emergent Compatibilism7. 1 Analysis of inference to the best explanation7. 1. 1 Inference to the best explanation on specific hypotheses7. 1. 2 Inference to the best explanation on general theories7. 1. 3 Copernicus versus Ptolemy7. 1. 4 Explanatory virtues7. 1. 5 Summary7. 2 Bayesian account8 Conclusion. (shrink)

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide (...) additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

Adults design utterances to match listeners' informational needs by making both “generic” adjustments (e.g., mentioning atypical more often than typical information) and “particular” adjustments tailored to their specific interlocutor (e.g., including things that their addressee cannot see). For children, however, relevant evidence is mixed. Three experiments investigated how generic and particular factors affect children's production. In Experiment 1, 4‐ to 5‐year‐old children and adults described typical and atypical instrument events to a silent listener who could either see or not see (...) the events. In later extensions, participants described the same events to either a silent (Experiment 2) or an interactive (Experiment 3) addressee with a specific goal. Both adults and 4‐ to 5‐year‐olds performed generic adjustments but, unlike adults, children made listener‐particular adjustments inconsistently. These and prior findings can be explained by assuming that particular adjustments can be costlier for children to implement compared to generic adjustments. (shrink)

The probabilistic corroboration of two or more hypotheses or series of observations may be performed additively or multiplicatively . For additive corroboration (e.g. by Laplace's rule of succession), stochastic independence is needed. Inferences, based on overwhelming numbers of observations without unexplained counterinstances permit hyperinduction , whereby extremely high probabilities, bordering on certainty for all practical purposes may be achieved. For multiplicative corroboration, the error probabilities (1 - Pr) of two (or more) hypotheses are multiplied. The probabilities, obtained by reconverting the (...) product, are valid for both of the hypotheses and indicate the gain by corroboration.. This method is mathematically correct, no probabilities > 1 can result (as in some conventional methods) and high probabilities with fewer observations may be obtained, however, semantical independence is a prerequisite. The combined method consists of (1) the additive computation of the error probabilities (1 - Pr) of two or more single hypotheses, whereby arbitrariness is avoided or at least reduced and (2) the multiplicative procedure . The high reliability of Empirical Counterfactual Statements is explained by the possibility of multiplicative corroboration of "all-no" statements due to their strict semantical independence. (shrink)

Visual attention evolved as an adaptive mechanism allowing us to cope with a rapidly changing environment. It enables the facilitated processing of relevant information, often automatically and governed by implicit motives. However, despite recent advances in understanding the relationship between consciousness and visual attention, the functional scope of unconscious attentional control is still under debate. Here, we present a novel masking paradigm in which volunteers were to distinguish between varying orientations of a briefly presented, masked grating stimulus. Combining signal detection (...) theory and subjective measures of awareness, we show that performance on unaware trials was consistent with visual selection being weighted towards repeated orientations of Gabor patches and reallocated in response to a novel unconsciously processed orientation. This was particularly present in trials in which the prior feature was strongly weighted and only if the novel feature was invisible. Thus, our results provide evidence that invisible orientation stimuli can trigger the reallocation of history-guided visual selection weights. (shrink)

This paper introduces what is called the intersubjective interpretation of the probability calculus. Intersubjective probabilities are related to subjective probabilities, and the paper begins with a particular formulation of the familiar Dutch Book argument. This argument is then extended, in Section 3, to social groups, and this enables the concept of intersubjective probability to be introduced in Section 4. It is then argued that the intersubjective interpretation is the appropriate one for the probabilities which appear in confirmation theory whether of (...) a Bayesian or a Popperian variety. The final section of the paper states and tries to answer an objection due to Putnam. (shrink)

Geven, Ben‐Shakhar, Kindt and Verschuere point out that research on deception detection usually employs instructed cheating. They experimentally demonstrate that participants show slower reaction times for concealed information than for other information, regardless of whether they are explicitly instructed to cheat or whether they can freely choose to cheat or not. Finding this ‘cognitive signature of lying’ with self‐initiated cheating too is argued by the authors to strengthen the external validity of deception detection research. [75].

