The Paradox of Induction
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The paradox of induction and the claim that probability is all we ought to seek
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There is another passage from Russell introducing another attempt to "solve" the paradox. "It must be conceded, to begin with, that the fact that two things have been found often together and never apart does not, by itself, suffice to prove demonstratively that they will be found together in the next case we examine. The most we can hope is that the oftener things are found together, the more probable it becomes that they will be found together another time, and that, if they have been found together often enough, the probability will amount almost to certainty. It can never quite reach certainty, because we know that in spite of frequent repetitions there sometimes is a failure at the last, as in the case of the chicken whose neck is wrung. Thus probability is all we ought to seek." However, the claim that "probability is all we ought to seek" also fails to solve the paradox of induction; it is only another example of the previous attempt to justify induction by induction, and is circular. What makes this not clear at first is the ambiguous use of the term "probable" in the argument. This term has two meanings: (a) When we say, "There is a 1 in 6 probability that a die throw will be a six", we are giving an example of a scientific general law. The only way to establish this is by throwing the die a very large number of times and finding the ratio of the number of times 6 comes up to the total number of throws. (b) When we say, "The existence of God is probable" we are not expressing a scientific general law. We are using the word "probably" to express a belief in the existence of God, but one that also expresses an element of doubt. When we say "probability is all we ought to seek" we have to ask, are we using "probable" in sense (a) or sense (b). If it is sense (b) then we are really saying that induction is something we believe in, but is not certain, so we have not even attempted to solve the paradox of induction. If it is sense (a), then we are trying to justify induction by appeal to another inductive generalisation, so such an approach is circular.
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Contents of
The Paradox of Induction
1 Prescriptive philosophy of science
2 The problem or paradox of induction
3 Hume and the formulation of the paradox of induction
4 Attempts to solve the paradox of induction
5 The paradox of induction and the claim that probability is all we ought to seek
6 Swinburn and confirmation theory
7 Falsificationism and the paradox of induction
8 Extrapolation and interpolation
9 Occam razor and the paradox of induction
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