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.

Contemporary philosophers interested in value theory appear to be largely concerned with questions of the following sort:What is value?What is the meaning of the word ‘good’?Does the attribution of value to an object have a cognitive, or merely an emotive, significance?The first question is metaphysical; to ask it is analogous to asking in physics:What is matter?What is electricity?The others are generally treated as semantical questions; to ask them is analogous to asking in statistics:What is the meaning of the word ‘probable’?Does (...) an attribution of probability express an objective fact, or merely a subjective attitude? (shrink)

The central concept of Carnap's probabilistic theory of induction is a triadic relation, c, the probability or degree of confirmation of the hypothesis, h, on evidence, e. The relation is a purely logical one. The value of c can be computed from a knowledge of h, of e, of the structure of the language, and of the inductive rule to be employed.

These essays are intended to illustrate various ways in which ideas about language may be used to clarify philosophic problems. They contain careful interpretations and criticisms of theories of language.

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

1. Introduction. It is generally admitted that a large part of man's knowledge is based on inductive arguments. Hence any philosophical theory concerning the nature of inductive arguments constitutes an epistemological theory. Any such philosophical theory of induction must, if it is to be satisfactory, take adequate account of Hume's criticism of inductive arguments. One way of treating his criticism is to say that the validity of inductive arguments is in an important sense relative to some broad factual assumptions about (...) the general nature of the universe and that these general factual assumptions are presupposed in a certain way by the users of inductive arguments. Let us call any theory of this general type a postulate theory of induction. (shrink)

But even with respect to inductive arguments there are a number of different philosophical problems. One is to make explicit the fundamental or most general pattern or patterns of inductive argument. Once these patterns are known a second and third problem arise. The second is to justify man's use of and faith in inductive arguments. And the third is to formulate some general propositions about nature which could reasonably be accepted by users of inductive arguments and which when added to (...) the premises of these arguments make them explicitly deductive. (shrink)