The appearance of the body signals socially relevant states and traits, but the how these cues are perceived is not well understood. Here we examined judgments of emotion and sex from the body’s ap...

Harold Jeffreys' ideas on the interpretation of probability and epistemology are reviewed. It is argued that with regard to the interpretation of probability, Jeffreys embraces a version of logicism that shares some features of the subjectivism of Ramsey and de Finetti. Jeffreys also developed a probabilistic epistemology, characterized by a pragmatical and constructivist attitude towards notions such as ‘objectivity’, ‘reality’ and ‘causality’. 1 Introductory remarks 2 The interpretation of probability 3 Jeffreys' probabilistic epistemology.

Subliminal primes are assumed to produce weaker and short-lived effects on subsequent behavior compared to clearly visible primes. However, this difference in priming effect may be due to differences in signal strength, rather than level of awareness. In the present study we manipulated prime discriminability by using metacontrast masks and pseudomasks, while keeping the prime strength equal. This manipulation resulted in large differences in discriminability of the primes. However, both immediate response priming and long-term response priming was equal for the (...) poorly discriminable and well discriminable primes, and equal for groups that differed markedly in terms of how well they could discriminate the primes. Our findings imply that discriminability of information is independent of both the immediate and long-term effects that information can have on behavior. (shrink)

The likelihood theory of evidence (LTE) says, roughly, that all the information relevant to the bearing of data on hypotheses (or models) is contained in the likelihoods. There exist counterexamples in which one can tell which of two hypotheses is true from the full data, but not from the likelihoods alone. These examples suggest that some forms of scientific reasoning, such as the consilience of inductions (Whewell, 1858. In Novum organon renovatum (Part II of the 3rd ed.). The philosophy of (...) the inductive sciences. London: Cass, 1967), cannot be represented within Bayesian and Likelihoodist philosophies of science. (shrink)

The central problem with Bayesian philosophy of science is that it cannot take account of the relevance of simplicity and unification to confirmation, induction, and scientific inference. The standard Bayesian folklore about factoring simplicity into the priors, and convergence theorems as a way of grounding their objectivity are some of the myths that Earman's book does not address adequately. 1Review of John Earman: Bayes or Bust?, Cambridge, MA. MIT Press, 1992, £33.75cloth.

Previous work showed that the beginning of a sound is more important for the perception of loudness than later parts. When a short silent gap of sufficient duration is inserted into a sound, this primacy effect reoccurs in the second sound part after the gap. The present study investigates whether this temporal weighting occurs independently for different frequency bands. Sounds consisting of two bandpass noises were presented in four different conditions: a simultaneous gap in both bands, a gap in only (...) the lower frequency band, a gap in only the higher frequency band, or no gap. In all conditions, the temporal loudness weights showed a primacy effect at sound onset. For the frequency bands without a gap, the temporal weights decreased gradually across time, regardless of whether the other frequency band did or did not contain a gap. When a frequency band contained a gap, the weight at the onset of this band after the gap was increased. This reoccurrence of the primacy effect following the gap was again largely independent of whether or not the other band contained a gap. Thus, the results indicate that the temporal loudness weights are frequency specific. (shrink)

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)

The idea that perceptual and cognitive systems must incorporate knowledge about the structure of the environment has become a central dogma of cognitive theory. In a Bayesian context, this idea is often realized in terms of “tuning the prior”—widely assumed to mean adjusting prior probabilities so that they match the frequencies of events in the world. This kind of “ecological” tuning has often been held up as an ideal of inference, in fact defining an “ideal observer.” But widespread as this (...) viewpoint is, it directly contradicts Bayesian philosophy of probability, which views probabilities as degrees of belief rather than relative frequencies, and explicitly denies that they are objective characteristics of the world. Moreover, tuning the prior to observed environmental frequencies is subject to overfitting, meaning in this context overtuning to the environment, which leads (ironically) to poor performance in future encounters with the same environment. Whenever there is uncertainty about the environment—which there almost always is—an agent's prior should be biased away from ecological relative frequencies and toward simpler and more entropic priors. (shrink)

