The Problem of Induction

Author: Kenneth Blake Vernon
Category: Philosophy of Science, Epistemology, Logic and Reasoning
Word Count: 1000

1. Aulë’s Artifacts

Suppose you are an ethnographer newly arrived in Middle Earth, making land on the western shore, at the Gray Havens. You follow the East Road, traveling over the Misty Mountains and through the Mirkwood, eventually reaching Erebor, where you have planned your fieldwork. There you meet Durin’s Folk, a clan of dwarves living in the Lonely Mountain. Having dutifully acquired IRB1 approval, you carefully and meticulously note your observations of their behavior. You note, for example, that they are quick to laughter and quick to anger, that they are a hardy folk, stonehard even, but they are also prickly about their honor and terribly stubborn.2 You also note with much admiration that they have a certain felicity for blacksmithing.3 To your dismay, however, you find that the dwarves fall far short of ecological nobility, for they tend to depress local resources, notably trees, with nary an eye for sustainability.4 And everyone has a beard, both men and women.

While studying these curious people, you come to learn of another clan living in the Iron Hills to the east. You wonder. Are the dwarves of the Iron Hills talented blacksmiths, too? Do the surrounding trees also “feel the bite of their iron?” Are they as stonehard as those in your current ethnographic sample? Do their women grow beards? In asking such questions, you are trying to determine whether you can infer from sentences like:

  1. Dwarves of the Lonely Mountain, that you have observed, are talented blacksmiths.

Other sentences like:

  1. Dwarves of the Iron Hills, that you have not observed, are also talented blacksmiths.

Your problem is finding some way to ensure that you can safely infer certain facts about things not yet observed (like (2)) from facts about things you have observed (like (1)). This is the problem of induction.

Lonely Mountain

2. Necessary Connection

It is commonly supposed that the inference from (1) to (2) is a good inference only if there is, in Hume’s terms, a necessary – as opposed to accidental – connection between being a dwarf and being a talented blacksmith. What is a necessary connection? To answer that question, consider the following generalizations:

  1. Dwarves are talented blacksmiths.
  2. Everyone living in the Lonely Mountain is a dwarf.

Philosophers typically mark the difference between these two types of generalization by saying that while (3), if true, is necessarily true, (4), if true, is only accidentally true.

Some philosophers argue that what makes generalizations like (3) necessary is that they support counterfactuals (Goodman 1947; cf Bennett 1984; Hempel 1965; Jackson 1977; Mackie 1962; Strawson 1952). Without going into too much detail, the gist of the idea is this. The folks living in the Lonely Mountain are not dwarves because they live in the Lonely Mountain. It is possible, after all, that dwarvish settlement patterns never led them to Erebor. Another way of making this point is to say that a human ranger who found their way into the Lonely Mountain would not somehow magically become a dwarf because they entered the mountain. So, (4) is only accidentally true.

The same is not true of (3). Take someone who is not, in fact, a dwarf. What (3) tells us, assuming it is true, is that if she were a dwarf, she would be a talented blacksmith. So, (3), if true, is necessarily true. And it is necessarily true generalizations like (3) that are understood to express the necessary connection between things like being a dwarf and being a talented blacksmith. And it is that necessary connection that licenses the inference from observed to unobserved cases. 

To continue the example, you can infer that unobserved dwarves at the Iron Hills ought to be talented blacksmiths because they are dwarves. If it turns out they are not talented blacksmiths, we would not necessarily take that fact as evidence against (3), but rather as something that calls for its own explanation. To take an extreme example, we might say they ought to be good blacksmiths, and the reason they are not (assuming they are not) is that they all, or nearly all of them, share a birth defect that prevents them from, say, developing hands.

That, at least, is one route to solving the riddle of induction, but it is not without its critics. Perhaps the most famous critic is Quine (1980), who was profoundly suspicious of any talk of counterfactuals. As he saw it, their use entails Aristotelian essentialism, a thesis that, for various philosophical reasons, he rejected.5 As a consequence, he and his later followers were required to look elsewhere for a solution to the problem of induction.6

Although Hume’s argument was not garbed in the sophisticated predicate logic employed by Quine, their two views are largely the same. It is profoundly anachronistic to put it this way, but Hume would have denied that there was any necessary connection between things like being a dwarf and being a talented blacksmith. Instead, he argued that the persistent observation of dwarves who are also talented blacksmiths forms a habit or compulsion on the part of the observer to infer a felicity for blacksmithing upon any observation of a dwarf. It was inferential compulsion, a fact about human reasoning, that Hume believed philosophers confused for a fact about a relation between things in the world.

