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Hume’s Problem of Induction

Patrick Brissey exposes a major unprovable assumption at the core of science.

Will the sun rise tomorrow? The answer seems simple: an emphatic “Yes!” But how do you know? We can imagine the following commonsense response: “Well, every morning, the sun rises; at least from my perspective. Wait until tomorrow; you’ll see!” The reasoning is that, based on past observations, we know that the sun will more than likely rise in the morning. Notice that this conclusion is not certain: the argument is not a purely logical deduction. There are, after all unlikely science fiction scenarios where the sun is suddenly destroyed. These scenarios show that the claim the sun will rise in the morning is possibly false. Despite this, there seems to be a very good probability that it will rise.

In his Enquiry Concerning Human Understanding (1748), David Hume (1711-1776) asserts that even this argument is not good. Hume thinks the skeptical answer – ‘We Don’t Know!’ – is the logical response to this sort of inductive (past-experience-based) argument. For him, we ought to withhold belief on inductive assertions about the future, even over such likely questions as whether the sun will rise in the morning. But perhaps this does not seem right to you: We all know that the sun will rise in the morning, don’t we?

Let’s see how Hume gets to his conclusion.

The ‘Future Will Resemble the Past’ Principle

Imagine someone playing a game of pool. She hits the cue ball, and it collides with the eight ball. What should happen next?

Based on past experience, one would think that the eight ball will travel in a straight line away from the cue ball until impeded by another object. But this is only one hypothesis. Consider the following alternative hypotheses:

Hypothesis 1: The eight ball follows a rectangular path.

Hypothesis 2: The eight ball follows a circular path.

Hypothesis 3: The eight ball combusts.

Hypothesis 4: The eight ball becomes extremely heavy and sinks through the table.

Hypothesis 5: The eight ball hovers over the table.


The original straight-line hypothesis is consistent with our experience; but Hume argues that judgments like this simply assume that the future will resemble the past. But how do we know that this principle that the future will resemble the past is true?

In fact, a key issue concerning the plausibility of scientific arguments, which are inductive arguments (since they generate scientific laws from a limited number of observations) is whether we can prove the Future Will Resemble The Past Principle. If we can demonstrate that this principle is true, we can be confident in our scientific and other probabilistic inferences. However, if we can’t prove it, then, like Hume, we should stop thinking that we have good logical reasons to believe that the sun will rise in the morning.

Can We Prove the Principle?

Hume devises a strategy to prove his skeptical conclusion. He asks us to imagine that we could prove the principle that the future will resemble the past. How would we construct such a proof?

Well, as Hume tells us, a proof needs a plausible argument, and there are two kinds of plausible arguments: deductive arguments (which are certain) and inductive ones (which are only probable and depend on the amount of evidence gathered). So, we would need to prove with either certainty or probability that the future will resemble the past. Then we can be confident (at least to the extent of the probability) that the sun will rise tomorrow, and a whole host of other predictions about the future based on past experiences.

So first, can we prove the principle with an argument that is certain (deductive)?

Hume provides a plausible argument that we cannot. First, he says all knowledge comes to us through our senses. We shall only count as evidence that which someone can see, smell, touch, taste, or hear. Second, he says The Future Will Resemble The Past Principle is a universal principle, meaning that it asserts that the future will always resemble the past. Third, it is impossible to empirically prove any universal, as to do so would require observing all possible instances of its application. So we would need to have the sum total of all possible experiences as evidence to prove that the future will always resemble the past. For instance, we would need to know about all future sunrises, which is impossible. To have this kind of knowledge would necessitate that we live forever; and even then, we would not have experienced the mornings before we were born. Thus Hume concludes that we cannot have definitive proof (that is, certainty) of the principle.

Can we prove the principle with an argument that is probable (inductive), then? Again Hume provides a compelling argument that we cannot.

The proposal is now that we can have an inductive argument for our The Future Will Resemble The Past Principle. However, this is a logical fallacy, since in order to operate, all inductive arguments must presume the future resembles the past. In inductive arguments, the arguer makes observations, and infers general rules or conclusions using the idea that future observations will be like the past observations. So, if we attempt to justify the principle that the future will resemble the past by an inductive argument – by for instance saying it has done so on previous occasions, so it will do so again – then we would be effectively proving the principle by assuming it, what is committing the fallacy of circular reasoning. We can indeed summarise the problem by saying that in order to prove induction through an inductive argument, we need to first assume the validity of inductive argument. In this kind of argument, nothing is proven, for the conclusion is presumed in the argument. Hume concludes therefore that we cannot justify the principle of induction with an inductive argument.

So the conclusion is that the essential inductive (and therefore scientific) principle that the future will resemble the past cannot be proven. No certain (deductive) or probable (inductive) arguments can justify the Future Will Resemble The Past Principle. So we cannot reasonably hold that the sun will rise in the morning even with probability, because this assumes the Future Will Resemble The Past Principle, which Hume has shown cannot be proven.

Sylvie induction
© Sylvie Reed 2024

What’s the Big Deal?

What’s the problem? Why should we care about Hume’s conclusion?

Hume explains that if we cannot prove the Future Will Resemble The Past Principle, then we have no good reason to believe that the future will resemble the past, meaning, logically speaking, that the future is unknown. Given this, we don’t know (either with certainty or with probability) that when we eat bread it will nourish us; whether the sun will rise tomorrow; or that we should trust the conclusions of the sciences. The big deal, then, is that we cannot demonstrate the reasonableness of much of what we believe, at least concerning future events, and this includes scientific predictions about the world or about future experimental results.

However, if we ought not to make claims of knowledge about future events, how can we live? Life necessitates that we make practical choices; but if Hume’s highly abstract conclusion is true, and we only want to do whatever we can demonstrate is reasonable, then we cannot live. Nearly everyone would agree that practical action is more valuable than Hume’s skeptical position. Thus, they propose that it’s Hume who has a problem here.

Hume was well aware of this kind of objection. His response is that we ought to live not according to pure reason (which to Hume can prove virtually nothing about the world), but according to our feelings. For Hume, then, we do not know that the sun will rise tomorrow, but we have a strong inclination to believe that it will, and we ought to act on that. Our feelings, for Hume, are sufficient for practical action. Hume’s further rejoinder is that his skeptical view provides moral and practical guidance about the limits of knowledge.

So, do you know whether the sun will rise tomorrow? How would you respond to Hume’s argument?

© Dr Patrick Brissey 2024

Patrick Brissey is an Instructor in the Department of Philosophy at the University of South Carolina.

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