A frequentist confidence interval can be constructed by inverting a hypothesis test, such that the interval contains only parameter values that would not have been rejected by the test. We show how a similar definition can be employed to construct a Bayesian support interval. Consistent with Carnap’s theory of corroboration, the support interval contains only parameter values that receive at least some minimum amount of support from the data. The support interval is not subject to Lindley’s paradox and provides an (...) evidence-based perspective on inference that differs from the belief-based perspective that forms the basis of the standard Bayesian credible interval. (shrink)

The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version (...) of CP canthus be maintained. (shrink)

There is widespread agreement among philosophers about the Mens Rea Asymmetry (MRA), according to which praise requires intent, whereas blame does not. However, there is evidence showing that MRA is descriptively inadequate. We hypothesize that the violations of MRA found in the experimental literature are due to what we call “moral compositionality,” by which we mean that people evaluate the component parts of a moral problem separately and then reach an overall verdict by aggregating the verdicts on the component parts. (...) We have subjected this hypothesis to the test and here report the results of our experiment. We explore several explanations of the experimental findings and conclude that they present a puzzle to moral theory. (shrink)

Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events then when we order events? de Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. (...) While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence. (shrink)

The idea that simplicity matters in science is as old as science itself, with the much cited example of Ockham's Razor, 'entia non sunt multiplicanda praeter necessitatem': entities are not to be multiplied beyond necessity. A problem with Ockham's razor is that nearly everybody seems to accept it, but few are able to define its exact meaning and to make it operational in a non-arbitrary way. Using a multidisciplinary perspective including philosophers, mathematicians, econometricians and economists, this 2002 monograph examines simplicity (...) by asking six questions: what is meant by simplicity? How is simplicity measured? Is there an optimum trade-off between simplicity and goodness-of-fit? What is the relation between simplicity and empirical modelling? What is the relation between simplicity and prediction? What is the connection between simplicity and convenience? The book concludes with reflections on simplicity by Nobel Laureates in Economics. (shrink)

In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...) of explanatory pluralism both within philosophy of science and psychiatry – namely moderate/temporary pluralism, anything goes pluralism, isolationist pluralism, integrative pluralism and interactive pluralism. Next, I discuss the pros and cons of these different understandings of explanatory pluralism. Finally, I raise the question of how to implement or operationalize explanatory pluralism in scientific practice; how to structure the “genuine dialogue” or shape “the pluralistic attitude” Campaner is referring to. As tentative answers, I explore a question-based framework for explanatory pluralism as well as social-epistemological procedures for interaction among competing approaches and explanations. (shrink)

This thesis has two goals. Firstly, we consider the problem of model selection for the purposes of prediction. In modern science predictive mathematical models are ubiquitous and can be found in such diverse fields as weather forecasting, economics, ecology, mathematical psychology, sociology, etc. It is often the case that for a given domain of inquiry there are several plausible models, and the issue then is how to discriminate between them – this is the problem of model selection. We consider approaches (...) to model selection that are used in classical [also known as frequentist] statistics, and fashionable in recent years methods of Akaike Information Criterion [AIC] and Bayes Information Criterion [BIC], the latter being a part of a broader Bayesian approach. We show the connection between AIC and BIC, and provide comparison of performance of these methods. Secondly, we consider some philosophical arguments that arise within the setting of the model selection approaches investigated in the first part. These arguments aim to provide counterexamples to the epistemic thesis of scientific realism, viz., that predictively successful scientific theories are approximately true, and to the idea that truth and predictive accuracy go together. We argue for the following claims: 1) that none of the criticisms brought forward in the philosophical literature against the AIC methodology are devastating, and AIC remains a viable method of model selection; 2) that the BIC methodology likewise survives the numerous criticisms; 3) that the counterexamples to scientific realism that ostensibly arise within the framework of model selection are flawed; 4) that in general the model selection methods discussed in this thesis are neutral with regards to the issue of scientific realism; 5) that a plurality of methodologies should be applied to the problem of model selection with full awareness of the foundational issues that each of these methodologies has. (shrink)

Non-trivial calculi of inductive inference are incomplete. This result is demonstrated formally elsewhere. Here the significance and background to the result is described. This note explains what is meant by incompleteness, why it is desirable, if only it could be secured, and it gives some indication of the arguments needed to establish its failure. The discussion will be informal, using illustrative examples rather than general results. Technical details and general proofs are presented in Norton.

