A basic system of inductive logic; An axiomatic foundation for the logic of inductive generalization; A survey of inductive systems; On the condition of partial exchangeability; Representation theorems of the de finetti type; De finetti's generalizations of excahngeability; The structure of probabilities defined on first-order languages; A subjectivit's guide to objective chance.

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)

A major difficulty for currently existing theories of inductive inference involves the question of what to do when novel, unknown, or previously unsuspected phenomena occur. In this paper one particular instance of this difficulty is considered, the so-called sampling of species problem.The classical probabilistic theories of inductive inference due to Laplace, Johnson, de Finetti, and Carnap adopt a model of simple enumerative induction in which there are a prespecified number of types or species which may be observed. But, realistically, this (...) is often not the case. In 1838 the English mathematician Augustus De Morgan proposed a modification of the Laplacian model to accommodate situations where the possible types or species to be observed are not assumed to be known in advance; but he did not advance a justification for his solution. (shrink)

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive (...) logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis. (shrink)