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. (shrink)

We must restrict to mere probability not only statements of comparatively great uncertainty, like predictions about the weather, where we would cautiously ...

First published in 1949 expressly to introduce logical positivism to English speakers. Reichenbach, with Rudolph Carnap, founded logical positivism, a form of epistemofogy that privileged scientific over metaphysical truths.

Wesley Salmon is renowned for his seminal contributions to the philosophy of science. He has powerfully and permanently shaped discussion of such issues as lawlike and probabilistic explanation and the interrelation of explanatory notions to causal notions. This unique volume brings together twenty-six of his essays on subjects related to causality and explanation, written over the period 1971-1995. Six of the essays have never been published before and many others have only appeared in obscure venues. The volume includes a section (...) of accessible introductory pieces, as well as more advanced and technical pieces, and will make essential work in the philosophy of science readily available to both scholars and students. (shrink)

This paper deals with the problem of vindicating a particular type of inductive rule, a rule to govern inferences from observed frequencies to limits of relative frequencies. Reichenbach's rule of induction is defended. By application of two conditions, normalizing conditions and a criterion of linguistic invariance, it is argued that alternative rules lead to contradiction. It is then argued that the rule of induction does not lead to contradiction when suitable restrictions are placed upon the predicates admitted. Goodman's grue-bleen paradox (...) is considered, and an attempt to resolve it is offered. Finally, Reichenbach's pragmatic argument, hinging on convergence properties, is applied. (shrink)

Two chief problems of the theory of knowledge are the question of meaning and the question of verification. The first question asks under what conditions a sentence has meaning, in the sense of cognitive, factual meaning. The second one asks how we get to know something, how we can find out whether a given sentence is true or false. The second question presupposes the first one. Obviously we must understand a sentence, i.e. we must know its meaning, before we can (...) try to find out whether it is true or not. But, from the point of view of empiricism, there is a still closer connection between the two problems. In a certain sense, there is only one answer to the two questions. If we knew what it would be for a given sentence to be found true then we would know what its meaning is. And if for two sentences the conditions under which we would have to take them as true are the same, then they have the same meaning. Thus the meaning of a sentence is in a certain sense identical with the way we determine its truth or falsehood; and a sentence has meaning only if such a determination is possible. (shrink)

Experience and Prediction was Hans Reichenbach’s major epistemological treatise1 He regarded it as his refutation of logical positivism. The main theme of this book — the foundation for his critique of positivism — is his thoroughgoing probabilism. It is interesting to note that in 1933 Reichenbach published a glowing review of Rudolf Carnap’s Der Logische Aufbau der Welt, his only criticism being an inability to see how probability could fit into the picture. In the first chapter of Experience and Prediction (...) he presents his version of the verifiability theory of cognitive meaning. Instead of demanding, as the logical positivists had, the conclusive verifiability of a sentence if it is to qualify as cognitively meaningful, he insists upon probabilistic verifiability. A sentence is cognitively meaningful if and only if it is physically possible to have empirical evidence in terms of which a probability can be assigned to it. (shrink)

This volume thus clears the ground for the productive and fruitful integration of these new developments into philosophy of science.

Reichenbach sought to resolve Hume's problem of the justification of induction by means of a pragmatic vindication that relies heavily on the convergence properties of his rule of induction. His attempt to rule out all other asymptotic methods by an appeal to descriptive simplicity was unavailing. We found that important progress in that direction could be made by invoking normalizing conditions (consistency) and methodological simplicity (as a basis for invariance), but that they did not do the whole job. I am (...) proposing that, in the end, Reichenbach's own distinction between discovery and justification holds the key to the solution. (shrink)

The principle of uniformity of nature has sometimes been invoked for the purpose of justifying induction. This principle cannot be established "a priori", And in the absence of a justification of induction, It cannot be established "a posteriori". There is no justification for assuming it as a postulate of science. Use of such a principle is, However, Neither sufficient nor necessary for a justification of induction. In any plausible form, It is too weak for that purpose, And hence, It is (...) insufficient. Since a justification which does not rely upon this principle can be given, It is not necessary. (shrink)

The first part of the article deals with the theories of probability and induction put forward by Hans Reichenbach and Rudolf Carnap. It will be argued that, despite fundamental differences, Carnap's and Reichenbach's views on probability are closely linked with the problem of meaning generated by logical empiricism, and are characterized by the logico-semantical approach typical of this philosophical current. Moreover, their notions of probability are both meant to combine a logical and an empirical element. Of these, Carnap over the (...) years put more and more emphasis on the logical aspect, while for Reichenbach the empirical aspect has always been predominant. Seen in this light, Carnap's and Reichenbach's theories of probability can be taken to represent the Viennese and Berlinese mainstreams of the common logical empiricist approach. The second part of the article contrasts the position of these authors with that of the Bruno de Finetti, who is the main representative of the subjective interpretation of probability. Though the latter is sometimes associated with the position taken by Carnap in his late writings, it will be argued that the two are in many ways irreconcilable. (shrink)

La philosophie scientifique de nos jours prend son point de départ, non dans les propositions certaines des mathématiques, suivant l’exemple de Descartes, mais dans les énoncés probabilitaires des sciences empiriques, dont le modèle est la physique. Les mathématiques sont certaines, mais vides de contenu : ce sont de pures tautologies qui n’imposent aucune restriction au réel. Les éпоncés de la physique sont doués de contenu, mais ils ne sont pas certains parce qu’ils formulent des prédictions : ils ne sont pas (...) à considérer comme des propositions vraies, mais comme les mises d’un joueur, et, comme tels, ils relèvent d’une logique probabilitaire, dont la logique classique n’est qu’un cas très particulier. (shrink)

This volume honors and examines the founders of the philosophy of logical empiricism. Historical and interpretive essays clarify the scientific philosophies of Carnap, Reichenbach, Hempel, Kant, and others, while exploring the main topics of logical empiricist philosophy of science.