Probabilistic logic is a modern type of inductive logic

2022-07-17 0 By

Probabilistic logic (Chinese pinyin: Gailv Luoji;English: Probabilistic Logic), a modern type of inductive Logic.It is characterized by the use of modern logic and mathematical tools, mainly the use of mathematical logic and probability theory of inductive logic, inductive methods formalized, quantitative research.Aristotle once put forward the idea of frequency explanation similar to probability when discussing the problem of induction.G.W. leibniz used three values (0, 1, 1/2) to describe the characteristics of probability approximately, and proposed to take probability as a branch of logic.J.S. Mill, in The System of Logic, and G. Boole, in On the Laws of Thought, both discussed the relationship between induction and probability at considerable length.It can be seen that inductive studies are metrically probability dependent.In mathematics, probability theory from the 17th century, through B. Basgal, P. Fermat, J.By the 19th century, the work of Bernoulli, P. S. Laplace and others had become complete and widely used in science and technology.At the end of the 19th century and the beginning of the 20th century, some axiom systems of probability calculus gradually appeared, among which the Soviet UNION A.N.The axiomatic system proposed by Kolmogorov in 1933 was more influential.In logic, due to the introduction of formal and mathematical methods, deductive logic has been developed more perfect in the early 20th century.The principia mathematica, written by B. Russell and A.N. Whitehead in 1910, can be regarded as a result of a certain degree of perfection in mathematical logic.In the history of philosophy, D. Hume denounced induction.Classical inductive doctrine represented by F. Bacon and Mill faces severe challenges.Positivism and logical empiricism In order to cope with the “induction problem” put forward by Hume and give corresponding explanations to scientific theories, they changed the problem of proof of inductive propositions into the problem of “confirmation” and took probability value as the measurement of confirmation. Thus, probabilistic logic emerged in the 1920s.Johnson was the first to study the problem of probabilistic logic, but it is generally accepted that J.M. Keynes proposed the first axiomatic system of probabilistic logic.J. Nichold, F. Weissman, H. Jeffries, G.H. Von Wright, and H.Reichenbach and others have done significant work to establish probabilistic logic.One of the most influential was the work of R. Carnap in the 1950s.Probabilistic logic system has encountered many difficulties in theory and practice.In essence, probabilistic logic is the deduction of inductive logic, but there are some problems in methodology, and several inductive paradoxes have been put forward in logic.Since the 1950s, probabilistic logic has made progress in many aspects under the influence of modern mathematics and mathematical logic tools. It is increasingly combined with modern science and technology and facing new breakthroughs.