Many people regard utility theory as the only rigorous foundation for subjective probability, and even de Finetti thought the betting approach supplemented by Dutch Book arguments only good as an approximation to a utility-theoretic account. I think that there are good reasons to doubt this judgment, and I propose an alternative, in which the probability axioms are consistency constraints on distributions of fair betting quotients. The idea itself is hardly new: it is in de Finetti and also Ramsey. What is (...) new is that it is shown that probabilistic consistency and consequence can be defined in a way formally analogous to the way these notions are defined in deductive (propositional) logic. The result is a free-standing logic which does not pretend to be a theory of rationality and is therefore immune to, among other charges, that of “logical omniscience”. (shrink)

Information received from different sources can be inconsistent. Even when the sources of information can be ordered on the basis of their trustworthiness, it turns out that extracting an acceptable notion of support for information is a non-trivial matter, as is the question what information a rational agent should accept. Here it is shown how a support ordering on the information can be generated and how it can be used to decide what information to accept and what not to accept. (...) This ordering, it turns out, is closely related to notions such as Epistemic Entrenchment and Grove spheres studied in belief revision. (shrink)

I address the philosophical debate over whether the mathematical theory of probability arose on the basis of empirical observations or of purely theoretical speculations. The debate tends to pose a strict dichotomy between empirical problem-solving and pure theorizing. I alternatively suggest that, in the case of mathematical probability, an empirical problem-context acted as an enabling condition for the possibility of mathematical innovation, but that the activity of the early mathematical probabilists gradually became the study of a theoretical system of ideas. (...) This case has some implications for a more general philosophical view on the context of mathematical discovery. ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ----------------------------------------. (shrink)

The group theorist William Burnside devoted much of the last decade of his life to probability and statistics. The work led to contact with Ronald Fisher who was on his way to becoming the leading statistician of the age and with Karl Pearson, the man Fisher supplanted. Burnside corresponded with Fisher for nearly three years until their correspondence ended abruptly. This paper examines Burnside’s interactions with the statisticians and looks more generally at his work in probability and statistics.

For Ivor Grattan-Guinness on the occasion of his retirement. The work of Augustus De Morgan on symbolic logic in the mid-nineteenth century is familiar to historians of logic and mathematics alike. What is less well known is his work on probability and, more specifically, the use of probabilistic ideas and methods in his logic. The majority of De Morgan's work on probability was undertaken around 1837???1838, with his earliest publications on logic appearing from 1839, a period which culminated with the (...) publication of his Formal Logic in 1847. This article examines the overlap between his work on probability theory and logic during the earliest period of his interest in both. (shrink)

Frente a problemas de decisión colectiva de cierta complejidad, distintos métodos de votación pueden considerarse igualmente democráticos. Ante esta situación, argumento que es posible investigar cuáles de esos métodos producen mejores resultados epistémicos sobre asuntos fácticos. Comienzo ilustrando la relación entre democracia y métodos de votación con un sencillo ejemplo. Muestro cómo el uso de modelos idealizados permite descubrir algunas propiedades de los métodos de votación; varios de estos descubrimientos muestran que, frente a problemas de cierta complejidad, no hay una (...) respuesta clara acerca de cuál es el resultado de una elección democrática. Frente a esto, sugiero que deberíamos tomar en cuenta un rasgo epistémico instrumental de varios métodos de votación: su capacidad para generar respuestas correctas ante varias situaciones. Esta intuición ofrece lecciones importantes para el diseño de instituciones electorales. (shrink)

The modern discussion on the concept of truthlikeness was started in 1960. In his influential Word and Object, W. V. O. Quine argued that Charles Peirce's definition of truth as the limit of inquiry is faulty for the reason that the notion 'nearer than' is only "defined for numbers and not for theories". In his contribution to the 1960 International Congress for Logic, Methodology, and Philosophy of Science at Stan­ ford, Karl Popper defended the opposite view by defining a compara­tive (...) notion of verisimilitude for theories. The concept of verisimilitude was originally introduced by the Ancient sceptics to moderate their radical thesis of the inaccessibility of truth. But soon verisimilitudo, indicating likeness to the truth, was confused with probabilitas, which expresses an opiniotative attitude weaker than full certainty. The idea of truthlikeness fell in disrepute also as a result of the careless, often confused and metaphysically loaded way in which many philosophers used - and still use - such concepts as 'degree of truth', 'approximate truth', 'partial truth', and 'approach to the truth'. Popper's great achievement was his insight that the criticism against truthlikeness - by those who urge that it is meaningless to speak about 'closeness to truth' - is more based on prejudice than argument. (shrink)

