The argument goes like this: David Hume, skeptic par excellence, showed that a particular kind of reasoning called induction–in which we infer that a past pattern of experiences will probably continue–cannot be rationally justified, except as a habit that sometimes works. Why?

1. First: It’s logically possible the future won’t resemble the past. Induction differs from deduction, like math and formal logic, in that its assumptions cannot guarantee its conclusions. 
2. Second: We can’t use the evidence that induction worked in the past in order to justify it. We would be invoking “the future resembled the past” in the past, in order to prove “the future will continue to resemble the past” in the future, thus assuming the conclusion we had set out to prove and twisting ourselves into a logical pretzel. 

Science need not rely on induction to reach conclusions. Hume’s problem—while real—is avoidable.

This is known as Hume’s Problem of Induction (POI), one of the most famous problems in philosophy.https://www.gutenberg.org/files/9662/9662-h/9662-h.htm” rel=”noreferrer”>¹ While the views of philosophers, scientists and science popularizers vary widely, here we will argue that science need not rely on induction to reach conclusions. Hume’s problem—while real—is avoidable.

The problem gets worse.

Induction seems essential to navigate our world: the Sun rose every day until now, thus we infer it will probably rise again tomorrow. That’s induction, and it seems indispensable. Some argue that science itself, since it rests on predictions about the future from past empirical data, would collapse without it. Bertrand Russell said if the POI could not be addressed within an empirical framework, there would be “no intellectual difference between sanity and insanity.”https://archive.org/details/westernphilosoph035502mbp/page/700/mode/2up” rel=”noreferrer”>²

Imagine that: science—the method underpinning everything from cardiac surgery to space exploration—relying upon an innate form of reasoning we cannot escape or rationally justify.

At this stage, some scientists might shrug and get back to the lab, acknowledging we are primates doing the best we can and this is just the hand we’ve been dealt. Others in the popular sphere go further. Sabine Hossenfelder, physicist and internet personality with 1.8 million YouTube subscribers, concludes “Science, too, is based on faith”: 

Then how do we know that the laws of nature will continue to function tomorrow? We don’t know. We can’t know. The only thing we can do is have faith in the laws of nature … Yes that’s right, science is ultimately based on our faith that the laws of nature will just continue to work.https://www.youtube.com/watch?v=K0K9cRbQ_5M” rel=”noreferrer”>³

Appropriately for her “faith” descriptor, a biblical creationist website called Answers in Genesis would seem to agree:

… we can only have a guarantee that the future will be like the past if we have a good reason to assume uniformity … it’s vitally important we have a justification for this assurance because without it, we couldn’t know anything at all based on our experiences, and science would be meaningless.https://answersingenesis.org/logic/biblical-worldview-only-answer-for-induction/ ” rel=”noreferrer”>⁴

The author, a self-described Young Earth Creationist working in the “secular rocket science (i.e., aerospace) field,” concludes: “the Biblical worldview is the only answer for induction … God’s Word provides a basis for the universe being logical and orderly, thus providing a solid foundation for induction.” 

Even if science relies on induction, the argument goes, it remains distinguishable from faith as an empirical method of formulating and testing hypotheses. Yet induction is just one tool in the science toolkit. Is it really an indispensable one?

A Good Sense of Hume

To grapple with these problems, we have to clearly understand the specific kind of inference targeted by Hume’s POI—what it is and what it isn’t. Consider this reasoning:

All the eggs I’ve tried taste good. Therefore, the next egg will probably taste good.

The step bridging from premise to conclusion—therefore—is the kind of inductive inference deemed problematic by Hume. It starts from experiences in the past and concludes the pattern will probably continue in the future. Or it could start from experiences at one end of the egg carton and conclude the pattern will probably continue at the other end.

We see that whether induction works as a shortcut depends on an implicitly assumed model of the situation: the farmer is feeding me vs. the farmer is fattening me.

This type of reasoning often works, but the conclusion does not strictly—i.e., deductively—follow. It doesn’t even probably follow. Past experience by itself does not logically establish the probability it will continue, as the prospectus of any Wall Street mutual fund cautions (“past performance does not guarantee future results”). 

Russell illustrated the unreliability of induction with the story of a chicken. (Philosophers like to think about chickens and eggs.) The chicken concluded from a pattern of prior experience that its farmer would probably continue feeding it. Actually, the chicken was being fattened, and one day the chicken ended up feeding the farmer, instead.⁵ Sabine Hossenfelder used this story to argue that scientists, despite seeing how things worked out for the chicken, have faith in its reasoning anyway.

We see that whether induction works as a shortcut depends on an implicitly assumed model of the situation: the farmer is feeding me vs. the farmer is fattening me. This suggests we should really be examining our models to make predictions about the future. More on this later.

