This article aims to provide an overview of the problem of induction as it relates to the philosophy of science. After finding the problem of induction’s place in the history of philosophy, the difference between induction, projection, and explanatory inferences will be covered. The "Ravens problem" will be explained, along with Nelson Goodman’s "New Riddle of Induction," and the effect it has had on subsequent developments in the philosophy of science.

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Statue of David Hume, 1995, photograph by Sheila1988, 2019, via Wikimedia Commons.

The problem of induction is arguably one of the most significant and long-lasting philosophical problems for philosophers of science to deal with. It is a philosophical problem first posed by David Hume, a Scottish philosopher of the mid-to-late 18th century. Hume put the problem in terms of patterns in experience, which made sense given his empiricist leanings (he thought that all we knew was derived from experience).

We can paraphrase his framing of the problem of induction with the following question: what reason do we have for thinking that patterns observed in our past experience will hold into the future? Simply put, when we see something happen over and over again (the sun rising, for instance), what is it about our seeing it over and over that gives us a reason to think that these things will continue to happen?

Hume’s view was that there is no rational basis for the thought that the future will resemble the past, even though it is extremely psychologically natural to make that claim. In the context of the philosophy of science, the problem of induction is often framed in terms of the confirmation of theories: what connection is there between a certain observation and a theory which makes that observation evidence for the theory? (Here, as elsewhere, this article is indebted to the framing and organization of these questions in Peter Godfrey-Smith’s Theory and Reality).

Science, Generalization, Observation

Portrait of Charles Sanders Peirce, ca.1870, via NOAA Photo Library.

On one conception of science, science is simply the generalization of observations. This is what the logical positivists, among others, thought. However, as is a recurring theme in the philosophy of science, large swathes of actual scientific practices evade that conception.

For example, the theory of evolution is not based on generalizing from individual cases of evolution—rather, it involves the interpretation of our observations in order to locate instances of a certain thing, before any relationship between our observations and general theories can be established.

It is worth saying something about the meaning of the term "induction" at this stage. Sometimes, especially in the philosophy of science, induction is used in a more limited way than the way we have been using it up until now (which is as a kind of catchall for "knowing things based on experience/observation").

Man of Science, 1839, via National Gallery of Art.

Induction can be used to mean simply inferences from particular to general observations. A related phenomenon, known as projection, refers to inferring to the next case of a certain thing. Inference to a hypothesis or structure which would explain an observation goes by various names—C.S Peirce called it abduction, Gilbert Harman gave it the name most often favored by contemporary philosophers of science, which is "inference to the best explanation."

The Sense Of Sight Artwork By Philippe Mercier, ca. 1744-1747, via Yale Center for British Art.

These various ways of understanding the relationship between observations and theories are of practical significance partly because whichever one we choose to take as more fundamental, more basic, will make a difference for how we conceptualize science as a whole.

If we take induction to be basic, then we might claim that explanatory inferences can be broken down into their component, inductive parts—that is, theories can be reduced down to the observations of which they consist. If, by contrast, we take explanatory inferences to be more basic than anything else (as the aforementioned Gilbert Harman did), then we can go the other way and claim that some instance of induction is justified only if it can be established within the relevant explanatory framework. Often, in the course of actual scientific practice, a decision needs to be made based on whether induction or explanatory inferences are taken to be more basic.

Photograph of a common raven by Alexas_Fotos, 2018, via Pixabay.

We will now turn to look at induction in the sciences through the prism of one of the most famous thought experiments in the philosophy of science—"the ravens problem." This problem is concerned with how it is that repeated observations of black ravens confirm the generalization that all ravens are black.

As should be obvious, this is not a new problem, but rather a way of reframing the initial issue. Why? Well, perhaps it is easier to deal with this specific case than a general formulation of it, and in any case, philosophers have decided it is so, so here we are.

One response we could give to the ravens problem is to limit our concern to the epistemic status of any particular (black) raven we happen across. That is, we might say that each such raven is one less raven which could disprove our hypothesis that all ravens are black. One problem is that if we are dealing with infinitely many instances of a certain thing, this would not help at all. Moreover, this response hardly offsets a concern about projection—it has little bearing on questions to do with the next raven we shall see.

The Logic of Support

An Experiment on a Bird in the Air Pump by Joseph Wright, 1768, via the National Gallery.

Carl Gustav Hempel offered a famous solution to this problem, which was an attempt to articulate the "logic of support:"

"Any observation of an F that is also G supports the generalisation All Fs are G."

Moreover, Hempel accompanied this with the claim that any evidence which confirms a hypothesis H (such as that generalization above) can confirm any hypothesis which is the logical equivalent of H. This seems innocuous enough, until we recognize that all ravens are black is logically equivalent to all non-black things are not ravens, and as the latter can be confirmed without our ever seeing a raven, so too can our hypothesis about ravens.

As Nelson Goodman had it, it is possible to do rather a lot of "indoor ornithology" with this way of thinking. One possible solution to this problem comes from I.J Good, who held that observing a white object or a black raven may or may not confirm the hypothesis that "all ravens are black"—to confirm that, we would have to seek recourse to other factors. What might the background conditions for that hypothesis be? What might it be mutually exclusive with?

This response points towards another way of deflating this as a problem. Namely, no biologist cares the slightest bit whether all ravens are or are not black! Indeed, the existence of (say) albino ravens and other exceptions of this kind probably wouldn’t trouble a scientist who does research on the reasons why ravens tend to be black. in short, the relationship between observation and explanation in science is not quite as simple as we are suggesting here.

A photograph of Nelson Goodman, via Store Norske Leksikon.

We will conclude by returning to Nelson Goodman, and looking at his "New Riddle of Induction." Goodman wanted to show that there could not be a purely formal theory of confirmation. What does that mean? Well, to offer a formal theory of confirmation would be to theorize about it based merely on the pattern of an argument, rather than its (factual) content. That is how things tend to work when we are dealing with deduction—we can show that if Socrates is a man, and all men are mortal, then Socrates is mortal without appealing to any particular fact.

To do this, Goodman will try and show us that what appear to be perfectly viable forms of inductive arguments can, without making any formal changes, become utterly bizarre and unusable.

Take the argument "all emeralds found in the year 2023 or before are green, therefore all emeralds are green." This seems a fairly reasonable argument. All that it means really is that, up until now, we haven’t found any emeralds which aren’t green. But consider "all emeralds found in the year 2023 or before are grue," where "grue" (a made-up term) means green before 2023, and blue after. Now we’re in trouble, because while this doesn’t differ in any formal sense from our first argument, it is a rubbish one!

Proun 99 by El Lissitzky, ca. 1923-1925, via Yale University Art Gallery.

The second inductive argument suggests that, after 2023, emeralds will be blue going forward. In short, two inductive arguments can have the same form, but one can be good while the other is bad.

We may wish to suggest that the problem here is the concept grue—grue is just not the kind of concept about which we can make sensible inductive inferences. The onus would then shift to determining what does make a concept viable in this way. That’s far from straightforward to do. There’s no reason, in principle, why grue or something like it couldn’t crop up in a natural language—certainly, it isn’t difficult to see what it means!

Most philosophers didn’t like the idea that what counts as a good inductive inference could become language-dependent. Much of the response to Goodman’s new riddle of induction focused on if and how we can understand terms like "green" as picking out properties, classes, or kinds which are not language-relative.

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