How should probabilities be interpreted in causal models in the social and health sciences? In this paper we take a step towards answering this question by investigating the case of cancer in epidemiology and arguing that the objective Bayesian interpretation is most appropriate in this domain.

Proponents of Bayesian confirmation theory believe that they have the solution to a significant, recalcitrant problem in philosophy of science. It is the identification of the logic that governs evidence and its inductive bearing in science. That is the logic that lets us say that our catalog of planetary observations strongly confirms Copernicus’ heliocentric hypothesis; or that the fossil record is good evidence for the theory of evolution; or that the 3oK cosmic background radiation supports big bang cosmology. The definitive (...) solution to this problem would be a significant achievement. The problem is of central importance to philosophy of science, for, in the end, what distinguishes science from myth making is that we have good evidence for the content of science, or at least of mature sciences, whereas myths are evidentially ungrounded fictions. The core ideas shared by all versions of Bayesian confirmation theory are, at a good first approximation, that a scientist’s beliefs are or should conform to a probability measure; and that the incorporation of new evidence is through conditionalization using Bayes’ theorem. While the burden of this chapter will be to inventory why critics believe this theory may not be the solution after all, it is worthwhile first to summarize here the most appealing virtues of this simple account. There are three. First, the theory reduces the often nebulous notion of a logic of.. (shrink)

The aim of this thesis is to improve our understanding of how to assess and communicate uncertainty in areas of research deeply afflicted by it, the assessment and communication of which are made more fraught still by the studies’ immediate policy implications. The IPCC is my case study throughout the thesis, which consists of three parts. In Part 1, I offer a thorough diagnosis of conceptual problems faced by the IPCC uncertainty framework. The main problem I discuss is the persistent (...) ambiguity surrounding the concepts of ‘confidence’ and ‘likelihood’; I argue that the lack of a conceptually valid interpretation of these concepts compatible with the IPCC uncertainty guide’s recommendations has worrying implications for both the IPCC authors’ treatment of uncertainties and the interpretability of the information provided in the AR5. Finally, I show that an understanding of the reasons behind the IPCC’s decision to include two uncertainty scales can offer insights into the nature of this problem. In Part 2, I review what philosophers have said about model-based robustness analysis. I assess several arguments that have been offered for its epistemic import and relate this discussion to the context of climate model ensembles. I also discuss various measures of independence in the climate literature, and assess the extent to which these measures can help evaluate the epistemic import of model robustness. In Part 3, I explore the notion of the ‘weight of evidence’ typically associated with Keynes. I argue that the Bayesian is bound to struggle with this notion, and draw some lessons from this fact. Finally, I critically assess some recent proposals for a new IPCC uncertainty framework that significantly depart from the current one. (shrink)

Statistical tests that detect and measure deviation from the Hardy-Weinberg equilibrium (HWE) have been devised but are limited when testing for deviation at multiallelic DNA loci is attempted. Here we present the full Bayesian significance test (FBST) for the HWE. This test depends neither on asymptotic results nor on the number of possible alleles for the particular locus being evaluated. The FBST is based on the computation of an evidence index in favor of the HWE hypothesis. A great deal of (...) forensic inference based on DNA evidence assumes that the HWE is valid for the genetic loci being used. We applied the FBST to genotypes obtained at several multiallelic short tandem repeat loci during routine parentage testing; the locus Penta E exemplifies those clearly in HWE while others such as D10S1214 and D19S253 do not appear to show this. (shrink)

