Constructive Perspectives on Inductive Logic

Philosophica, 1968

The explicata for 'degree of confirmation (corroboration)' proposed by Carnap and Popper may be described as follows: a. Carnap's c-function is, as he defines himself, the relative logical probability of a hypothesis h, given an evidence e. c (h, e) = m (h, e) or, more generally c (h, e) = P (h, e) (2) The function C 1 (h, e) = E1 (h, e) [ 1 + P (h) P (h, e)] which may be defined from the last E-function, is ranging from 0 to + 00, and provides the value 1 + p2 (h) for neutral evidence (P (h) = P (h, e)).

2019

Science neither aims at having the monopoly over the truth about the world nor establishing a dogmatic knowledge. Natural light of experience is held by empiricists to be the reliable source of human knowledge. Inductive logic has been a leading tool of empirical experiments in justifying and confirming scientific theories with evidence. Science cannot reach where it has reached without inductive logic. Inductive logic has, therefore, played an important role in making science what it is today. Inductive logic helps science to justify its theories not form convictional opinions of scientists but from factual propositions. However, inductive logic has been problematic in the sense that its logic of justification led philosophers of science to demarcation, the distinction of episteme from doxa. At present, some philosophers of science and scientists attempt to justify why science carries out a reliable knowledge. Some have argued for structuralism and realism of scientific theories rather than believing in the course of miracles and others for their historicity. Both views are explanatories of how science works and progresses. This essay recalls the arguments for structures of scientific theories and their historicity. First, the essay analyses the controversy between Rudolf Carnap and Karl Popper on how the problem of inductive logic in confirming scientific theories can be solved. In so doing, the essay refers to empirical probabilities as well as the limits calculus. Second, the essay merges frequentist and Bayesian approaches to determine how scientific theories are to be confirmed or refuted. Third, the use of a new form of Bayesian Theorem will show how mathematical and logical structures respond to some of the important questions that arise from the historical and realistic views about scientific theories. The essay argues for epistemic objectivity behind inductive probability, the key issue of the controversy in question, and proves that the truth about the world is symmetric. Keywords: Science; Induction; Probability; Demarcation; Deduction; Frequentism; Bayesianism.

Theoretical Concepts and Hypothetico-Inductive Inference, 1973

Midwest Studies in Philosophy, 1993

The weak and strong atheoretical theses. The two main problems of classical empiricism: inductive justification and inductive method. The one main problem of neoclassical empiricism: weak inductive justification (degree of confirmation). (a) Carnap abandons the Jeffreys-Keynes postulate. Qualified (b) The weak atlieoretical thesis : confirmation theory without (c) The conflation of the weak and the strong atheoretical (d) The interconnection between the weak and strong atheo-(e) A Carnapian logic of discovery. quotients. (a) Are degrees of evidential support probabilities ? (b) Are 'degrees of rational belief' degrees of evidential support or are they rational betting quotients Z (c) Are rational betting quotients probabilities ?

In his last work on inductive logic, Carnap listed three outstanding problems for future research: inductive logic for a value continuum, inductive logic sensitive to "analogy by proximity" and inductive logic sensitive to "analogy by similarity". The first problem is completely solved by work of Ferguson and Blackwell and MacQueen. Bayesian statistics also throws light on Carnap's two problems of analogy.

Dialogue, 1967

Machine Intelligence and Pattern Recognition, 1990

Probability theory, epistemically interpreted, provides an excellent, indeed th e best available account of inductive reasoning. This is so because there are general and definite rules for the change of subjective probabilities through information or. experience; induction and belief change are one and same topic, after all. The most basic of these rules is that one simply has to conditionalize with respect to the in formation received. Thus, a fundamental reason for the epistemological success of probability theory is that there at all exists a well-behaved concept of conditional probability. Still, people have, and have reasons for, various concerns over probability the ory. One of these is my starting point: Intuitively, we have the notion of plain belief; we believe propositionsl to be true (or to be false or neither). Probability theory, however, offers no fonilal counterpart to this notion. Believing A is not the same as .