Friday, 12 October 2012

Problem of Induction explained simply... (from my book The Philosophy Gym)

Why Expect the Sun to Rise Tomorrow?

Philosophy Gym category:

Warm up
More challenging

Every morning we expect the sun to appear over the horizon. But according to one the philosopher David Hume (1711-76, our expectation is wholly irrational. This chapter gets to grips with Hume’s extraordinary argument. 

An absurd claim?

MacCruiskeen, a scientist,is watching the sunrise. She’s accompanied by her close friend Pluck, a student of philosophy.

Pluck. Beautiful sunrise.
MacCruiskeen. Yes. And right on time too.
Pluck. Yet there was no good reason to expect it to rise this morning
MacCruiskeen. But the sun has risen every morning for millions of years. Of course it was going to rise this morning as well.
Pluck. There’s no reason to suppose it will rise tomorrow, either. In fact it’s just as sensible to expect that a huge million-mile wide bowl of tulips will appear over the horizon instead.


MacCruiskeen. I agree we can’t be certain the sun will rise tomorrow. Some cataclysmic event might destroy the Earth before then. But it’s very unlikely that anything like that will happen. The probability is that the sun will rise, surely?
Pluck. You misunderstand me. I’m not just saying we can’t be certain the sun will rise tomorrow. I’m saying we have no more reason to suppose that it will rise than we have to suppose that it won’t.
MacCruiskeen. That’s absurd. The evidence – such as the fact that the sun has risen every morning for millions of years – overwhelmingly supports my belief that the sun will rise tomorrow too.
Pluck. You’re mistaken.

Pluck’s position might seem ridiculous. But Hume has an argument that appears to show that she’s right. Not only is our belief that the sun will rise tomorrow wholly unjustified, so too are all our scientific theories.
Before we look at Hume’s argument I need briefly to explain the difference between deductive and inductive reasoning.


[FULL PAGE-WIDTH TEXT BOX. THINKING TOOLS: Inductive and deductive reasoning. An argument consists of one or more claims or premises and a conclusion arranged in such a way that the premises are supposed to supportthe conclusion. Arguments come in one of two forms: deductive and inductive.

1: Deductive arguments. Here is an example of a deductive argument:

All cats are mammals

My pet is a cat
Therefore: My pet is a mammal

Two things are required for a good deductive argument. First of all, the premises must be true. Secondly, the argument must be valid. The expression “valid”, in this context, means that the premises must logically entail the conclusion. In other words: to assert the premises but deny the conclusion would be to involve oneself in a logical contradiction. The above argument is valid. A person who claims that all cats are mammals and that their pet is a cat but who also denies their pet is a mammal has contradicted him or herself.

2: Inductive arguments. Suppose you observe one thousand swans and discover them all to be white. You don’t come across any non-white swans. Then surely you have pretty good reason to conclude that all swans are white. You might reason like this:

Swan 1 is white

Swan 2 is white

Swan 3 is white


Swan 1000 is white 

Therefore: All swans are white

This is an example of an inductive argument. Inductive arguments differ from deductive arguments in that their premises are supposed to support, but not logically entail, their conclusions. The above argument is not and is not intended to be deductively valid. To assert that the first one thousand swans one has examined are white but that not all are white is not to contradict oneself (in fact not all swans are white: black swans come from New Zealand)
Nevertheless, we suppose that the fact that if all the swans we have observed so far are white, then that makes it more likely that all swans are white. The premises supportthe conclusion. We believe that an inductive argument can justify belief in its conclusion, despite not providing logical guarantee that if the premises are true then the conclusion will be.
            END OF TEXT BOX]]]

Why is induction important?

We rely on inductive reasoning in arriving at beliefs about what we have not observed, including, most obviously, our beliefs about what will happen in future.
Take, for example, my belief that the next time I sit in a chair it will support my weight. How is this belief justified? Well, I have sat in a great many chairs and they have always supported my weight before. That leads me to think it likely that the next chair I sit in will support my weight too.
But notice that the statement that all the chairs I have ever sat in have supported my weight does not logically entail that the next chair will. There is no contradiction in supposing that even though I have never before experienced a chair collapse beneath me, that is what’s about to happen.
But it then follows that I can’t justify my belief that the next chair will not collapse by means of a deductive argument from what I have observed. So if my belief is justified at all, it must be by means of an inductive argument.
            Science is heavily dependent on induction. Scientific theories are supposed to hold for all times and places, including those we have not observed. Again, the only evidence we have for their truth is what we have observed. So, again, we must rely on inductive reasoning to justify them.

