Is it Rational to Believe in Induction?
Thomas Ash

The briefest acquaintance with modern philosophy - which is often taken to start with Descartes' 'radical doubt' as to whether all his experiences were plants from some evil demon or other deceptor - shows how few things we can uncontroversially know. We naturally want to move on from these sparse certainties - essentially just the existence of our selves and our current experiences[1] - and justify other beliefs. One of the most common methods for doing so is induction, a method used not only by scientists but also by us all every day when we expect the world to react or remain a certain way. Obviously, we do not directly see that it will do so without first having to make any inferences, in the way that we are directly aware of at least our own experiences.[2] How do we reason inductively, then? Is it rational?

Induction is often defined simply as taking the past as evidence of the future, but it is in fact broader than that. It takes place whenever we use specific, observed instances as evidence of the generalisations or laws they would fit into. It can, and has, been applied to the past, as in the fierce arguments in the early 19th century over whether the geological record proved a very ancient earth. This split uniformists from those who preferred denying induction and the similarity of the past to the present to denying Bible, which gave a genealogy of Adam's descendents used by Bishop Ussher to date the creation to 4004 BC. Likewise, when a birdwatcher argues from his lengthy observations that all swans are white, this is an instance of (overconfident) induction about the past, present and future. The most famous inductive argument, though, is that if a cause and effect seem to have been constantly conjoined, there exists a necessary connection between them (a natural law), which will continue to hold in the future.

David Hume, the great 18th century Scottish philosopher, first raised the 'problem of induction' with reference to this type of argument, but all his complaints and questions apply equally to inferences about past and present laws and generalisations. Nonetheless, for simplicity's sake, let us limit ourselves to the question Hume raised, and consider we think that past regularities will continue to hold in the future.

His central insight was that there can be no a priori reason, as laws of nature are never understood directly, but only known through experience: "Adam, though all his rational faculties be supposed, at the very first, entirely perfect, could not have inferred from the fluidity and transparency of water, that it would suffocate him."[3] In fact, he would have had no deductive or intuitively certain reason for thinking that there were uniform natural laws. "Gravity has always applied" does not logically imply "this rock won't levitate" - we could imagine it levitating. To make this a valid argument, we would have to assume a hidden premise - nature is uniform - and this begs the question of why we think this. This can only be because it seems to have been uniform in the past. So induction must be justified inductively, relying on past regularities - and this is circular, as a look at Hume's initial question shows. A circular reason can be no reason at all, or we would accept the spurious reasoning Descartes puts in the mouth of "learned" theologians: "...we must believe in the existence of God because it is a doctrine of Holy Scripture ... we must believe Holy Scripture because it comes from God..."[4]

This should make us worry that since we lack any reason for thinking inductively, we are being irrational in vast spheres of our life. Imagine a philosophy student who goes for lunch with a friendly scientist, who prides herself on her empiricism and rationality. Feeling that he ought to show that what he learnt that morning has some use (even if it is only in confusing the hungry), the philosopher asks his friend, just about to munch on a sausage roll: "How do you know that won't poison you?" Perplexed, the scientist points out that the eatery isn't that unhygienic, only to be given a rundown on the problem of induction, which cuts short her attempts to appeal to natural laws and medical observations. Eying her sausage roll suspiciously, she puts it down, only to see her friend start to eat his. "What are you doing? Are you crazy?", she cries. "I'm not in a philosophy lecture any more", he replies. His attitude reflects that of most philosophers who have been perplexed by the problem of induction. But, as we share her concern for rationality, we should sympathise with the worried scientist.

In fact, things are even worse than they might seem to the scientist. It is not just that she cannot know that the roll will not poison her; she has no justification for thinking this to be any more probable than it being poisonous, or bitter, or tasteless, or hallucinogenic. All options are equally justified, and thus not very well at all justified, unless she can establish the principle of the uniformity of nature a priori, without reference to the scientific observation which in fact convinces her (and the rest of us.) But nowadays, thanks in part to our scientist's empirically-minded forebears (and in part to 'empiricist' philosophers like Hume), we are suspicious of attempts to prove facts about the world a priori. This is what makes the problem of induction so serious. Were we still confident rationalists in the mould of Descartes, we could hope to argue that induction must work, perhaps because we thought we had some proof of a God who guaranted the reliability of our cognitive faculties. But, at least for the most, we are not. This means that we cannot regard the reliability of induction as necessary, but must see it as an empirical claim which could be falsified by future experience: and this is what seems to commit us to circularity, for we can only justify such claims by appeal to induction.

Another claim to which we cannot appeal is Occam's Razor, the powerful principle that, all else being equal, we should prefer the simplest explanation. For, assuming that we think it illegitimate to take such a claim as true a priori[5], it can only be justified inductions from our experience. And, as should by now be clear, that would be circular.

