We Need to Talk About the Problem of Induction

Edy Fung, November 2023, Santa Cruz

In his philosophical work Treatise and An Enquiry Concerning Human Understanding, Hume raised the central issue of the problem of induction. It concerns our ability to understand and justify causality, and hence to make inductive inferences.

Hume laid the foundation for the argument by positing that our default in associating ideas through resemblance, contiguity, and cause and effect. Our understanding of causality stems from past experience:

“It is by EXPERIENCE only, that we can infer the existence of one object from that of another” (1.3.6).

First, he suggested the inherent tendency of human beings to map observed regularities to causalities. In other words, we infer our experience of the observed to the unobserved, from finite to a greater scale. This act of using the confined information from today to conclude expectations in the unknown future is the formation of an inductive argument.

An example would be that we know it is true that when we clap our hands, a sound would be made. Hume would argue that this cause and effect was known based on our previous observation that a sound would follow after clapping. To him, this would be inadequate in justifying the actual causal relation. Similarities in each occurrence of events, or outcomes repeated resembling one another, cannot equate to causality. He recognised demonstrative reasoning could not exist in our knowledge of causal relations.

if Reason determin’d us, it would proceed upon that principle that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same. (T.

The second point, an extension of the above point, refers to our inclination to make associations between things that follow one another based on past experience; not only do we assume there is a correlation, we assume the future behaves the same way as in the past. Laws of nature can thus lose grounds — he held that presumptions of the future resembling the past cannot be demonstrated a priori for we are in every position to imagine that nature is not uniform and the course of nature can change.

There is no problem with the way we understand cause and effect until we talk about scientificity. The problem of induction causes issues in science. As deductive and inductive arguments come hand in hand with scientific explanations, Hume’s problem of induction has continued to serve ongoing inquiries and discourses on scientific methodology and our epistemological conditions.

Karl Popper’s response to the Problem of Induction

Popper took Hume’s viewpoint on the problem of induction but postulated that rather than justifying causality in constituting the truthiness of induction, emphasis should be put on pursuing accuracy in empirical testing.

In The Problem of Induction (1953, 1974), he initially called Hume’s problem of induction badly formulated due to the “philosophical tradition”. He quoted P. F. Strawson to show that various philosophers have believed that it was a misconception to require a justification for inductive inference. “Inductive inference is inductively valid just as deductive inference is deductively valid.” Popper did not see the seek for justification as the best course of action since to justify theories given they cannot be justified by induction might lead to a dead end.

Secondly, apart from being a pragmatic problem of formulation, Popper posited that it was a psychological problem as Hume had reference to customs and habits. This led to grounds for Popper not having to take the task of solving it as an epistemological problem.

As a result, Popper himself denied the necessity of induction: “I hold that neither animals nor men use any procedure like induction, or any argument based on the repetition of instances. The belief that we use induction is simply a mistake. It is a kind of optical illusion.” Hence Popper did not believe in dwelling on the problem of induction but instead avoiding entering the problem via Hume’s viewpoint—“there is no need any longer to be disturbed by Hume's negative results, since there is no need any longer to ascribe to human knowledge a validity derived from repeated observations. Human knowledge possesses no such validity.”

Popper suggested that our acquisition of knowledge was a trial and error process to reach some elimination of error. The best attempt we should aim for was the unfolding of all the possible better or worse conjectures and to improve upon them. In other words, discovering maximum possibilities and accuracy in empirical testing should have the most prominent role. For Popper, it is important that empirical testing was not done to confirm or verify, which would not escape inductive reasoning. Instead he argued that all theories should be formulated as provisional and subject to falsification, hopefully avoid some pitfalls of the induction problem.

Evaluation of the Problem of Induction

If induction isn’t merely a psychological problem and indeed an epistemological problem, scientific deductions could lose grave authority. Rosenberg and McIntyre remind us that any deductive arguments require inductive arguments to be reliable. This applies to Popper’s falsification method which is deductive. Rosenberg and McIntyre has stated a full example:

“[C]onsider the deductive argument below:
  1. If a practice has been reliable in the past, it will be reliable in the future.
  2. In the past inductive arguments have been reliable.

  3. Inductive arguments will be reliable in the future.

This argument is deductively valid, but its first premise requires justification and the only satisfactory justification for the premise would be the reliability of induction, which is what the argument is supposed to establish. Any deductive argument for the reliability of induction will include at least one question-begging premise.” In the end, falsification method did not completely resolve the problem of induction. Furthermore, the viewpoint that “if a theory has been falsified in the past, it can never be true in the future” in itself does not bypass the presumption that the future resembles the past and thus in Hume’s words again, “that the course of nature continues always uniformly the same”. Expanding on Hume’s claim indicates that even accumulating past empirical data does not necessarily constitute any evidence of the relation between cause and effect, including the data that has proven a theory wrong.

Popper was not oblivious to this and stated that Hume’s account was unrelentingly rejecting the role of experience; whether one had more or fewer experiences was independent of justifying how certain or probable a belief was. So even though Popper did not voice disagreement with Hume, falsification as an alternative in itself accounts for empirical observation and testing and is based on experience being valid for justification of a belief.

Perhaps it is still beneficial for pure discussion, without needing to further ruminate the problem of induction. It can be a tool for helping us to recognise some of our minds’ habits of associating experience as absolute facts. Regardless of being possibly superseded one day, Hume’s account will always prompt our awareness of our ways of reasoning out of our limited and finite knowledge. 

Popper’s major contribution though, is to remedially provide a better framework and standards for scientific experiments and theory testing. Even Hume identified the problem of induction would not stop science from proceeding with hypotheses testing and experiments, establishing new laws from inductive inference that are claimed uniform everywhere, authoritative and bulletproofed.


[1] Hume, David. A treatise of human nature. Clarendon Press, 1896. Book 1, Part iii, section 6 (“Of the inference from the impression to the idea”)

[2] Hume, David. Enquiries concerning the human understanding: and concerning the principles of morals. Clarendon press, 1902. Section iv (“Skeptical doubts concerning the operations of the understanding”)

[3] Holyoak, Keith J., and Robert G. Morrison, eds. The Cambridge handbook of thinking and reasoning. Cambridge University Press, 2005, p.95

[4] Popper, Karl. Popper Selections (Edited by David W. Miller), New Jersey: Princeton University Press, 1985. In the book, Popper states “Hume showed that it is not possible to infer a theory from observation statements; but this does not affect the possibility of refuting a theory by observation statements. The full appreciation of this possibility makes the relation between theories and observations perfectly clear.” p. 101

[5] Popper, Karl. Popper Selections, 1985. p.102

[6] Ibid., p.103

[7] Popper, Karl. The Logic of Scientific Discovery (New York: Basic Books, 1959), p.8

[8] Popper, Karl. Popper Selections, p.104

[9] Ibid.

[10] Alex Rosenberg and Lee McIntyre, Philosophy of science: a contemporary introduction (Routledge, 2000), p.182.

[11] Popper, Karl. Popper Selections, p.107