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

The conservative idea that it is a philosopher’s job to clarify common sense beliefs about ordinary concepts is being weeded out from the population and replaced by a revisionist agenda: philosophers should not merely describe but also analyze and suggest ways to improve our concepts. This project is called "conceptual engineering." The conceptual engineering literature is growing rapidly as more philosophers undertake normative conceptual work. However, many philosophers are practicing conceptual engineering untethered to an explicit methodology. Analyses addressing how we (...) should engineer a concept and what should be considered successful are scarce. The thesis of this dissertation is that Carnapian Explication solves this methodological deficiency. (shrink)

In this paper I argue that it is finally time to move beyond the Nagelian framework and to break new ground in thinking about epistemic reduction in biology. I will do so, not by simply repeating all the old objections that have been raised against Ernest Nagel’s classical model of theory reduction. Rather, I grant that a proponent of Nagel’s approach can handle several of these problems but that, nevertheless, Nagel’s general way of thinking about epistemic reduction in terms of (...) theories and their logical relations is entirely inadequate with respect to what is going on in actual biological research practice. (shrink)

Millions of children in the United States experience parental incarcera- tion, yet it is unclear how this experience might shape social cognition. We asked children of incarcerated parents (N = 24) and children whose parents were not incarcerated (N = 58) to describe their parents. Both groups of children also rated the extent to which they agree that they feel positive and, separately, negative emotions when thinking about their parent and best friend. This approach allowed us to test between two (...) alternative hypotheses. On the one hand, cultural narratives in the United States convey negative messages about incarcerated people, and these messages could prompt children to report negativity when thinking about their incarcerated parents. On the other hand, chil- dren’s positivity toward close others is robust. Thus, when thinking about their incarcerated parents, children may report a great deal of positivity. Consistent with the latter possibility, children were more likely to describe their incarcerated parents using positive rather than negative terms. Moreover, children of incarcerated parents were more likely to agree that thinking about close others made them feel posi- tive emotions than they were to agree that thinking about close others made them feel negative emotions. A similar pattern of results emerged among children whose parents were not incarcerated. These findings demonstrate the robustness of children’s positivity and can inform debates regarding contact between incarcerated par- ents and their children. (shrink)

The aim of this article is to discuss the conditions under which functional neuroimaging can contribute to the study of higher cognition. We begin by presenting two case studies—on moral and economic decision making—which will help us identify and examine one of the main ways in which neuroimaging can help advance the study of higher cognition. We agree with critics that functional magnetic resonance imaging (fMRI) studies seldom “refine” or “confirm” particular psychological hypotheses, or even provide details of the neural (...) implementation of cognitive functions. However, we suggest that neuroimaging can support psychology in a different way—namely, by selecting among competing hypotheses of the cognitive mechanisms underlying some mental function. One of the main ways in which neuroimaging can be used for hypothesis selection is via reverse inferences, which we here examine in detail. Despite frequent claims to the contrary, we argue that successful reverse inferences do not assume any strong or objectionable form of reductionism or functional locationism. Moreover, our discussion illustrates that reverse inferences can be successful at early stages of psychological theorizing, when models of the cognitive mechanisms are only partially developed. (shrink)

In probability textbooks, it is widely claimed that zero probability does not mean impossibility. But what stands behind this claim? In this paper I offer an explanation to this claim based on Kolmogorov's formalism. As such, this explanation is relevant to all interpretations of Kolmogorov's probability theory. I start by clarifying that this claim refers only to nonempty events, since empty events are always considered as impossible. Then, I offer the following three reasons for the claim that nonempty events with (...) zero probability are considered as possible: The main reason is simply because they are nonempty. Hence, they are considered as possible despite their zero probability. The second reason is that sometimes the zero probability is taken to be an approximation of some infinitesimal probability value. Such a value is strictly positive and as such does not imply impossibility in a strict sense. Finally, the third reason is that there are interpretations according to which the same event can have different probabilities. Specifically, it is assumed that an event with exactly zero probability can have strictly positive probabilities. This means that such an event can be possible which implies that its zero probability does not mean impossibility. (shrink)

