In his Enquiry Concerning Human Understanding (1748), David Hume famously argued that (enumerative) induction cannot be epistemically justified. Induction assumes that our future experiences will be similar to our past experiences, Hume points out, and that assumption cannot be justified in a non-circular way:
If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgment, these arguments must be probable only.... But that there is no argument of this kind, must appear, if our explication of that species of reasoning be admitted as solid and satisfactory. We have said, that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition, that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question. (Enquiry, 4.19)
As Hume observes, inductive inferences seem to presuppose that the future will be like the past in certain respects. As noted above, many inductive inferences rely on the principle of the uniformity of nature (PUN)—the assumption that all of nature exhibits the same general laws, regularities, or patterns. PUN is not a logically necessary truth (it’s not a tautology), nor can it be deductively inferred from observations. It seems the only way to justify PUN would be infer it by induction. However, an inductive argument for PUN would commit the fallacy of circular reasoning, since induction assumes the very principle in question! So, it appears that we cannot justify PUN, and thus (according to Hume) inductive inferences are also unjustified. Hume’s objection is known as the problem of induction.
To appreciate the force of Hume’s objection, imagine encountering someone who doesn’t reason inductively. Instead, he habitually draws the opposite conclusion: he infers the negation of what enumerative induction would conclude. For example, from the fact that the sun has risen every day in his experience, he concludes that the sun won’t rise tomorrow. Let’s call this imaginary person a “counterinductivist.” Now, imagine trying to convince the counterinductivist that he is reasoning incorrectly:
“Look, all of your counterinductive inferences have yielded incorrect conclusions in the past,” you point out. “You’ve been wrong every time!”
“Yes, that’s true,” the counterinductivist admits. “I’ve been consistently wrong in my counterinductive predictions until now. But this leads me to conclude—counterinductively—that counterinductive inferences will start yielding accurate predictions from now on!”
“That’s circular reasoning,” you protest. “You can’t use a counterinductive inference to justify your conclusion about counterinduction itself.”
“Ok,” the counterinductivist replies. “Then how do you justify your own inductive inferences? You can’t just say that induction has worked well so far, and therefore it will continue to work in the future. Your prediction that induction will continue to work is itself an inductive inference, so you’re reasoning in a circle too!”
How can we respond to this objection? Some philosophers regard Hume’s problem of induction as spurious: it doesn’t need a solution. For example, in his book Introduction to Logical Theory (1952), P. F. Strawson argues that we don’t have to justify deduction in order to be epistemically justified in making deductive inferences; so, analogously, we shouldn’t have to justify induction in order to make justified inductive inferences. We can determine whether deductive inferences are valid or invalid by applying the rules of formal logic, without having to prove that deduction itself is valid. Indeed, it makes no sense to ask whether deduction itself is valid, because the term ‘valid’ applies to inferences, not the method of inference. Likewise, Strawson says, we can ask whether a specific inductive inference is justified, but it makes no sense to ask whether induction itself is justified. Thus, according to Strawson, Hume’s skeptical challenge to induction can be dismissed. Our inability to justify induction is no more of a problem than our inability to justify deduction.
However, Strawson’s analogy between induction and deduction raises a deeper question. There are clearly-defined rules for determining when a deductive inference is valid or invalid: the rules of deductive logic. Are there analogous rules of inductive logic, which we could use to determine whether an inductive inference is justified? Unfortunately, the answer to that question is a definitive “no,” as we’ll see on the next page.