We survey a variety of possible explications of the term “Individual Risk.” These in turn are based on a variety of interpretations of “Probability,” including classical, enumerative, frequency, formal, metaphysical, personal, propensity, chance and logical conceptions of probability, which we review and compare. We distinguish between “groupist” and “individualist” understandings of probability, and explore both “group to individual” and “individual to group” approaches to characterising individual risk. Although in the end that concept remains subtle and elusive, some pragmatic suggestions for (...) progress are made. (shrink)

How can we determine the adequacy of a probabilistic coherence measure? A widely accepted approach to this question besides formulating adequacy constraints is to employ paradigmatic test cases consisting of a scenario providing a joint probability distribution over some specified set of propositions coupled with a normative coherence assessment for this set. However, despite the popularity of the test case approach, a systematic evaluation of the proposed test cases is still missing. This paper’s aim is to change this. Using a (...) custom written computer program for the necessary probabilistic calculations a large number of coherence measures in an extensive collection of test cases is examined. The result is a detailed overview of the test case performance of any probabilistic coherence measures proposed so far. It turns out that none of the popular coherence measures such as Shogenji’s, Glass’ and Olsson’s, Fitelson’s or Douven and Meijs’ but two rather unnoticed measures perform best. This, however, does not mean that the other measures can be rejected straightforwardly. Instead, the results presented here are to be understood as a contribution among others to the project of finding adequate probabilistic coherence measures. (shrink)

In this paper I consider whether there is a measure of coherence that could be rightly claimed to generalize the notion of logical equivalence. I show that Fitelson’s (2003) proposal to that effect encounters some serious difficulties. Furthermore, there is reason to believe that no mutual-support measure could ever be suitable for the formalization of coherence as generalized logical equivalence. Instead, it appears that the only plausible candidate for such a measure is one of relative overlap. The measure I propose (...) in this paper is quite similar to Olsson’s (2002) proposal but differs from it by not being susceptible to the type of counterexample that Bovens and Hartmann (2003) have devised against it. (shrink)

This paper is a excursus into a philosophy of science for deployment in the study of sport. It argues for the virtues of Thomas Kuhn's account of the philosophy of science, an argument conducted strategically by contrasting that account with one derived from views of Karl Popper. In particular, it stresses, first, that Kuhn's views have been widely misunderstood; second, that a rectified Kuhnianism can give due weight to truth in science, while recognising that social sciences differ in crucial ways (...) from natural sciences. For, as Kuhn recognised, social sciences do not function in the paradigm-relative way characteristic of natural sciences. Yet there Kuhn's jargon, and especially misguided talk of ?paradigms?, is almost ubiquitous. These thoughts have relevance for three groups. First, as both sports scientists and exercise scientists come to grips with the claims to scientificity of their work, they will need increasingly to locate it within an epistemological framework provided by philosophy of science. So they must begin to take Kuhn's view seriously. Second, social scientists of sport ? faced with the predominant scientism of colleagues in sport and exercise science ? must also recognise alternatives to a postmodernist rejection of the concept of truth, where Kuhn's picture of natural science clarifies one such. Finally, philosophers writing on sport must not let antipathy to scientism close off the options they present or the terms in which they (we!) present them. And that may require debate among ourselves on abstract issues not immediately connected with sport. (shrink)

After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of p-values rather than as formal procedures for ‘acceptance‘ and ‘rejection‘. A number of types of null hypothesis are described and a principle for evidential interpretation set out governing the implications of p- values in the specific circumstances of each application, as contrasted with a long-run interpretation. A number of more complicated situ- ations are discussed (...) in which modification of the simple p-value may be essential. (shrink)

Theories of statistical testing may be seen as attempts to provide systematic means for evaluating scientific conjectures on the basis of incomplete or inaccurate observational data. The Neyman-Pearson Theory of Testing (NPT) has purported to provide an objective means for testing statistical hypotheses corresponding to scientific claims. Despite their widespread use in science, methods of NPT have themselves been accused of failing to be objective; and the purported objectivity of scientific claims based upon NPT has been called into question. The (...) purpose of this paper is first to clarify this question by examining the conceptions of (I) the function served by NPT in science, and (II) the requirements of an objective theory of statistics upon which attacks on NPT's objectivity are based. Our grounds for rejecting these conceptions suggest altered conceptions of (I) and (II) that might avoid such attacks. Second, we propose a reformulation of NPT, denoted by NPT*, based on these altered conceptions, and argue that it provides an objective theory of statistics. The crux of our argument is that by being able to objectively control error frequencies NPT* is able to objectively evaluate what has or has not been learned from the result of a statistical test. (shrink)