The unjustified assumption

We have seen that inductive reasoning is important. Science depends upon it. If it can be shown that inductive reasoning is wholly irrational, that would be a catastrophic result. Yet that’s precisely what Hume believes he can show.
Let’s return to Hume’s argument. Hume believes it is no more rational to suppose the sun will rise tomorrow than it is to suppose that it won’t. Hume’s argument, in essence, is simple: it’s that induction rests on a wholly unjustified and unjustifiable assumption. What is this assumption? Pluck proceeds to explain.

Pluck. Your belief that the sun will rise tomorrow is irrational. Hume explained why. Whenever you reason to a conclusion about what you haven’t observed, you make an assumption.
MacCruiskeen: What assumption?
Pluck: You assume that nature is uniform.
MacCruiskeen: What do you mean?
Pluck: I mean you assume that those patterns that we have observed locally are likely to carry on into those portions of the universe that we haven’t observed, including the future and the distant past.
MacCruiskeen: Why do I assume that?
Pluck: Well, put it this way: if you didn’t believe that nature is uniform, then the fact that the sun has, in your experience, risen every day wouldn’t lead you to expect it to continue to rise, would it?
MacCruiskeen: I guess not.
Pluck. So you see – it’s only because you assume nature is uniform that you conclude that the sun will continue to rise in the future.

It appears Pluck is right. Whenever we reason inductively, we make an assumption about the uniformity of nature. We assume that the universe is patterned throughout in just the same way.
Imagine an ant sitting in the middle of a bedspread. The ant can see that its bit of the bedspread is paisley-patterned. So the ant assumes the rest of the bedspread  – the bits it can’t see – are paisley patterned too. But why assume this? The bedspread could just as easily be a patchwork quilt. The bedspread could be paisley here, but plaid over there and polka-dotted over there.


Or perhaps, just over the ant’s horizon, the print on the bedspread turns to a chaotic mess, with blobs, lines and spots muddled up quite randomly.
We are in a similar position to the ant. The universe could also be a huge patchwork, with local regularities, such as the ones we have observed – the sun rising everyday, trees growing leaves in the Spring, objects falling when released, and so on – but no overall regularity. Or perhaps the universe becomes a chaotic mess just over the horizon, with events happening entirely randomly. What reason have we to suppose this isn’t the case?
As Pluck is about to explain, it seems we have none.

Pluck: So the problem is this: unless you can justify your assumption that nature is uniform, your use of induction is itself unjustified. But then so too are all those conclusions based on inductive reasoning, including your belief that the sun will rise tomorrow.
MacCruiskeen: True.
Pluck: So how do we justify the assumption that nature is uniform?

We have just two options: we can either appeal to experience – to what you have observed – or you might try to justify the assumption independently of experience. MacCruiskeen is happy to admit that we cannot know that nature is uniform without observing nature.

MacCruiskeen: Obviously we can’t know independently of experience that nature is uniform
Pluck: I agree. Our five senses – sight, touch, taste, hearing and smell – provide our only window on the world. Our knowledge of nature is dependent on their use.
MacCruiskeen: True.
Pluck: Which means that, if the assumption that nature is uniform is to be justified at all, it must be by appeal to what we have experiencedof the world around us.
MacCruiskeen: Yes. But isn’t the claim that nature is uniform justified by experience?
Pluck: No. To say that nature is uniform is to make a claim about what holds for all times and places.
MacCruiskeen: True.
Pluck: But you can’t directly observe all of nature, can you? You can’t observe the future. And you can’t observe the distant past.
MacCruiskeen. Also true.
Pluck. But then your justification of the claim that nature is uniform must take the following form. You observe nature is uniform round here at the present time. Then you infer that nature is also like that at all those other times and places. Correct?
MacCruiskeen. I suppose so.
Pluck. But that is itself an inductive argument!
MacCruiskeen: Yes, it is.
Pluck: Your justification is, therefore, circular.

