· Introduction: The Nature of Probability Theory· The Sample Space· Elements of Combinatorial Analysis· Fluctuations in Coin Tossing and Random Walks· Combination of Events· Conditional Probability· Stochastic Independence· The Binomial and Poisson Distributions· The Normal Approximation to the Binomial Distribution· Unlimited Sequences of Bernoulli Trials· Random Variables· Expectation· Laws of Large Numbers· Integral Valued Variables· Generating Functions· Compound Distributions· Branching Processes· Recurrent Events· Renewal Theory· Random Walk and Ruin Problems· Markov Chains· Algebraic Treatment of Finite Markov Chains· The Simplest Time-Dependent (...) Stochastic Processes. (shrink)

Classic analysis of the subject and the development of personal probability; one of the greatest controversies in modern statistcal thought.

APA PsycNET abstract: This is the first volume of a two-volume work on Probability and Induction. Because the writer holds that probability logic is identical with inductive logic, this work is devoted to philosophical problems concerning the nature of probability and inductive reasoning. The author rejects a statistical frequency basis for probability in favor of a logical relation between two statements or propositions. Probability "is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (...) (or premises)." Furthermore, all principles and theorems of inductive logic are analytic, and the entire system is to be constructed by means of symbolic logic and semantic methods. This means that the author confines himself to the formalistic procedures of word and symbol systems. The resulting sentence or language structures are presumed to separate off logic from all subjectivist or psychological elements. Despite the abstractionism, the claim is made that if an inductive probability system of logic can be constructed it will have its practical application in mathematical statistics, and in various sciences. 16-page bibliography. (PsycINFO Database Record (c) 2016 APA, all rights reserved). (shrink)

In his new foreword to this edition, Hilary Putnam forcefully rejects these nativist claims.

Then, in 1960, Carnap drew up a plan of articles for Studies in Inductive Logic and Probability — a surrogate for Volume II of the ...

Dieses Buch stellt eine neue, von CARNAP entwickelte Theorie der Induktion und Wahrscheinlichkeit dar, die durch die folgenden grund legenden Auffassungen charakterisiert ist. 1. Jedes induktive Schließen, im weiten Sinne des nichtdeduktiven oder nichtdemonstrativen Schlu߭ folgerns, ist ein Schließen auf Grund von Wahrscheinlichkeit. 2. Daher ist die induktive Logik als Theorie von den Prinzipien des induktiven Schließens dasselbe wie Wahrscheinlichkeitslogik. 3. Der Begriff der Wahrscheinlichkeit, der als Grundbegriff der induktiven Logik dienen soll, ist eine logische Relation zwischen zwei Aussagen oder (...) Sätzen, näm lich der Grad der Bestätigung einer Hypothese auf der Grundlage gegebe ner Prämissen. 4. Der sogenannte Häufigkeitsbegriff der Wahrschein lichkeit, wie er in statistischen Untersuchungen verwendet wird, ist zwar an und für sich ein wichtiger wissenschaftlicher Begriff, als Grundbegriff der induktiven Logik jedoch unbrauchbar. 5. Alle Prinzipien und Lehr sätze der induktiven Logik sind analytisch. 6. Daher hängt die Gültig keit des induktiven Schließens nicht von irgendwelchen synthetischen Voraussetzungen ab, wie etwa dem vielumstrittenen Prinzip der Gleich förmigkeit der Welt. Die erste Aufgabe dieses Buches ist die Erörterung der allgemeinen philosophischen Probleme betreffend die Natur der Wahrscheinlichkeit und des induktiven Schließens, die uns zu den eben erwähnten Auffassun gen führen wird. Das zweite Ziel ist der tatsächliche Aufbau eines Systems der induktiven Logik, einer Theorie, die auf den angeführten Prinzipien beruht. Ein besonderes Augenmerk wurde in diesem Buch darauf gelegt, die intuitive philosophische Grundlegung klar von dem technischen Aufbau des Systems der induktiven Logik zu trennen. (shrink)

One of Ian Hacking's earliest publications, this book showcases his early ideas on the central concepts and questions surrounding statistical reasoning. He explores the basic principles of statistical reasoning and tests them, both at a philosophical level and in terms of their practical consequences for statisticians. Presented in a fresh twenty-first-century series livery, and including a specially commissioned preface written by Jan-Willem Romeijn, illuminating its enduring importance and relevance to philosophical enquiry, Hacking's influential and original work has been revived for (...) a new generation of readers. (shrink)

Carnap's early system of inductive logic make degrees of confirmation depend on the languages in which they are expressed. They are sensitive to which predicates are, in the language, taken as primitive. Hence they fail to be ‘linguistically invariant’. His later systems, in which prior probabilities are assigned to elements of a model rather than sentences of a language, are sensitive to which properties in the model are called primitive. Critics have often protested against these features of his work. This (...) paper shows how to make his systems independent of any choice of primitive predicates or primitive properties.The solution is related to another criticism of inductive logic. It has been noticed that Carnap's systems are too all-embracing. Hisc(h, e) is defined for all sentencesh ande. Yet for manyh ande, the evidencee does not warrant any assessment of the probability ofh. We need an inductive logic in whichc(h, e) is defined only whene really does bear onh. This paper sketches the measure theory of such a logic, and, within this measure theory, provides ‘relativized’ versions of Carnap's systems which are linguistically invariant. (shrink)