David Hume: The Problem of Induction


The Scottish empiricist philosopher David Hume (d. 1776), perhaps best known in his day as a historian and for his History of Great Britain (1754-1761), was much interested in the justification of knowledge (epistemology). He is particularly noted for introducing doubt into what people take for accepted knowledge of the world, namely knowledge derived through inductive reasoning. This has become the so-called “Problem of Induction” that will be noted in this article.

Hume argues for several views in his Treatise of Human Nature (1739). First, he doubted that human beings are born with innate ideas (a view held by rationalists) by dividing the contents of the mind into two phenomena: impressions (direct experiences) and ideas (faint copies of our impressions, such as thoughts and reflections).

Secondly, Hume introduces two types of statements: demonstrative and probable, and this is where we begin to find our problem of induction. A demonstrative statement is one whose truth or falsity is self-evident. This is the case for mathematical and logical statements; for example, the statement “2+2=4” is self-evidently true and cannot be denied. To deny that 2+2=4 is to fail to understand what is meant by “2”, “4”, “+”, “=“. Similarly, that “all bachelors are unmarried” or “all triangles are three-sided” are also self-evidently true and cannot be denied. These demonstrative statements are what are known as a-priori: that they do not rely on our experience of the world and are true or false prior to experience. In contrast, probable statements are not self-evident. The statement “the cat is on the table in the next room” is not a self-evident claim because it requires experience of the world. This makes it an a-posteriori statement because it is predicated on the need for experience: to verify this statement one would need to go to the next room to see if the cat is really on the table. There is nothing self-evidently true about probable statements. Hume then claims that all statements must be demonstrative or probable otherwise they are meaningless.

So far Hume has not presented us with any issues but we are close to seeing the problem of induction. The problem arises when Hume applies this logic to inductive reasoning itself. Inductive reasoning is simply inferring future events from past experiences; for example, because I have always observed the sun rising every morning, I infer that this will be the case tomorrow and for every day for the rest of this week. Inductive reasoning assumes that nature will act in an orderly, uniform way. But although we tend to take inductive reasoning to be a reliable form of knowledge, Hume’s logic undermines its justification. To Hume, inductive reasoning is based on neither a demonstrable nor probable statement. Because my claim that the sun will rise tomorrow is not a demonstrative statement it means that claiming the opposite (that the sun will not rise tomorrow) is not logically incoherent. Hume also argues that it is not a probable statement because we cannot experience the sun’s future. So if my claim that the sun will rise tomorrow is neither demonstrative nor probable, then is it meaningless?

Hume also applies this reasoning to causal statements such as “Event X causes event Y.” Such a statement seems like one that can be verified through experience (hence being a probable statement), but Hume renders doubt. For instance, the statement cannot be confirmed experientially because one cannot observe every X to see if it is followed by Y. In other words, from our limited experience of “X causes Y”, this is never rational grounds for believing that Y will always follow X. It is therefore not a probable statement. Further, there is no logical contradiction in denying that X causes Y, so it cannot be a demonstrative statement (true by necessity or as self-evident). Thus, the statement that “Event X causes event Y” is neither demonstrative nor probable, which motivates Hume to say that our beliefs based on inductive reasoning are never justified.

Another way to see the problem regarding inductive reasoning is to argue in its favour is arguing in a circle. The conclusion that “the future will be like the past” is based on the premise of past experience which means that we need to posit that we have inductive grounds for believing in induction. One could represent it like this:

Premise: In the past, the future has resembled the past
Conclusion: So in the future, the future will resemble the past.

The circularity of the argument in favour of induction becomes clear and few think that circular reasoning provides a justified grounds for belief. How does Human resolve this problem? He doesn’t, but what he does say is that engaging in inductive reasoning is just part of human nature. Hume says that “after the constant conjunction of two objects, heat and flame, for instance, weight and solidity, we are determined by custom alone to expect the one from the appearance of the other.” Inductive reasoning is thus a mental habit immune to justification by rational argument. This does not, however, suggest that inductive reasoning is useless; to the contrary, it is useful as a guide.


Buckingham, Will., Burnham, Douglas., Hill, Clive., King, Peter., Marenbon, John., and Weeks, Marcus. 2018. The Little Book of Philosophy. Penguin Random House. p. 91-94

Garvey, James., and Stangroom, Jeremy. 2012. The Story of Philosophy: A History of Western Thought. London: Hachette UK. p. 240-244



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