Problem of Induction - Formulation of The Problem - David Hume

David Hume

Few philosophers are as associated with induction as David Hume. There is a difficulty, however, in discussing induction and Hume. For Hume himself rarely used the term and when he did, he used it to justify some point he was making. He gave no indication that he saw any problem with induction. Induction became associated with Hume only in the early twentieth century. John Maynard Keynes may have been the first to draw the connection. The connection is now standard, but it must be remembered (as in the following) that what is meant is a connection between Hume's philosophy and what is nowadays called "induction," not what went by that name in Hume's day.

David Hume described the problem in An Enquiry concerning Human Understanding, §4, based on his epistemological framework. Here, "reason" refers to deductive reasoning and "induction" refers to inductive reasoning.

First, Hume ponders the discovery of causal relations, which form the basis for what he refers to as "matters of fact." He argues that causal relations are found not by reason, but by induction. This is because for any cause, multiple effects are conceivable, and the actual effect cannot be determined by reasoning about the cause; instead, one must observe occurrences of the causal relation to discover that it holds. For example, when one thinks of "a billiard ball moving in a straight line toward another," one can conceive that the first ball bounces back with the second ball remaining at rest, the first ball stops and the second ball moves, or the first ball jumps over the second, etc. There is no reason to conclude any of these possibilities over the others. Only through previous observation can it be predicted, inductively, what will actually happen with the balls. In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise; for Hume, this is because the negation of the claim does not lead to a contradiction.

Next, Hume ponders the justification of induction. If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects." One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced or inferior people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If that the justification of induction cannot be deductive, then it would beg the question for induction to be based on an inductive assumption about a connection. Induction, itself, cannot explain the connection.

In this way, the problem of induction is not only concerned with the uncertainty of conclusions derived by induction, but doubts the very principle through which those uncertain conclusions are derived.