What is the problem of induction? Discuss two proposed solutions to this problem, and explain why (in your view) they are adequate solutions or defective ones.

The problem of induction is the question: Is induction a trustworthy means of obtaining knowledge? The majority of scientific reasoning necessarily leans heavily on induction—it is, after all, impossible to observe every star in the universe, or every duck on Earth, or the psychological patterns of all humans, for example. Thus, any scientific reasoning which purports to rise to the level of a universal explanation or law must rely on induction to arrive at its conclusion: “We have observed things to obey rules X, Y, and Z in all known instances. Given the regularity of the universe, it follows that things obey rules X, Y, and Z everywhere.” The question is whether the leap between the premises and the conclusion is warranted: is it reasonable to suppose that things scientists have not observed (whether because they are out of observational range, or because they are in the future) behave the same way as those they have observed?

Mark Lange helpfully summarizes the problem in the form of a simple argument: since all arguments are either deductive or inductive, the middle link in the argument for the reliability of induction must be either deductive or inductive. But it cannot be an inductive argument; that would simply be a circular argument: “If inductive reasoning holds, it is valid to use inductive reasoning, and inductive reasoning has always worked in the past, so we induce that it will continue to work in the future, ergo it is valid to use inductive reasoning.”

Unfortunately, the argument may also not be deductive. There is an infinite number of logically possible explanations for the apparent success of induction to date. For example, it is logically possible that all objects believed to be green—and which inductive reasoning would therefore suggest will be green tomorrow as well—are in fact the mysterious and previous unobserved color “grue”: a color which appears green until an unspecified date, after which it is blue. This is just as logically consistent with all observations as the idea that induction holds. Thus, no deductive argument can demonstrate the validity of induction, for there is no deductive manner of choosing between such possibilities.

One proposed solutions is a pragmatic argument. If the universe behaves uniformly, then induction will work; if the universe does not behave uniformly, then no method will work. Therefore, scientists are justified in acting as though induction works. Unfortunately, this argument at best establishes a matter of reasonable policy for scientists, without providing warrant for belief. That is, however reasonable and even necessary it may be for scientists to proceed as though induction holds and is valid, the argument provides no evidence that induction does in fact hold.¹

Another solution is the argument from Christian theism: given God’s creation covenant to maintain order (Genesis 9), the goodness and providence of God (derived from statements to that effect throughout Scripture), and the claim to efficacy of the Proverbs, it is theologically necessary that the universe continue to work as it has in the past. In its favor, this suggestion has the form of an argument, and is not directly reliant on the evidence of past uniformity as a basis for future uniformity. However, this sort of reasoning from Scripture is itself inductive. It takes a specific interpretation of the texts under consideration, and a belief that things are at a certain point in cosmological/theological history (i.e. the eschaton has not yet arrived) and extrapolates to the notion that God will continue upholding the previous pattern of laws of nature. Moreover, even if the argument were to hold, it would not be a scientific but a philosophical-theological argument. (This is, perhaps, unsurprising given that though the problem of induction is especially applicable to the practice of science, it is a far more general problem.)