The problem of induction is a notorious philosophical problem concerning inductive inferences; more specifically, whether that form of reasoning is generally reliable or rationally justified. An inductive inference aims to draw a general conclusion from a series of particular observations. For example, if I observe one thousand swans, and every one of those swans is white, I can infer inductively that probably all swans are white, and on that basis predict that any future swans I observe will (probably) be white. Unlike deductive inferences, in which the conclusion follows necessarily from the premises, inductive inferences cannot deliver absolute certainty—for example, the possibility of observing a non-white swan in the future cannot be decisively ruled out—but all else being equal, the greater the number of past observations confirming a general law or pattern, the stronger the inductive conclusion becomes.
Inductive inferences have been widely used in scientific research to discover laws of nature. To take one example, Newton’s universal law of gravitation was inferred inductively from empirical observations of the attractive forces between two masses. We haven’t observed the forces between every pair of masses in the universe at every point in time, of course, so we don’t have direct and infallible knowledge of a universal law. Nevertheless, we have made enough observations to be confident that they are instances of a universal law, and we can make reliable predictions about future events by positing that the universal law holds.
At least, so we think. In the eighteenth century, the Scottish Enlightenment philosopher David Hume raised what is now called “the problem of induction.” Hume discerned that inductive inferences (like the one used to establish the universal law of gravitation) depend on a crucial presupposition, a principle known as the uniformity of nature. Our inductive inferences about the natural world take for granted that nature is basically uniform across both space and time, such that observations in one location (e.g., in our solar system) are reliable indicators of how nature behaves in all other locations, and such that past observations are reliable indicators of future occurrences. If the principle of the uniformity of nature does not hold, then inductive inferences should not be considered reliable. Hume asked a question that has proven to be remarkably tricky to answer: How do we rationally justify this presupposition? On what basis do we assume that nature is in fact uniform across time and space?
After all, the uniformity of nature isn’t a logical necessity. There’s nothing inherently contradictory about a cosmos that behaves in an irregular, unpredictable fashion. Chaos may be inconvenient, but it isn’t logically impossible! So we can’t appeal to logic alone to justify our presupposition of the uniformity of nature. A very common response is to suggest that the uniformity of nature, and thus the reliability of induction, has been confirmed empirically over time. Every time (or nearly every time) we’ve made predictions based on an inductive inference we’ve turned out to be correct, and therefore we’re justified in assuming that the same will be true in the future—in other words, that induction is generally reliable. The trouble with this answer, as Hume pointedly observed, is that it’s based on circular reasoning: it assumes the very thing in question, namely, that past observations are a reliable guide to the future. In other words, this answer tries to justify inductive inference with an inductive inference. That approach simply presupposes the reliability of induction rather than giving an independent justification for it. As Hume argued, it’s impossible in principle to justify induction on purely experiential grounds, because we will always have to extrapolate from what we have observed to what we haven’t observed.
Various other solutions to the problem of induction have been offered, but none has been widely accepted and the issue has proven to be an enduring challenge. At the heart of the problem is the fact that only an omniscient being could possess direct and infallible knowledge of the uniformity of nature across space and time. But this insight also suggests a distinctively Christian solution to the problem of induction. According to a Christian worldview, the God revealed in the Bible is a God of order (1 Cor. 14:33) who created the natural world and exercises sovereign control over it (Gen. 1:1; Isa. 42:5; 45:12; 48:13). God knows that nature is uniform precisely because he is the author of nature and continually sustains it (Jer. 31:35–36). Furthermore, God is the creator of human beings, including our cognitive faculties, which allow us to “think God’s thoughts after him.” As such, our inductive inferences are reliable precisely because God has designed them to be reliable. For those who hold to a Christian worldview, with its robust doctrines of creation, providence, and revelation, the problem of induction need be no problem at all.
James N. Anderson, Ph.D. is Carl W. McMurray Professor of Theology and Philosophy and Academic Dean at Reformed Theological Seminary. An ordained minister in the Associate Reformed Presbyterian Church, his scholarly interests primarily lie in philosophical theology, religious epistemology, Cornelius Van Til, and Christian apologetics.
Professor Anderson's Recommended Further Reading on the Topic:
· James N. Anderson, “Secular Responses to the Problem of Induction” (2000?).
· James N. Anderson, David Hume, Great Thinkers (P&R, 2019), Chapter 8.
· Leah Henderson, “The Problem of Induction,” Stanford Encyclopedia of Philosophy
· David Hume, An Enquiry concerning Human Understanding (1748), Section IV.