Logical foundations of probability

The purpose of this work. This book presents a new approach to the old problem of induction and probability. The theory here developed is characterized by the following basic conceptions: (1) all inductive reasoning, in the wide sense of nondeductive or nondemonstrative reasoning, is reasoning in terms of probability; (2) hence inductive logic, the theory of the principles of inductive reasoning, is the same as probability logic; (3) the concept of probability on which inductive logic is to be based is a logical relation between two statements or propositions; it is the degree of confirmation of a hypothesis (or conclusion) on the basis of some given evidence (or premises); (4) the so-called frequency concept of probability, as used in statistical investigations, is an important scientific concept in its own right, but it is not suitable as the basic concept of inductive logic; (5) all principles and theorems of inductive logic are analytic; (6) hence the validity of inductive reasoning is not dependent upon any synthetic presuppositions like the much debated principle of the uniformity of the world. One of the tasks of this book is the discussion of the general philosophical problems concerning the nature of probability and inductive reasoning, which will lead to the conceptions just mentioned. However, the major aim of the book extends beyond this. It is the actual construction of a system of inductive logic, a theory based on the conceptions indicated but supplying proofs for many theorems concerning such concepts as the quantitative concept of degree of confirmation, relevance and irrelevance, the (comparative) concept of stronger confirmation, and a general method of estimation. This system will be constructed with the help of the methods of symbolic logic and semantics. (However, previous knowledge of these fields is not necessarily required; all symbols and technicalkterms used win be explained in this book.) In this way it will for the first timee be possible to construct a system of inductive logic that can take its rightful place beside the modern, exact systems of deductive logic. The systepn to be constructed here is not yet applicable to the entire language of science with its quantitative magnitudes like mass, temperature, etc., but fnly to a language system that is much simpler (corresponding to what if known technically as lower functional logic including relations and identity ) though more comprehensive than the language to which deductive logic was restricted for more than two thousand years, .from Aristotle to Boole.