The official view of theory testing in the philosophy of science, the deductive model, does not reflect the way ambiguous, vague and ill formulated theories are tested. A new model of theory testing, the explicative model, is outlined which reflects how such theories are tested. This model is illustrated in the actual testing of psychoanalysis, a typical case of an ambiguous, vague and ill formulated theory and is contrasted with Kuhn's notion of the articulation of a paradigm.

Different notions of analysis have been both theorized and put to use in early analytic philosophy. Two of them stand out: connective analysis and analysis as paraphrase. The latter played a central role in the development of analytic philosophy from Frege to Quine and beyond. With the advent of formal semantics of natural language in the 1970s, paraphrase came to be characterizable as translation into a formal “target language”. While I claim that the method cannot achieve its original philosophical aims, (...) I insist that, in spite of them, it is far from being a theoretically empty operation and that it lives on in some contemporary philosophical enterprises. (shrink)

The main aim of this paper is to elucidate, from a logical point of view, the phenomenon of Simpson reversal — the paradox of a statistical reasoning. We define a binary relation of supporting in the following way: a sentence A supports a sentence B if and only if the probability of B is higher when A is true, than when A is false. It appears that a statistical argument occurring in Simpson paradox cannot be formalized by means of a (...) binary relation. We generalize the relation of support introducing the third parameter. Then we argue that it properly mirrors main features of the statistical argument occurring in Simpson paradox. (shrink)

We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...) the qualitative part of probabilistic inference leads to a very broad class of 'proto-probability' functions. (shrink)

The λ-continuum of inductive methods was derived from an assumption, called λ-condition, which says that the probability of finding an individual having property $x_{j}$ depends only on the number of observed individuals having property $x_{j}$ and on the total number of observed individuals. So, according to that assumption, all individuals with properties which are different from $x_{j}$ have equal weight with respect to that probability and, in particular, it does not matter whether any individual was observed having some property similar (...) to $x_{j}$ (the most complete proof of this result is presented in Carnap, 1980). The problem thus remained open to find some general condition, weaker than the λ-condition, which would allow for the derivation of probability functions which might be sensitive to similarity. Carnap himself suggested a weakening of the λ-condition which might allow for similarity sensitive probability functions (Carnap, 1980, p. 45) but he did not find the family of probability functions derivable from that principle. The aim of this paper is to present the family of probability functions derivable from Carnap's suggestion and to show how it is derived. In Section 1 the general problem of analogy by similarity in inductive logic is presented, Section 2 outlines the notation and the conceptual background involved in the proof, Section 3 gives the proof, Section 4 discusses Carnap's principle and the result, Section 5 is a brief review of the solutions which have previously been proposed. (shrink)

The word ‘probability’ in ordinary language has two different senses, here called inductive and physical probability. This paper examines the concept of inductive probability. Attempts to express this concept in other words are shown to be either incorrect or else trivial. In particular, inductive probability is not the same as degree of belief. It is argued that inductive probabilities exist; subjectivist arguments to the contrary are rebutted. Finally, it is argued that inductive probability is an important concept and that it (...) is a mistake to try to replace it with the concept of degree of belief, as is usual today. (shrink)

This paper seeks to defend the following conclusions: The program advanced by Carnap and other necessarians for probability logic has little to recommend it except for one important point. Credal probability judgments ought to be adapted to changes in evidence or states of full belief in a principled manner in conformity with the inquirer’s confirmational commitments—except when the inquirer has good reason to modify his or her confirmational commitment. Probability logic ought to spell out the constraints on rationally coherent confirmational (...) commitments. In the case where credal judgments are numerically determinate confirmational commitments correspond to Carnap’s credibility functions mathematically represented by so—called confirmation functions. Serious investigation of the conditions under which confirmational commitments should be changed ought to be a prime target for critical reflection. The necessarians were mistaken in thinking that confirmational commitments are immune to legitimate modification altogether. But their personalist or subjectivist critics went too far in suggesting that we might dispense with confirmational commitments. There is room for serious reflection on conditions under which changes in confirmational commitments may be brought under critical control. Undertaking such reflection need not become embroiled in the anti inductivism that has characterized the work of Popper, Carnap and Jeffrey and narrowed the focus of students of logical and methodological issues pertaining to inquiry. (shrink)

