Define the principle of Induction after Russell. Explain how can we justify the
principle of Induction.
Answers
Explanation:
In his The Problems of Philosophy, Russell formulated the principle of induction in the following terms:
(I)a. When a thing of a certain sort A has been found to be
associated with a thing of another certain sort B and has never been found not to be associated with a thing of sort B, the greater is the probability that they will be associated in a fresh case in which one of them is known to be present. (I)b. Under the same circumstances, a sufficient number of cases of association will make the probability of a fresh association nearly a certainty and will make it approach certainty with
out limit
(II)a. The greater the number of cases in which a thing of the sort A has been found associated with a thing of the sort B. the more probable it is (if no cases of failure of association are known) that A is always associated with B. (II)b. Under the same circumstances, a sufficient number of cases of the association of A with B will make it nearly certain
that A is always associated with B and will make this general
law approach certainty without limit.
It is difficult to say precisely what Russell really meant by his principle (what kind of probability he had in mind, etc.). However, we simply want to remark here that there is a sense in which it can be envisaged as providing a rationale for induction.
In effect we shall show that (Ia) to (Ilb) are, with certain restrictions,
Answer:
principal of induction is a way of proving that p(n)is true for intreger in n>= this principle is very useful in problem solving