Before concluding, it should be noted that the problem as discussed here is only one form of a more general pattern known as enumerative induction or universal inference (Carnap 1963). Nevertheless, the points made here ought to generalize to other forms of induction. It should also be noted that the problem of induction ought to apply to any empirical pursuit. Had we discussed copper and its melting point, for example, or the planets and their orbits, or something near and dear to us like our selves and our all too human dispositions to be sometimes kind and other times cruel, the problem would have been the same. The question then remains: What allows us to infer from things observed to things unobserved?


1For those less familiar with the ethics of scientific research, IRB stands for Institutional Review Board. The IRB consists of a committee that decides on the ethical qualifications of any research involving human test subjects. Link to Wikipedia article:

2See, e.g., Chapter 2 of the Quenta Silmarillion in The Silmarillion (1977), where Tolkien describes dwarves, saying that they are “stonehard, stubborn, fast in friendship and in enmity, and they suffer toil and hunger and hurt of body more hardily than all other speaking peoples; and they live longer, far beyond the span of Men, yet not forever.”

3Chapter 10 of the Quenta Silmarillion, “The Naugrim [dwarves] smithied for him; for they were greatly skilled in such work… [and] in the tempering of steel alone of all crafts the Dwarves were never outmatched even by the Noldor, and in the making of mail of linked rings, which was first contrived by the smiths of Belegost, their work had no rival.”

4Chapter 2 of the Quenta Silmarillion, “They will delve in the earth, and the things that grow and live upon the earth they will not heed. Many a tree shall feel the bite of their iron without pity.”

5Then there are those, like David Lewis (1968), who happily embrace Aristotelian essentialism. For Lewis and his followers, presumably, there is no straightforward difficulty for solving the riddle of induction – assuming, at least, that they have the right analysis of counterfactuals.

6In addition, it is widely agreed that there are good Darwinian reasons for rejecting Aristotelian essentialism (Mayr 1959; Hull 1965; Sober 1980). But if Quine is right, then biologists, by implication, are forced to deny counterfactuals as well, and also to look for a solution to the problem of induction elsewhere. That, or find an analysis of counterfactuals that does not entail essentialism.


Bennett, Jonathan (1984). “Counterfactuals and Temporal Direction.” Philosophical Review, Vol. 43, pp. 57-91.

Carnap, Rudolf (1962). Logical Foundations of Probability, 2nd ed. Chicago, IL: The University of Chicago Press.

Goodman, Nelson (1947). “The Problem of Counterfactual Conditionals.” The Journal of Philosophy, Vol. 44, No. 5, pp. 113-128.

 Hempel, Carl (1965). Aspects of Scientific Explanation and Other Essays in the Philosophy of Science. New York, NY: The Free Press.

 Hull, D. (1965), “The Effect of Essentialism on Taxonomy: 2000 Years of Stasis,” British Journal for the Philosophy of Science Vol 15, p. 314-16.

 Jackson, Frank (1977). “A Causal Theory of Counterfactuals.” Australasian Journal of Philosophy, Vol. 55, pp. 3-21.

Lewis, David (1968). “Counterpart Theory and Quantified Modal Logic.” The Journal of Philosophy, Vol. 65(5), pp. 113-126.

Mackie, J.L. (1962), “Counterfactuals and Causal Laws”, in R.S. Butler (ed.), Analytic Philosophy. New York: Barnes and Noble, pp. 66-80.

 Mayr, E. (1959), “Typological versus Population Thinking,” in Evolution and Anthropology: A Centennial Appraisal: p. 409-12.

Sober, Eliot (1980). “Evolution, Population Thinking, and Essentialism.” Philosophy of Science, Vol. 47(3), pp. 350-383.

Strawson, P.F. (1952), Introduction to Logical Theory. London: Methuen.

For Further Reading

Henderson, Leah, “The Problem of Induction”, The Stanford Encyclopedia of Philosophy (Summer 2018 Edition), Edward N. Zalta (ed.), URL = <>. 

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About the Author

Kenneth is a graduate student studying philosophy at the University of Utah. He has an MA from Northern Illinois University and a BA from the University of Central Arkansas. He specializes in the philosophy of archaeology and is competent in philosophy of biology and anthropology. His favorite thing to do on the weekend is to go hiking in the Wasatch range. He likes to think of hiking as philosophy by other means, and he feels in good company in this regard, like William James wondering off into the Adirondacks. He is especially fond of that old aphorism by Nietzsche, “Only thoughts reached by walking have value.”

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