In this paper I offer an account of the normative dimension implicit in D. Bernoulli’s expected utility functions by means of an analysis of the juridical metaphors upon which the concept of mathematical expectation was moulded. Following a suggestion by the late E. Coumet, I show how this concept incorporated a certain standard of justice which was put in question by the St. Petersburg paradox. I contend that Bernoulli would have solved it by introducing an alternative normative criterion rather than (...) a positive model of decision making processes. (shrink)

My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...) problems from current work in history of engineering and technology studies. I then model Carnap’s practice based on those lessons and uncover ways in which Carnap’s technical work in inductive logic takes some of these lessons on board. This shows ways in which Carnap’s philosophical project subtly changes right through his late work on induction, providing an important corrective to interpretations that ignore the work on inductive logic. Specifically, I show that paying attention to the historical details of Carnap’s attempt to apply his work in inductive logic to decision theory and theoretical statistics in the 1950s and 1960s helps us understand how Carnap develops and rearticulates the philosophical point of the practical/theoretical distinction in his late work, offering thus a new interpretation of Carnap’s technical work within the broader context of philosophy of science and analytical philosophy in general. (shrink)

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)

Using “brute reason” I will show why there can be only one valid interpretation of probability. The valid interpretation turns out to be a further refinement of Popper’s Propensity interpretation of probability. Via some famous probability puzzles and new thought experiments I will show how all other interpretations of probability fail, in particular the Bayesian interpretations, while these puzzles do not present any difficulties for the interpretation proposed here. In addition, the new interpretation casts doubt on some concepts often taken (...) as basic and unproblematic, like rationality, utility and expectation. This in turn has implications for decision theory, economic theory and the philosophy of physics. (shrink)

Par risques majeurs, on entend ceux qui s’attachent à des événements dont les conséquences défavorables, pour l’humanité ou pour l’environnement, sont d’une gravité exceptionnelle. On n’ajoutera ni que ces événements sont d’une intensité physique extrême, ni qu’ils surviennent rarement, car ce n’est pas toujours le cas. Seuls des risques majeurs de nature civile seront considérés dans cet ouvrage, et il s'agira, plus limitativement, de risques naturels, comme ceux d’inondation et de submersion marine, illustrés par la tempête Xynthia en 2010, de (...) risques technologiques industriels, comme celui d’une explosion d'usine, illustré par la catastrophe AZF en 2001, et de risques nucléaires, pour autant qu’ils mettent en jeu les dangers de la radioactivité, et qu’illustrent, hors de France, les catastrophes de Three Miles Island (1979), Tchernobyl (1986) et Fukushima (2011), -/- Conçu comme un rapport destiné au Conseil d'analyse économique (CAE) du Premier Ministre français, l'ouvrage comporte une introduction traitant du risque majeur pris en général (section 1). Dans sa partie principale, il aborde les trois risques majeurs qu'il a sélectionnés à travers les prismes successifs de la géographie et de la technologie (section 2), de l’histoire institutionnelle et juridique (section 3), enfin d’un bilan normatif accompagné de recommandations pour l'action publique (section 4). -/- Neuf compléments spécialisés, dus à d'autres auteurs, complètent l'ouvrage. Ils portent sur des aspects technologiques (F. Ménage; A. Quantin et D. Moucoulon; P. Saint-Raymond), juridiques (V. Sanseverino-Godfrin), économiques généraux (C. Grislain-Letrémy et B. Villeneuve; R. Lahidji; J. Percebois; A. Schmitt et S. Spaeter) et financiers (M. Pappalardo) et ils concernent principalement le risque nucléaire. -/- Dans cet ensemble de vaste format, on espère avoir su proposer, non seulement des évaluations et des préconisations destinées aux pouvoirs publics, comme il convenait au projet initial de rapport, mais aussi une synthèse qui soit utilisable par tous ceux - décideurs, scientifiques ou simples observateurs - que préoccupent les questions de risques majeurs. (shrink)

The history of the mathematical probability includes two phases: 1) From Pascal and Fermat to Laplace, the theory gained in application fields; 2) In the first half of the 20th Century, two competing axiomatic systems were respectively proposed by von Mises in 1919 and Kolmogorov in 1933. This paper places this historical sketch in the context of the philosophical complexity of the probability concept and explains the resounding success of Kolmogorov’s theory through its ability to avoid direct interpretation. Indeed, unlike (...) experimental sciences, and despite its numerous applications, probability theory cannot be tested per se. Rather it relates to practical matters by means of transition hypotheses or bridging principles that match the structure of practical problems with abstract theory. In this respect probability theory has a very special status among scientific disciplines. (shrink)