The idea that probability is a degree of rational belief seemed too vague for a foundation of a mathematical theory. It was certainly not obvious that degrees of rational belief had to be governed by the probability axioms as used by Laplace and other prestatistical probabilityst. The axioms seemed arbitrary in their interpretation. To eliminate the arbitrariness, the stat- isticians of the early 20th century drastically restricted the possible applications of the probability theory, by insisting that probabilities had to be (...) interpreted as relative frequencies, which obviously satisfied the probability axioms, and so the arbitrariness was removed. But the frequentist approach turned more subjective than the prestatistical approach, because the identifications of outcome spaces, the choices of test statistics, the declarations of what rejection regions are, the choices of null-hypothesis among alternatives, the contradictory choices between sizes and powers etc., depend on thoughts or even whims of the experimenter. Frequentists thus failed to solve the problems that motivated their approach, they even exacerbated them. The subjective Bayesianism of Ramsey and de Finetti did not solve the problems either. Finally Cox provided the missing foundation for probability as a degree of rational belief, which makes the Bayesian probability theory (which is based on this foundation) the best theory of probable inference we have. Hence, it is quite unbelievable that it is not even mentioned in recent philosophy textbooks devoted to the probable inference. The reason could be that it requires fairly sophisticated mathematics. But not even to mention it? We explain the history and prove Cox theorem in a novel way. (shrink)

After a brief review of ontic and epistemic descriptions, and of subjective, logical and statistical interpretations of probability, we summarize the traditional axiomatization of calculus of probability in terms of Boolean algebras and its set-theoretical realization in terms of Kolmogorov probability spaces. Since the axioms of mathematical probability theory say nothing about the conceptual meaning of “randomness” one considers probability as property of the generating conditions of a process so that one can relate randomness with predictability (or retrodictability). In the (...) measure-theoretical codification of stochastic processes genuine chance processes can be defined rigorously as so-called regular processes which do not allow a long-term prediction. We stress that stochastic processes are equivalence classes of individual point functions so that they do not refer to individual processes but only to an ensemble of statistically equivalent individual processes. Less popular but conceptually more important than statistical descriptions are individual descriptions which refer to individual chaotic processes. First, we review the individual description based on the generalized harmonic analysis by Norbert Wiener. It allows the definition of individual purely chaotic processes which can be interpreted as trajectories of regular statistical stochastic processes. Another individual description refers to algorithmic procedures which connect the intrinsic randomness of a finite sequence with the complexity of the shortest program necessary to produce the sequence. Finally, we ask why there can be laws of chance. We argue that random events fulfill the laws of chance if and only if they can be reduced to (possibly hidden) deterministic events. This mathematical result may elucidate the fact that not all nonpredictable events can be grasped by the methods of mathematical probability theory. (shrink)

The idea that a serious threat to scientific realism comes from unconceived alternatives has been proposed by van Fraassen, Sklar, Stanford and Wray among others. Peter Lipton's critique of this threat from underconsideration is examined briefly in terms of its logic and its applicability to the case of space-time and particle physics. The example of space-time and particle physics indicates a generic heuristic for quantitative sciences for constructing potentially serious cases of underdetermination, involving one-parameter family of rivals T_m that work (...) as a team rather than as a single rival against default theory T_0. In important examples this new parameter has a physical meaning and makes a crucial _conceptual_ difference, shrinking the symmetry group and in some case putting gauge freedom, formal indeterminism vs. determinism, the presence of the hole argument, etc., at risk. Methodologies akin to eliminative induction or tempered subjective Bayesianism are more demonstrably reliable than the custom of attending only to "our best theory": they can lead either to a serious rivalry or to improved arguments for the favorite theory. The example of General Relativity vs. massive spin 2 gravity, a recent topic in the physics literature, is discussed. Arguably the General Relativity and philosophy literatures have ignored the most serious rival to General Relativity. (shrink)