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Russell is undoubtedly one of the most prominent and influential philosophers of England because he had opinions about several different domains as well as authoring many essays and books.

There is no doubt that his opinions played a major role in remodeling the thinking of Vienna’s Circle. His efforts for reduction of mathematics to logic and his relative success at that time provided an opportunity for more Empiricism among the contemporary scholars who had formed the Vienna’ Circle and the logical Empiricism that ended in logical positivism developed undoubtedly under the influence of Russell’s thoughts and opinions. 

In his time as a philosopher, Russell had some ups and downs but a strong string linked all his activities together and that was his effort to explain “Knowledge to Universe” through experience.

Even when he tried to reduce mathematics to logic he intended to show that science can be based only on experience by excluding mathematics from the science domain. That’s why the traces of explanation of science in which induction is defined as its tool, can be found in most of his works. Although in this line of explanation he had different and sometimes contradictory opinions, he ultimately paves a perfective empiricism path. The evolution of Russell’s philosophical thoughts is obvious in his works. Induction is a concept that is indicated in almost all of his theoretical philosophy. He expressed the Problem of Induction in most books and essays.

The observations themselves do not establish the validity of inductive reasoning, except inductively. Russell illustrated this point in The Problems of Philosophy:

Domestic animals expect food when they see the person who usually feeds them. We know that all these rather crude expectations of uniformity are liable to be misleading. The man who has fed the chicken every day throughout its life, at last, wrings its neck instead, showing that more refined views as to the uniformity of nature would have been useful to the chicken.

In several publications, it is presented as a story about a turkey, fed every morning without fail, who following the laws of induction concludes this will continue, but then his throat is cut on Thanksgiving Day.

Russell’s notion of Induction is divided into two distinctive periods. In the first period, following his precedents, Russell presumed induction as obvious, innate, needless to prove and required for empiricism science. Here, he believed that what justified the occurrence of a phenomenon in the future was its occurrence in the past but all one could gather from an experience in the past was the increased probability of its occurrence in the future henceforth one should not expect anything else other than probability.

In the second period, influenced by Keynse's research, Russell tried to provide a logical explanation of probability to base Induction Logic on it and /ustify science and experiment. He figured out that to explain Induction, it is required to assume some innate principals which he called ultra-logical principals and introduced five postulates that could be achieved by analyzing the experiment. The postulate of quasi – permanence, The postulate of the separable causal line The postulate of spatio – temporal continuity, The structural postulate, The postulate of analogy are these principles. Russell thought that these postulates are alternatives to vague concepts like ”Causality” and “Uniformity of Nature” that most of the philosophers use them in justification of scientific knowledge. However, he confesses that he’s not sure of them but can’t avoid them for empirical justification. He describes his effort for Scientific justification as such:

“Ever since I was engaged in Principia Mathematical I have had a certain method of which at first I was scarcely conscious, but which has gradually become more explicit in my thinking. The method consists in an attempt to build a bridge between the world of sense and the world of science. I accept both as, in broad outline, not to be questioned. As in making a tunnel through an Alpine mountain, work must proceed from both ends in the hope that at last the labor will be crowned by a meeting in the middle. “

Russell is Hume’s follower. Hume’s notion is, we have habitual beliefs that are necessary for life. The belief of continuous and independent being and the belief that what begins to exist needs a cause are the beliefs that make life possible. As science progress, Russell expressed these beliefs with another language that was near to science language.

Russell and Hume believe that the Problem of Induction is solved with animal nature and reason are not useful. As Hume, Russell couldn’t avoid the challenge of skepticism. He couldn’t ensure the credibility of scientific statements because he couldn’t prove the credibility of extra logical postulates.

References

-      Dacosta Newton C. A. & French Steven (1991) "On Russell’s Principle on Induction", Syntheses 86, 285 – 295. 

-      Hay, W. H. (1950) "Bertrand Russell on the Justification of Inductions", Philosophy of Science, Vol. 17, No. 3, 266-277. 

-      Keynes, J. M. (1963) A Treatise on Probability, Macmillian, 1963.

-      Russell, Bertrand (1927) An Outline of Philosophy, London: George & Unwin Allen. 

-      Russell, Bertrand (1948) Human Knowledge: It’s Scope And Limits, London: George Allen & Unwin LID, Humanities press Inc. 

-      Sainsbury R.M (1989) "On Induction and Russell’s Postulates, Reading Russell: Essays on Bertrand Russell’s Metaphysics and Epistemology", Minnesota studies in the philosophy of science, Vol. 12, University of Minnesota press, 200 – 219.