Some have boldy tried to argue that the reliability of induction can be non-circularly be established on the basis of experience. F.L. Will offers the example of a pasture inhabited by chicken farmers who cannot wander or gaze outside, but do steadily reclaim new land. As the pasture expands, the new roosters it gains are always more aggressive than the hens - don't the farmers have grounds for thinking that roosters outside are more aggressive? They would argue that they have a large, and growing, body of evidence for this. The relevance to the problem of induction is obvious - the pasture represents the past, the steadily reclaimed land the future. Will accuses sceptics of induction of constantly shifting the definition of 'the future' forwards to neutralise our evidence that laws will continue to hold, just like a sceptical chicken farmer might complain that the newly reclaimed land is no longer an example of what's outside the pasture. This consciously contradicts Bertrand Russell's dictum that past futures can never be evidence of future futures.

Suppose for the sake of argument that we see things the same way Will does. Even so, induction will not be vindicated yet. For besides Hume's old riddle, there is what Nelson Goodman christened 'The New Riddle of Induction'.

Hasn't induction proved to hold true a vast number of times, more than any individual law? This is certainly true, and without a doubt why we do in fact believe in induction, as Hume observed (though the psychological fact that regularities lead us to infer general principles does not prove anything - witness the way in which we are disposed to believe all sorts of pleasant superstitions on tenuous evidence.) But on its own, it is not sufficient reason for favouring the sorts of unchanging laws we want to favour over a law which changes tomorrow, or the day after. As Nelson Goodman pointed out in his seminal lecture on "The New Riddle of Induction", the evidence fits the hypothesis that all emeralds are 'grue' (green up until tomorrow, blue afterwards) just as well it fits them remaining 'green.' Perhaps, it's just human favouritism to see the latter as being better confirmed. Simon Blackburn has challenged this, claiming that 'green' really is a simpler concept which we should interpret the evidence as suggesting, because unlike 'grue' it makes no reference to specific times or places. Whether this criticism works or not depends again on whether Occam's Razor can be justified a priori, and whether we can objectively define simple.

A sceptic of induction can always question this, and any other justification we might offer, pointing out either its circularity or its question-begging assumption of a priori principles. Perhaps he is being unfair, though. After all, what on earth would he count as a reason? The answer is clearly "nothing." Paul Edwards has argued that this reveals a misunderstanding of the word 'reason', since past instances of a law clearly do count as a reason for believing that law, in our sense of the word. This argument would not convince the most tentative sceptic. Not only does it ignore Goodman's riddle of which law to accept (are all emeralds 'green' or 'grue'?); it is at bottom a piece of semantic sleight-of-hand - we understand the sceptic's worry that induction may not constitute a real reason, however you wish to phrase it. As Simon Blackburn has pointed out, the mere fact that we use the principle of induction as a reason for beliefs does not mean that it is analytic, any more than our frequent appeals to majority opinion make that a good reason for thinking anything.

Nonetheless, there is more than a grain of truth to the complaint that the sceptic is being unreasonable in his demands. He is in effect asking us to give a deductive argument for inductive reasoning, and it should be no surprise that this is impossible. Deductive reasoning, of the sort that mathematicians and logicians use to prove things, is a wholly different method, concerned not with establishing natural laws and other putative facts about the world, but with syllogisms (eg. if all as are bs and all bs are cs, then some as are cs.) It should be no surprise that it can provide no foundation for induction. Philosophers generally favour deductive arguments and justifications (often derived from analyses of the meaning of words, as in Edwards' defence of induction.) But perhaps we can begin to see the best response - though it can only be a response, not a solution - to the seeming invulnerable problem of induction when we recognise that we cannot deductively justify deduction either, at least not without being accused of circularity.

What we seem to be left with, then, are two completely different modes of thinking, deduction and induction. Do both have to stand on themselves for their own justification? Well, we have seen that induction certainly does. Deduction is often seen as more basic, thanks to its employment in pure reasoning and mathematics, but in fact it may have arisen from induction. It is historically far more likely that the first cavemen started from observations like "All apples are fruit, all fruit grows on plants - and apples grow on plants!" than that they sat down to invent a formal syllogistic system which proved useful enough to endure. On a more theoretical level, it is difficult to see how a disembodied brain separated from any experience of our universe could come up with such laws of inference, let alone the concept of discreet objects that they operate on.

Now if deduction stands on induction, this doesn't help us, but only spreads the contagious scepticism we have encountered. And if it stands on itself, it seems no better off than induction. What have we accomplished then, beyond calling maths and logic into as much doubt as science and sausage rolls? Well, we have come up with a response to the sceptic: if he wants to be consistent, he will have to give up deduction too. If he accepts this, then we have no counterattack. But if he doesn't, then he will have to accept that he has somehow set his standards too high. Like P.F. Strawson, he will have to accept that asking what reason we have for following these modes of reasoning is like asking: "Is the law legal?"[6]

But if we can't find any reason for it, outside its own standards, doesn't that make it irrational and arbitrary? Imagine someone came up with a method of justification - there's no need to imagine, people have - called faithduction. This would simply state if something feels true, right and beautiful, then it is true. Clearly we need some grounds for preferring deduction and induction to faithduction. Since all three set themselves up as basic ways of thinking, we can't ask why faithduction is correct any more than we can justify deduction and induction in this way. We will have to use the same tactic employed a moment ago, teasing out consequences a fan of faithduction will not want to accept, and then pragmatically showing why we should employ deduction and induction in our reasoning.