Weighted averaging is a method for aggregating the totality of information, both regimented and unregimented, possessed by an individual or group of individuals. The application of such a method may be warranted by a theorem of the calculus of probability, simple conditionalization, or Jeffrey's formula for probability kinematics, all of which average in terms of the prior probability of evidence statements. Weighted averaging may, however, be applied as a method of rational aggregation of the probabilities of diverse perspectives or persons (...) in cases in which the weights cannot be articulated as the prior probabilities of statements of evidence. The method is justified by Wagner's Theorem exhibiting that any method satisfying the conditions of the Irrelevance of Alternatives and Zero Unanimity must, when applied to three or more alternatives, be weighted averaging. (shrink)

Pensons aux divers énoncés qui peuvent être composés à partir d'un ensemble fini ou dénombrable d'énoncés atomiques à l'aide de, disons, ‘˜’ et ‘&’; soit A n'importe lequel de ces énoncés; et soit l'ensemble SA des composantes atomiques de A. La valeur de vérité de A dépend évidemment des valeurs de vérité de certains membres de SA. En effet, si aux valeurs de vérité Vrai et Faux sont substitués les entiers 1 et 0, respectivement; la valeur de vérité VVV d'une (...) négation ˜A est 1–VV; et la valeur de vérité VV d'une conjonction A & B est min, VV), alors la valeur de vérité de A s'avère être une fonction numérique des valeurs de vérité de certains membres de SA. Et les fonctions de valeurs de vérité sont dites, à titre de résultat, récursivement définissables. (shrink)

Intuitionistic meta-methodologies, which abound in recent philosophy of science, take the criterion of success for theories of scientific rationality to be whether those theories adequately explicate our intuitive judgments of rationality in exemplary cases. Garber's (1985) critique of Laudan's (1977) intuitionistic meta-methodology, correct as far as it goes, does not go far enough. Indeed, Garber himself advocates a form of intuitionistic meta-methodology; he merely denies any special role for historical (as opposed to contemporary or imaginary) test cases. What all such (...) positions lack is a base from which to inform, criticize, or restructure our core methodological intuitions. To acquiesce in this is to deny that exemplary cases can serve the sort of warranting role required for intuitionism. This point is reinforced by a series of reasons for denying the warranting role of pre-analytic judgments of rationality. These reasons point the way toward an improved approach to meta-methodology. (shrink)

We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.

This paper analyzes the logical truths as (very roughly) those truths that would still have been true under a certain range of counterfactual perturbations.What’s nice is that the relevant range is characterized without relying (overtly, at least) upon the notion of logical truth. This approach suggests a conception of necessity that explains what the different varieties of necessity (logical, physical, etc.) have in common, in virtue of which they are all varieties of necessity. However, this approach places the counterfactual conditionals (...) in an unfamiliar foundational role. (shrink)

Two notions of evidence are focused on in this essay, Carnap's positive-relevance notion of evidence (1962, pp. 462 ff.), and Achinstein's notion of potential evidence (1978; and 1983, pp. 322–350). Achinstein creates several interesting examples in his attempt to find faults in Carnap's notion of evidence; his motive, ultimately, is to impel us towards potential evidence. The purpose of this essay is to show that positive relevance is significantly more promising than potential evidence with respect to capturing the scientific sense (...) of the term evidence. This is accomplished by finding faults in the notion of potential evidence, and by defending positive relevance against Achinstein's examples. (shrink)

Over the years several non-equivalent probabilistic measures of coherence have been discussed in the philosophical literature. In this paper we examine these measures with respect to their empirical adequacy. Using test cases from the coherence literature as vignettes for psychological experiments we investigate whether the measures can predict the subjective coherence assessments of the participants. It turns out that the participants’ coherence assessments are best described by Roche’s coherence measure based on Douven and Meijs’ average mutual support approach and the (...) conditional probability. (shrink)