Hume’s Habit

Why do we feel psychologically impelled to use induction? Hume, Russell and others recognized that our impulses exhibit a likeness to other organisms. Like us, other organisms behaviorally respond as if they are using induction. Repeatedly shock a sea slug, and it retracts its gills for longer. Ring a bell associated with dinnertime, and Pavlov’s dogs salivate. These behaviors have to do with circuits of neurons that feed back on themselves, becoming easier to stimulate next time—classical conditioning. Even individual cells move in response to local chemical gradients. The impulse, then, results from biological architecture.

Why did organisms evolve this architecture? Because it worked well enough for survival. Time is costly, and survival requires snap judgments balanced by acceptable false-alarm rates—whether the triggers are “rational” or not. Hence illusions, prejudices, approximations, superstitions and perhaps, induction. Hume simply called it a habit.

Organisms like us must be able to generate models instinctively, without the cost of having examined them. Maybe that’s why we use induction, but science can proceed more methodically. 

Now that we’ve defined the kind of induction that falls afoul of the POI, let’s survey other tools scientists have at their disposal. Here’s a partial list:

Entertaining assumptions to see where they lead; making guesses; collecting data; fitting models to past data; using deductive reasoning; using statistics or Bayesian reasoning; computing predictions entailed by hypotheses; having beliefs that are not guaranteed to be true; forming conclusions about probabilities; being uncertain; being wrong sometimes; having values; making a selection of what to test based on our values (e.g. prioritizing a new kind of medicine over a new kind of sandwich).

That’s a lot. We arguably have enough to do science with this toolset. Hume’s POI doesn’t touch anything on this list. (A caveat: while statistics and Bayesian reasoning are often considered to be a formalized logic of induction, they aren’t the bare extrapolations from past experience to a probable continuation targeted by Hume.) 

It is sometimes mistakenly suggested that any probabilistic or uncertain conclusion uses induction. Not so. Suppose 75 percent of stars in our galaxy are red dwarfs. Then, if a star in our galaxy is selected at random from a representative sample, the probability that we observe a red dwarf is 75 percent. This is a deductive conclusion about a probability. Are we certain about our conclusion? Not necessarily, unless we are certain about our assumptions. Only the inference—the bridge from assumption to conclusion—is certain. Maybe our assumption about red dwarf abundance was wrong. Or maybe our telescopes don’t collect representative samples because red dwarfs are harder to see than brighter stars, so our other assumption was wrong. 

As this example illustrates, we do not automatically contaminate science with illusory certainty when we use tools other than induction. Instead, we simply make the models underpinning our reasoning more explicit, so when the data shows we are wrong, we can diagnose which assumptions were at fault.

Revisiting the Problem of Induction

Many thinkers seem to agree with Hume that the POI is insoluble.https://plato.stanford.edu/archives/win2024/entries/induction-problem/ The 2014 version, which seems more charitable to Popper’s approach, appears here: https://plato.stanford.edu/archives/spr2018/entries/induction-problem/” rel=”noreferrer”>^6, https://skepticalinquirer.org/wp-content/uploads/sites/29/2019/03/Issue-03-24.pdf” rel=”noreferrer”>⁷ However, as we have seen, the reasonableness of induction in a particular situation depends on an unspoken model of that situation. 

One conventional view of the scientific method, originally formulated by Karl Popper, involves stating our models explicitly and falsifying them with data.https://epistemologies.wordpress.com/wp-content/uploads/2007/09/the-logic-of-scientific-discovery-by-karl-popper.pdf (Original work published 1934)” rel=”noreferrer”>⁸ We have a rational basis to consider well-tested models as candidates for truth, yet we never attain certainty. We can rationally update our credence in hypotheses conditioned on the agreement between their predictions and observations. Richard Feynman beautifully captured this approach:

In general, we look for a new law by the following process. First, we guess it. … Then we compute the consequences of the guess … then we compare those computation results to nature or [to] experiment … If it disagrees with experiment, it’s wrong.https://www.youtube.com/watch?v=EYPapE-3FRw” rel=”noreferrer”>⁹

Notice this recipe does not demand that we conclude past experiences will probably recur. We may even conclude past experiences will probably not recur, using models to ask when this might happen. No induction, no POI. 

Guesses don’t require rational justification: we are free to beg, borrow, steal, or use a random number generator to produce them.

Surprisingly, the Stanford Encyclopedia of Philosophy entry on POI only mentions Popper and this perspective on scientific method in two paragraphs at the end. The entry concludes that Popper gives an incomplete account of the scientific method:

Popper’s account appears to be incomplete in an important way. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing. Yet, scientists will typically want to say that one is better supported by the evidence than the others … It appears doubtful then that pure deductivism can give an adequate account of scientific method.https://plato.stanford.edu/archives/win2024/entries/induction-problem/ The 2014 version, which seems more charitable to Popper’s approach, appears here: https://plato.stanford.edu/archives/spr2018/entries/induction-problem/” rel=”noreferrer”>¹⁰

Previous versions seemed more charitable.¹¹ In what follows, we will sketch a version of the Popper-Feynman view, so readers can judge for themselves whether it is inadequate. 

Surely you’re joking, Mr. Feynman! 

