problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by the Scottish philosopher David Hume (Hume, David) (1711–76), who noted that all such inferences rely, directly or indirectly, on the rationally unfounded premise that the future will resemble the past. There are two main variants of the problem; the first appeals to the uniformity observed in nature, while the second relies on the notion of cause and effect, or “necessary connection.”

If a person were asked why he believes that the Sun will rise tomorrow, he might say something like the following: in the past, the Earth has turned on its axis every 24 hours (more or less), and there is a uniformity in nature that guarantees that such events always happen in the same way. But how does one know that nature is uniform in this sense? It might be answered that, in the past, nature has always exhibited this kind of uniformity, and so it will continue to do so in the future. But this inference is justified only if one assumes that the future must resemble the past. How is this assumption itself justified? One might say that, in the past, the future always turned out to resemble the past, and so, in the future, the future will again turn out to resemble the past. This inference, however, is circular—it succeeds only by tacitly assuming what it sets out to prove—namely, that the future will resemble the past. Therefore, the belief that the Sun will rise tomorrow is rationally unjustified.

If a person were asked why he believes that he will feel heat when he approaches a fire, he would say that fire causes heat or that heat is an effect of fire—there is a “necessary connection” between the two such that, whenever the former occurs, the latter must occur also. But what is this necessary connection? Is it observed when one sees the fire or feels the heat? If not, what evidence does anyone have that it exists? All one ever has observed, according to Hume, is the “constant conjunction” between instances of fire and instances of heat: in the past, the former always has been accompanied by the latter. Such observations do not show, however, that instances of fire will continue to be accompanied by instances of heat in the future; to say that they do would be to assume that the future must resemble the past, which cannot be rationally established. Therefore, the belief that one will feel heat upon approaching a fire is rationally unjustified.

It is important to note that Hume did not deny that he or anyone else formed beliefs on the basis of induction; he denied only that people have any reason to hold such beliefs (therefore, also, no one can know that any such belief is true). Philosophers have responded to the problem of induction in a variety of ways, though none has gained wide acceptance.