Tomoji Shogenji is generally assumed to be the first author to have presented a probabilistic measure of coherence. Interestingly, Rudolf Carnap in his Logical Foundations of Probability discussed a function that is based on the very same idea, namely his well-known relevance measure. This function is largely neglected in the coherence literature because it has been proposed as a measure of evidential support and still is widely conceived as such. The aim of this paper is therefore to investigate Carnap’s measure (...) regarding its plausibility as a candidate for a probabilistic measure of coherence by comparing it to Shogenji’s. It turns out that both measures satisfy and violate the same adequacy constraints, despite not being ordinally equivalent exhibit a strong correlation with each other in a Monte Carlo simulation and perform similarly in a series of test cases for probabilistic coherence measures. (shrink)

This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference function do not satisfy (...) this condition and instead exhibit a previously unnoticed and rather puzzling behavior in certain cases of disconfirmation. This behavior also carries over to probabilistic measures of information change, causal strength, explanatory power and coherence. (shrink)

Epistemic systems are social processes generating judgments of truth and falsity. I outline a mathematical theory of epistemic systems that applies widely. Areas of application include pure science, torture, police forensics, espionage, auditing, clinical medical testing, democratic procedure, and the market economy. I examine torture and police forensics in relative detail. This paper is an exercise in comparative institutional epistemics, which considers how the institutions of an epistemic system influence its performance as measured by such things as error rates and (...) the volume of judgments generated. (shrink)

Probabilistic dependence and independence are among the key concepts of Bayesian epistemology. This paper focuses on the study of one specific quantitative notion of probabilistic dependence. More specifically, section 1 introduces Keynes’s coefficient of dependence and shows how it is related to pivotal aspects of scientific reasoning such as confirmation, coherence, the explanatory and unificatory power of theories, and the diversity of evidence. The intimate connection between Keynes’s coefficient of dependence and scientific reasoning raises the question of how Keynes’s coefficient (...) of dependence is related to truth, and how it can be made fruitful for epistemological considerations. This question is answered in section 2 of the paper. Section 3 outlines the consequences the results have for epistemology and the philosophy of science from a Bayesian point of view. (shrink)

Traditional logical empiricist and more recent historicist positions on the logic of discovery are briefly reviewed and both are found wanting. None have examined the historical detail now available from recent research on Darwin, from which there is evidence for gradual transition in descriptive and explanatory concepts. This episode also shows that revolutionary research can be directed by borrowed metascientific objectives and heuristics from other disciplines. Darwin's own revolutionary research took place within an ontological context borrowed from non evolutionary predecessors (...) with methodological objectives borrowed from and justified by their success in Newton's physics. The logic of discovery is not a special form of inference from observation to theory, but rather a theory of the rationality of research, including principles bearing upon the rational choice of problems, or epistemic objectives, and heuristic, or means to solving the problems. Such choices can be justified only locally in the context of a relatively stable background ontology and substantive epistemology, not globally for all science. (shrink)

The nature of the distinction between rational andnon-rational accounts of the development of science isanalyzed. These two kinds of accounts differ mostlyin the status which they give to methodologicalprinciples. It is shown that there are severaldimensions with respect to which the status of suchprinciples can resemble more or less the kind ofstatus that a paradigmatic rational account would givethem. It is concluded that, under the most plausibledefinitions of a rational account, the extent to whicha philosophical account of scientific change isrational (...) is a matter of degree, and that there is nosuch clear distinction between the two kinds ofaccounts which some supporters of rational and ofnon-rational accounts have assumed to exist. (shrink)

According to one view about the rationality of belief, such rationality is ultimately nothing other than the rationality that one exhibits in taking the means to one’s ends. On this view, epistemic rationality is really a species or special case of instrumental rationality. In particular, epistemic rationality is instrumental rationality in the service of one’s distinctively cognitive or epistemic goals (perhaps: one’s goal of holding true rather than false beliefs). In my (2003), I dubbed this view the instrumentalist conception of (...) epistemic rationality. (shrink)