Here we reach the nub of Hume’s argument. It seems that, if it can be confirmed at all, the assumption that nature is uniform can only be confirmed by observing that nature is uniform round here and then concluding that this is what she must be like overall.
But such a justification would itself be inductive. We would be using precisely the form of reasoning we’re supposed to be justifying. Isn’t there something unacceptably circular about such a justification.  

 The circularity problem 

 Pluck certainly thinks so.

MacCruiskeen. What is the problem with the justification being circular?
Pluck. Look, imagine that I think Mystic Madge, the psychic who works at the end of the pier, is a reliable source of information.
MacCruiskeen. That would be very foolish of you!
Pluck. But suppose my justification for trusting Mystic Madge is that she claims to be a reliable source of information. I trust her because she says she’s trustworthy.


MacCruiskeen. That would be no justification at all! You need some reason to suppose Mystic Madge is trustworthy before you trust her claim that she is.
Pluck. Exactly. Such a justification would be unacceptably circular because it would presuppose that Mystic Madge was reliable.
MacCruiskeen: I agree.
Pluck: But your attempt to justify induction is unacceptable for the very same reason. To justify induction you must first justify the claim that nature is uniform. But in attempting to justify the claim that nature is uniform you rely on induction. That won’t do. You’re just presupposing that induction is reliable. 

We can now sum up Hume’s extraordinary argument. All inductive reasoning, it seems, relies on the assumption that nature is uniform. How, then, might this assumption be justified? Only by experience, surely. But we cannot directly observe that nature is uniform. So we must infer that it is uniform from what we have directly observed, i.e. from a local uniformity. But such an inference would itself be inductive.Therefore we cannot justify the assumption. So our trust in induction is unjustified.

But induction works, doesn’t it?

Perhaps you’re not convinced. You might suggest that there is one very obvious difference between, say, trusting induction and trusting Mystic Madge. For induction actually works, doesn’t it? It has produced countless true conclusions in the past. It has allowed us successfully to build supercomputers, nuclear power stations, and even to put a man on the Moon. Mystic Madge, on the other hand, may well have a very poor track record of making predictions. That’s why we are justified in believing that induction is a reliable mechanism for producing true beliefs whereas trusting Mystic Madge is not.
The problem, of course, is that this is itself an example of inductive reasoning. We are arguing, in effect, that induction has worked until now, therefore induction will continue to work. Since the reliability of induction is what is in question here, it seems that this justification is, again, unacceptably circular. It is, after all, just like trying to justifying trust in the claims of Mystic Madge by pointing out that she herself claims to be reliable.

An astonishing conclusion

The conclusion to which we have been driven is a sceptical one. Sceptics claim that we do not know what we might think we know. In this case, the scepticism concerns knowledge of the unobserved. Hume and Pluck seem to have shown that we have no justification for our beliefs about the unobserved, and thus no knowledge of the unobserved.
Hume’s conclusion is a fantastic one. It’s a good test of whether someone has actually understood Hume’s argument that they acknowledge its conclusion is fantastic (many students new to philosophy misinterpret Hume: they think his conclusion is merely that we cannot be certain what will happen tomorrow.) In fact, so fantastic is Hume’s conclusion that MacCruiskeen cannot believe Pluck is really prepared to accept it.

MacCruiskeen: You’re suggesting that what we’ve observed to happen so far gives us no clue at all as to what will happen in the future?
Pluck: Yes. Things may continue on in the same manner. The sun may continue to rise. Chairs may continue to support our weight. But we have no justification whatsoever for believing any of these things.
MacCruiskeen: Let me get this straight. If someone were to believe that it’s just as likely that a huge bunch of tulips will appear over the horizon tomorrow morning, that chairs will vanish when sat on, that in future water will be poisonous and objects will fall upwards when released, we would ordinarily think them insane. Correct?
Pluck: Yes, we would.
MacCruiskeen: But if you’re right, these “insane” beliefs about the future are actually just as well-supported by the available evidence as is our “sensible” belief that the sun will rise tomorrow. Rationally, we should accept that these “insane” beliefs are actually just as likely to be true!
Pluck: That’s correct.
MacCruiskeen: You really believe that? You really believe it’s just as likely that a million-mile wide bowl of tulips will appear over the horizon tomorrow morning?
Pluck: Well, actually, no, I don’t.
MacCruiskeen: Oh?
Pluck: I do believe the sun will rise tomorrow. For some reason, I just can’t help myself. I see that, rationally, I shouldn’t believe. But while I realize my belief is wholly irrational, I can’t stop believing.

