Introduction: The problem of induction I intend to solve in this essay is stated by Bertrand Russell in the following words (and I quote a few of many similar passages he penned):
"The great scandals in the philosophy of science ever since the time of Hume have been causality and induction. We all believe in both, but Hume made it appear that that our belief is a blind faith for which no rational ground can be assigned." (Bertrand Russell, Let the people think p. 50)
(Hume's) "almost unexampled combination of acuteness with intellectual honesty led him to certain devastating conclusions: that induction is a habit without logical justification, and that the belief in causation is little better than a superstition." (idem p.62-3)
"This state of affairs is profoundly unsatisfactory, and becomes more so as science becomes more entangled with philosophy. We must hope that an answer will be found; but I am quite unable to believe it has been found." (idem p.50)
These words were written between 1935 and 1941, and although much has been written on the problem of induction since then (Note 1), it remains unsolved, and in fact has received an even sharper form than before, since Nelson Goodman published his sharpened form of the problem in the 1940-ies, which we shall explain and consider in the body of the text.
There is also a certain unclarity about what the problem of induction is, and it is useful to distinguish three different aspects of the problem of induction, namely:
a. The problem of how we learn from experience
The problem of induction is best construed as arising from the question "How do we learn from experience?", since this is clearly a very fundamental problem.
Now we learn from experience by setting up explanations for the facts in our experience we want to explain, and do this as follows:
Something like this - called abduction, discussed in a little more detail at the end of this essay - does happen when we attempt to explain things in our experience, and the problems Hume found with it (both causality and induction) stem from the fact that by introducing assumptions we go beyond the given evidence our experience affords: generally what we assume as cause is not fully or not at all given in experience, and neither are many of the predicted effects we deduce from these assumptions.