Philosophy Club

The Problem of Induction

Introduction

Practically of all of our reasoning falls into one or other of two categories: deductive or inductive. Here's an example of deductive reasoning:

1. All humans are mortal.
2. Plato is human.
3. Plato is mortal.

(1),(2) and (3) form a deductive argument. (1) and (2) are called the premises and (3) is called the conclusion. The above argument is an example of a valid argument The main feature of deductively valid arguments is that they are demonstrative. This means that if the premises are true then the conclusion must be true. It is contradictory for the premises to be true and the conclusion to be false. That's all I'm going to say about deduction. I want to discuss induction. Here's an example of an inductive argument:

1. Zebra(1) has stripes.
2. Zebra(2) has stripes.
3. Zebra(3) has stripes.
. .
. .
. .
1000. Zebra(1000) has stripes

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Therefore all zebras have stripes.

Inductive arguments typically move from particular to general - from a limited number of past observations of zebras we derive a general conclusion about all zebras. The main point, though, is that in contrast to deductive arguments, inductive arguments are non-demonstrative. In this case it is possible, even for what we think of as a good inductive argument, for the premises to be true and the conclusion to be false. The 1001st zebra may not have stripes. Much of our reasoning is inductive:

Watch out for funnel webs; they're always around at this time of year.
I'm bound to get a cold this winter; I get colds every winter.

Indeed a lot of our reasoning whether about sunrises, weather patterns, elections, human behaviour, food and so on is based on past experience. We form beliefs and expectations on the basis of past observation and experience. That is to say, we reason inductively.

The great Scottish philosopher David Hume, who lived in the !8th century, was sceptical about induction and raised what has become known as the Problem of Induction (Hume didn't actually use the word “induction”).

The Problem of Induction

Hume asked the question: What is the rational basis of inductive reasoning? Another way of putting this is: How can induction be rationally justified? In terms of our earlier example, the problem is this: Even if a suitably large number of zebras have been observed to have stripes, what reason have we for concluding that unobserved zebras have stripes? Why, that is, should we believe that the 1001st zebra will have stripes? Thus the problem of induction amounts to being able to show why it is that past experience provides a good reason for drawing general conclusions which go beyond the past experience. Drawing general conclusions based on a limited number of observations is risky. What if only zebras living in a certain region have stripes? Or perhaps only have them on a certain day of the week. Notice that there is no similar problem for deduction. If it's true that all humans are mortal and that Plato is human , than Plato must be mortal. To deny that Plato is mortal would be logically inconsistent with the truth of the two premises. The problem of induction arises just because there is no logical inconsistency in saying that 1000 (or10000000) zebras have stripes but that the 1001st (or 10000001st) will be stripeless.

Hume's argument

Consider now Hume's argument. Hume explains induction in the following way: “Those instances of which we have had no experience resemble those of which we have had experience, and that the course of nature continues always uniformly the same”. This can be expressed by saying that if a suitably large number of observed A's are without exception all B, then it is rational to infer that all A's are B's. On the basis of this principle we make inferences about unobserved black ravens, striped zebras, about metal expanding when heated, trees losing leaves in Autumn, the sun rising every day and so on. Hume rejects this principle of induction. Here's the argument. Hume begins by asking what justifies the conclusion that all A's are B's. The justification can't be deductive, he says, because there is no contradiction in asserting that all observed A's are B's but that some unobserved A is not B. Thus, for example, no matter how many striped zebras you have observed, the next one may not have stripes. But, Hume continues, if the inductive principle can't be deductively justified, then how? The only way, it seems, is on the evidence of past experience. Accordingly we point to the fact that in the past induction has worked with zebras, ravens, sunrises, heated metals, etc. Thus, we have good evidence, based on past experience, that induction will succeed in the future. The trouble is, as Hume pointed out, this reasoning is circular, for it is using induction to justify induction. To say that induction will be successful in the future because it has usually been successful in the past is to use inductive reasoning. And it is the rationality of this type of reasoning which Hume is questioning. To summarise Hume's argument:

1. Induction can be justified either deductively or on the basis of past experience.
2. Induction can't be justified deductively.
3. Induction can't be justified by past experience, for that would be circular.
4. Therefore, induction can't be rationally justified.

If Hume is right and induction has no rational foundation, then what if anything is it based on? According to Hume it is based on custom or habit. He believed that induction was more like a natural instinct than a process of reasoning.

Is Hume right about induction? Isn't the process of basing conclusions about the future on past observations fundamentally rational? Surely it's more than just custom or habit. And yet if we want to believe that then Hume's problem about induction has to be solved. But how?

Some attempts to solve the problem of induction

1. The use of probability: the idea here is that the conclusions of inductive arguments should be expressed in terms of probability. For example, rather than conclude that all zebras have stripes after observing say 1000 striped zebras, instead we should say “It is highly likely that all zebras have stripes”. We may even be able to assign numerical values to these probabilities. Thus, “The probability that all zebras have stripes is x”, where the value of x depends on how strong the evidence is. Does the use of probability in this context avoid the problem of induction? This attempted solution has problems of its own. Firstly, even if our inductive generalisations are modified by probability, they are still generalisations about the future which are based on past experience. The statement “All zebras are very probably striped” talks about unobserved zebras. What justifies this statement? Secondly, future populations whether of zebras, sunrises, metals or whatever are at least potentially infinite. Yet probability as used here is defined for finite sets - packs of cards, tosses of a die. So how can numerical values be assigned at all to probabilities concerning future zebras, ravens and the like?
   
   
2. The linguistic solution: according to this approach, the use of inductive reasoning is part of what we mean by the terms “rational” or “reasonable”. Thus, there can be no question of challenging the rationality of induction because to rely on induction is part of the very meaning of “rationality”. To ask whether induction is rational is much like asking whether the law is legal. If you have observed lots of striped zebras and none without stripes, and these observations have been made in a variety of circumstances, then it is part of what we mean by “rational” here to say that it is rational to believe that all zebras have stripes. Hume's challenge is simply misplaced.
   
   Does this proposed solution work? Who's to say that use of induction is part of the meaning of “rationality”? Can we really solve Hume's problem by appealing to the meaning of words?

Some questions for discussion

1. What distinguishes good from bad inductive arguments? Are there any rules for inductive reasoning?
2. Are there any non-inductive methods for reasoning about the future? How would these methods be justified?
3. If Hume is right and induction can't be rationally justified, what follows from this? Should we abandon induction?
4. If, as Hume says, induction is a natural instinct, then why should we worry about whether or not it is rational?
5. Is all scientific reasoning inductive?

References

1. David Hume, An Enquiry Concerning Human Understanding.
2. David Hume, A Treatise of Human Nature, Vol. 1

R.Neurath