Maria Carla Galavotti

This paper investigates the kind of empiricism combined with an operationalist perspective that, in the first decades of our Century, gave rise to a turning point in theoretical physics and in probability theory. While quantum mechanics was taking shape, the classical (Laplacian) interpretation of probability gave way to two divergent perspectives: frequentism and subjectivism. Frequentism gained wide acceptance among theoretical physicists. Subjectivism, on the other hand, was never held to be a serious candidate for application to physical theories, despite the fact that its philosophical back-ground strongly resembles that underlying quantum mechanics, at least according to the Copenhagen interpretation. The reasons for this are explored.

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.

One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach's inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises's perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach's inductivism, with special reference to his book Experience and prediction

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect. _A Philosophical Introduction to Probability_ showcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's “classical” interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability

This contribution claims that the two fundamental notions of causation at work in the health sciences are manipulative and mechanistic, and investigates what kinds of evidence matter for the assessment of causal relations. This article is a development of our 2007 article, ‘Plurality of Causality’, where we argue for a pluralistic account of causation with an eye to econometrics and a single medical example. The present contribution has a wider focus, and considers the notion of evidence within a whole range of disciplines belonging to the health sciences. Section 1 addresses the relations between kinds of evidence and causal accounts, and it is shown how different notions of causation can be employed in various medical cases. Section 2 calls attention to issues crucial for any adequate epistemological theory of causation, such as the distinctions between types and tokens, observational and experimental regimes, explanation and prediction. Lastly, the notion of context is articulated, highlighted in its role in the assessment of causal links. All these issues are tackled in the framework of what we label a ‘bottom–up’ epistemology.

Pragmatism, taken not just as a philosophical movement but as a way of addressing problems, strongly influenced the debate on the foundations of probability during the first half of the twentieth century. Upholders of different interpretations of probability such as Hans Reichenbach, Ernest Nagel, Rudolf Carnap, Frank Ramsey, and Bruno de Finetti, acknowledged their debt towards pragmatist philosophers, including Charles Sanders Peirce, William James, Clarence Irving Lewis, William Dewey and Giovanni Vailati. In addition, scientist-philosophers like Ernst Mach, Ludwig Boltzmann, Henri Poincaré, Pierre Duhem, and Karl Pearson, who heralded a conception of science and knowledge at large that was close to pragmatism, were very influential in that debate. Among the main interpretations of probability – frequentism, propensionism, logicism and subjectivism -, the latter is no doubt the closest to the pragmatist outlook. This paper concentrates on three representatives of the subjective theory, namely Frank Ramsey, Bruno de Finetti and Émile Borel.

Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is by far the most controversial, and fuels a heated debate, still ongoing. After a short historical sketch of the birth and developments of probability, its major interpretations are outlined, by referring to the work of their most prominent representatives. The final section addresses the question of whether any of such interpretations can presently be considered predominant, which is answered in the negative.

Galavotti begins her book by stressing the centrality of probability to a whole range of philosophical problems. She writes 1: "Probability invests all branches of philosophical investigation, from epistemology to moral and political philosophy, and impinges upon major controversies, like that between determinism and indeterminism, or between free will and moral obligation, and problems such as: ‘What degree of certainty can human knowledge attain?’ ‘What is the relationship between probability and certainty?’" She then explains that her book will focus on the interpretation of the notion of probability. Chapter 1 contains some general remarks about the notion of probability, and Chapter 2 presents a brief introduction to the formal calculus of probability. Then in the next five chapters Galavotti presents in turn the five main interpretations of probability, namely the classical, frequency, propensity, logical, and subjective.Galavotti's approach to the material is historical. She traces, through extensive quotations from, and discussions of, the principal authors, the development of each of the interpretations. In many cases, she deals with early advocates of the position who are often omitted, such as De Morgan, Boole, and Jevons in the case of the logical interpretation, and Donkin in the case of the subjective interpretation. At the same time, the story is often brought right up to the present with discussions of recent authors such as Richard Jeffrey and Patrick Suppes in the case of the subjective interpretation. Galavotti's book is an excellent advertisement for the virtues of …

One of the first to criticize the verifiability theory of meaning embraced by logical empiricists, Reichenbach ties the significance of scientific statements to their predictive character, which offers the condition for their testability. While identifying prediction as the task of scientific knowledge, Reichenbach assigns induction a pivotal role, and regards the theory of knowledge as a theory of prediction based on induction. Reichenbach’s inductivism is grounded on the frequency notion of probability, of which he prompts a more flexible version than that of Richard von Mises. Unlike von Mises, Reichenbach attempts to account for single case probabilities, and entertains a restricted notion of randomness, more suitable for practical purposes. Moreover, Reichenbach developed a theory of induction, absent from von Mises’s perspective, and argued for the justification of induction. This article outlines the main traits of Reichenbach’s inductivism, with special reference to his book Experience and prediction.

The philosophy of science took shape as an autonomous discipline in the first decades of the Twentieth Century in connection with the movement known as logical positivism or logical empiricism. According to logical empiricists philosophy of science ought to perform a “rational reconstruction” aimed at exhibiting the logical structure of scientific theories and inferential processes involved in the acquisition of scientific knowledge. While focusing on the syntactical and semantical aspects of scientific language, logical empiricists left out of the realm of the philosophy of science the sociological and psychological aspects of theory formation, as well as all methodological aspects belonging to experimentation. Starting from the early Sixties this conception gradually changed, and philosophy of science underwent a radical transformation, leading to a significant broadening of its scope. New issues and problems were addressed, belonging to fields neglected by the traditional approach. This paper sketches the main features of the discipline as it is understood today as opposed to its traditional outlook, and suggests that the term “philosophy of the sciences” is better suited than “philosophy of science” to describe its present state.

Probabilistic epistemology holds that probability is an essential ingredient of science and human knowledge at large, and that induction is a necessary constituent of the scientific method. Developed in some detail by a number of authors including Patrick Suppes, Richard Jeffrey and Brian Skyrms, this view has been embraced by so many, as to gradually become predominant. While probabilistic epistemology has been growing, awareness of its origins was somehow left behind. Probabilistic epistemology is usually seen as a product of the encounter of logical empiricism with American pragmatism. Without denying the impact of such an encounter, it is argued that the probabilistic approach was already part of the European scenario before the dissolution of logical empiricism in the late 1930s. Notably, such an approach is not linked to a particular interpretation of probability, having been endorsed by upholders of different probability notions, including Janina Hosiasson, Frank Plumpton Ramsey, Bruno de Finetti, Harold Jeffreys, and Hans Reichenbach, to mention only those authors whose contribution is addressed here. The list could extend to the French probabilists Émile Borel and Maurice Fréchet, and others not considered in this survey. The work of so many authors operating at the four corners of Europe in the first decades of the 19th century reflects a European tradition in probabilistic epistemology, somewhat overshadowed in the literature by the attention paid to logical empiricism