The flaw of faithduction is that, unlike deduction and induction, it leads us to results that we find unacceptable. It has made people believe in old superstitions, like that of a flat earth, which have proved hopelessly inadequate for navigating our world, and which no modern person would want to accept. When the choice is laid out between faithduction and a round earth, most people will choose the round earth. Another problem is that at any one time, there may be a number of mutually incompatible things which feel "true, right and beautiful" to us. A faithductionist could chose to accept them all, but she will soon find this an impossible way to go on living and thinking.

Induction and deduction are modes of reasoning that have been carefully adjusted to avoid giving patently false answers. For all the theoretical arguments against believing induction, you cannot accuse it of having let us down in the same way that faithduction does. People cite the example, given early on, of the birdwatcher who inductively assumes that all swans are white. But it is for this reason that refined induction specifies that all relevant facts about the world (for instance, our knowledge that colour can vary within species) have to be taken into account, and that narrow inductions about closely bound causes and effects are more reliable than others. The overconfident birdwatcher is to blame here.

The positive reason we have for believing these 'ductions' is that, in some way that we cannot understand, they seem lead us away from falsity and towards truth (their stem is derived from the Latin verb for leading, after all.) As Hume pointed out, we can't have any direct knowledge of uniform natural laws, which seem quite mysterious things. But we can have knowledge of specific instances where an apple snapping of a branch is conjoined with it falling to the ground: this is one of those concrete facts that we can know. And induction seems to lead us to these facts, just as deduction could lead us to the fact that apples grow on plants - this is why we accept it. We can always be surer of a specific inductive inference than of the general principle or law that seems to lie behind it. And Goodman's riddle shows the need for work understanding how our inductive thought distinguishes true possible hypotheses from false ones.

But our adoption of induction is practically justified by the facts about the world which led us to believe it in the first place. In this sense it is not irrational, though we cannot give the type of watertight reasoning for it that we can give for a conclusion inside a deductive system like logic. The difficult task of thinking about systems from inside them, from other systems, and from outside systems altogether (if that is possible - a matter for great debate) is what makes philosophy philosophy.


1. Strictly speaking, all we directly experience are the sense-data of objects like tables and chairs, not the objects themselves. Whether it is reasonable to take these as caused by an external, physical world is a matter for debate - see my essay 'Does the External, Physical World Exist?' Briefly, I conclude that belief in tables and chairs as part of an external world is eminently reasonable, and that this world is probably physical, in some minimal sense of the word.

2. "I think, therefore I am" - Descartes' famous first certainty, from which he restored certainty about most things... with the help of God, that is.

3. An Enquiry Concerning Human Understanding, David Hume, Section IV, paragraph 6

4. Meditations of First Philosophy, René Descartes - Dedicatory letter to the Sorbonne, paragraph 2

5. The sort of a priori argument in favour of Occam's Razor which a rationalist might have offered would have appealed to the existence of God (itself assumed to be demonstable a priori), who would, it was assumed, favour simplicity in his creation, where 'simplicity' meant uniform laws and similar features among similar groups. But if we accept that the existence of such a God is at the very least impossible to prove a priori, this is a hopelessly anthropomorphic concept of the universe. For in that case it is hard to supply a reason why laws we judge to be simpler should hold. Couldn't the universe just as well act randomly, or (from our perspective) switch its laws periodically?

6. Introduction to Logical Theory, P.F. Strawson (Methuen, 1952), p257


An Enquiry Concerning Human Understanding, David Hume (OUP, 1999)

Fact, Fiction, and Forecast, Nelson Goodman (Athlone Press, 1954)

Reason and Prediction, Simon Blackburn (CUP, 1973)

Think, Simon Blackburn (OUP, 2001)

An Introduction to Philosophical Analysis, 4th edition, John Hospers (Routledge, 1997)

"Bertrand Russell's Doubts about Induction", Paul Edwards in Logic and Language 1st series, Anthony Flew (ed.) (Blackwell, 1963)

"Will the Future be Like the Past", F.L. Will in Logic and Language 2nd series, Anthony Flew (ed.) (Blackwell, 1966)

© 2003

About the author...
Tom Ash is the webmaster of Big Issue Ground and Atheist Ground. He studied philosophy at Oxford and Cambridge, where he was president of the University Atheist and Agnostic Society. He currently does non-profit work and freelance web development. See more information about Tom Ash.

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