Hume’s explanation of why we believe

Like Pluck, Hume admitted that we can’t help but believe that the sun will rise tomorrow, that chairs will continue to support our weight, and so on. On Hume’s view, our minds are so constituted that when we are exposed to a regularity, we have no choice but to believe the regularity will continue. Belief is a sort of involuntary, knee-jerk response to the patterns we have experienced.

[[TEXT BOX: THINKING TOOLS: Reasons and causes - two ways of explaining why people believe what they do.
Hume’s explanation of why we believe the sun will rise tomorrow does not, of course, give us the slightest reason to suppose that this beliefs is actually true.
It is useful to distinguish two very different ways in which we can “give the reason” why someone believes something. We may give the grounds or evidence that a person has for holding a belief. Or we may explain what has caused this person to believe what they do.
It’s important to realize that to offer a causal explanation of a belief is not necessarily to offer any sort of rational justification for holding it. Consider these explanations:

Tom believes he is a teapot because he was hypnotized during a stage act.
Anne believes in fairies because she is mentally ill.
Geoff believes in alien abduction because he was indoctrinated by the Blue Meanie cult.

These are purely causal explanations. To point out that someone believes they are a teapot because they were hypnotized into having that belief during the course of a hypnotist’s routine is not to provide the slightest grounds for supposing that this belief is true.
The following explanation, on the other hand, gives the subject’s grounds for belief (which is not yet to say they are good grounds):

Tom believes in astrology because he finds newspaper astrology predictions are quite often correct.

Interestingly, ask the hypnotized person why they believe they are a teapot and chances are they will be unable to answer. The correct causalexplanation is unavailable to them (assuming they don’t know they have been hypnotized). But nor will they be able to offer a convincing justification for their belief. They may simply find themselves “stuck” with a belief that they may themselves recognize is irrational.
Hume admits that, similarly, his explanation of why we believe the sun will rise tomorrow does not supply the slightest grounds for supposing that this belief is true. Indeed, we have no such grounds. It is, again, a belief we simply find ourselves “stuck” with.END OF TEXT BOX]


If Hume is right, the belief that the sun will rise tomorrow is as unjustified as the belief that a million mile wide bowl of tulips will appear over the horizon instead. We suppose the second belief is insane. But if Hume is correct, the first belief is actually no more rational. This conclusion strikes us as utterly absurd, of course. But Hume even explains why it strikes us as absurd: we are made in such a way that we can’t help but reason inductively. We can’t help having these irrational beliefs.
Hume’s argument continues to perplex both philosophers and scientists. There’s still no consensus about whether Hume is right. Some believe that we have no choice but to embrace Hume’s sceptical conclusion about the unobserved. Others believe that the conclusion is clearly absurd. But then the onus is on these defenders of “common sense” to show precisely whatis wrong with Hume’s argument. No one has yet succeeded in doing this (or at least no one has succeeded in convincing a majority of philosophers that they have done so).

What to read next?

This chapter introduces scepticism about the unobserved. Chapter XX “The Strange Case of the Rational Dentist” and XX “Brain-snatched” introduce other forms of scepticism: scepticism concerning other minds and scepticism about the external world.

In chpt XX “Who Knows?” I discuss the possibility that justification not required for knowledge. Might this suggestion help us to defeat the sceptic?

Further reading

A good discussion of the problem of induction can be found in:

·      Chris Horner and Emrys Westacott, Thinking Through Philosophy (Cambridge: Cambridge University Press: 2000), chpt. 4.

A simple but effective introduction to the problem of induction and to some of the philosophical issues surrounding science is provided by:

·      Nigel Warburton, Philosophy: The Basics, second edition (London: Routledge, 1995), chpt. 5.

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