Suppose we want to study an observable, y. It could be the intensity of radiation from decaying isotopes, height of a projectile, number of bats in a population, or a quantity calculated from observables like wavelength, energy, momentum, etc. We study y over a range of other observables that vary in nature or can be controlled in our experiments, x. This might be time, location, temperature, pressure, chemical concentration, initial velocity, voltage, etc. or another calculated quantity. 

How do we choose which y’s and x’s to observe? As mathematician and physicist Henri Poincaré noted in Science and Method, we must make a careful selection, since we cannot observe them all.¹²

Of course, we may find our selection of facts yields an unintelligible pattern. According to a whimsical scenario cited by Feynman, if we choose y = the best day to go to the dentist and x = the position of stars viewed from Earth, we might get such useless results. 

Suppose our selections are well chosen or lucky and yield an intelligible pattern of data. What next? We do not use induction to conclude therefore, this pattern will probably continue. Instead, we build models of the past pattern. We treat them as hypotheses and try to think up ways to test them. How do we build models? Following Feynman, “first, we guess it.”

At this point, some may object that even the act of guessing smuggles induction. It doesn’t. First, induction is an inference from assumptions to a conclusion. A guess is not. Guesses don’t require rational justification: we are free to beg, borrow, steal, or use a random number generator to produce them. Second, we are free to guess the pattern will not continue, contra-induction. Third, even if we select an extrapolation of past patterns as meriting special attention, prioritizing research effort isn’t induction. Finally, for every guess the method admits the possibility of an anti-guess, i.e. that our guess is false. We don’t have to play favorites.

Our method seeks uniformity, if it exists, but nature decides if there is any to be found.

Another objection is that we have assumed “the uniformity of nature,” which is tantamount to smuggling induction. Yes, we tend to assume some degree of uniformity of nature in our models. That is because it is difficult to write down precise models without that assumption. However, our method leaves open the possibility of non-uniformity. If nature turns out to be non-uniform or “capricious,” to borrow the term used by Poincaré, then it is free to produce data that defies all description. Our method seeks uniformity, if it exists, but nature decides if there is any to be found.

In a sense, physicists can even test models of partially-uniform universes, where some quantities are invariant (rest mass or electric charge of a particle), others are not (velocity of a particle) or the form of the laws themselves changes over time and space. Now our assumptions are explicit again, not smuggled, and we return to the question of how to test them.

“If it disagrees with experiment, it’s wrong.”

One appeal of induction is it seems to provide a reason to believe things about the future, whereas using data to falsify models only tells us when we are wrong. Can we ever believe—even provisionally—that the predictions of our well-tested models are right? 

Let’s consider all the possible models that could fit a set of data. This leads to difficulties if we allow infinite possibilities. One workaround is to organize them into a finite number of classes: the model class that planets always have elliptical orbits, say, and the class that they don’t. 

Given all possible models, the probabilities of each model being true must sum to 100 percent. When we use data to falsify some model classes, that 100 percent probability mass must reallocate into a smaller set of surviving classes—though we may not know which models benefit in particular. Still, we now have a reason to increase our credence in the surviving classes and what those models predict about the future.¹³ That reason is conditioned on data, not faith. 

Critics may ask: why shouldn’t we be terrified of an upheaval at any moment—the planets switching to triangular orbits, perhaps? Such an upheaval would also fit the data up to now. However, this would require a model with new assumptions about triangular orbits, starting at a particular, arbitrary moment. And why assume that moment is “now” rather than a hundred years ago, or next week, or a hundred years from now? While we can’t rule it out, the model that there will be upheaval in the next moment is not on the same footing as the model there won’t be.  

We now have a reason to increase our credence in the surviving classes and what those models predict about the future. That reason is conditioned on data, not faith. 

This guarded confidence about the near future gives way to “expect the unexpected” in the far future, or under major changes in observing conditions. According to Poincaré, scientists seek out such “great upsettings” and do not necessarily conclude they are improbable, contra-induction:

This is one of many reasons for the interest of astronomical facts and of geological ages. By making long excursions in space or time, we may find our ordinary rules completely upset, and these great upsettings will give us a clearer view and better comprehension of such small change as may occur nearer us.¹⁴

Science tells us when the sun will not rise.

Does science really have to rely on induction: a deductively invalid and rationally unjustifiable habit of reasoning that only sometimes works?  

We see that a rigorous formulation of the scientific method has a rich toolset. A chicken sees a pattern of stimuli: food, food, food … and concludes it will probably continue. A scientist sees a pattern and asks which hypotheses can explain it, when they predict the pattern will change and how we can test them. Induction may still show up in practice as Hume’s psychological habit; as methodological shortcut; or as a rationally constrained convention for guesswork. 

Even if the simplified view of the scientific method sketched here is accurate, that would not make science an ironclad system of pure deductive logic. And even if this view is wrong, and science does rely on induction, it would not make science equivalent to faith. In either case, scientific thinking is conditioned by reasoning and evidence in ways that popular caricatures of Hume and the POI skip over.