Let us look at the grounds upon which we could rationally move from observed events to the unobserved events. Deductive reasoning, or reasoning concerning ‘relations of ideas’, would not work, as it is perfectly possible that the movement between the observed and the unobserved could fail. For example, imagine a chicken which has been fed by a farmer every day of its life. The chicken will obviously assume that it will also be fed tomorrow, when in fact the next day the farmer kills the chicken. Evidently here, the extrapolation has failed and it cannot be a matter of pure logic. Moral reasoning (previously also stated as ‘matter of fact’ or inductive reasoning) also fails to allow for a movement from the observed to the unobserved. Causation is the only thing enabling us to infer one thing from another; hence all factual inference is based upon causation. Knowledge of causal relations is founded on experience. A priori, we can know nothing of causation. Such inference from experienced events is founded on what is known as the ‘uniformity principle’. This is a principle of similarity requiring that we extrapolate from our experience, assuming that future experiences will be similar. All factual inference is founded on this ‘uniformity principle’, whereas intuition or deductive reasoning cannot establish such a principle. Crucially, factual inference itself is dependent upon this ‘uniformity principle’, so attempts to establish one by the other is a circular and irrational argument. It can be argued that there is no rational basis on which we can assume uniformity will occur and therefore there are no rational grounds for factual inference or induction.
Hume’s ‘solution’ to his problem of arguments from experience involves the idea of a principle of custom and habit. He said that ‘wherever the repetition of any particular act or operation produces a propensity to renew the same act or operation, without being impelled by any reasoning or process of the understanding, we always say, that this propensity is the effect of Custom’ (Section V; Sceptical Solution of These Doubts, Part 1). He reasons that all inferences from experience are not effects of reasoning, but of custom, and that our experience becomes useful to us because we have custom as our guide, making us expect similar events to occur under similar circumstances to those which we have observed in the past. I would say that whilst Hume makes an interesting point here, I would not in any sense call it a solution, as I see custom as the reason why we infer (i) from (ii) in the first place. It does not necessarily get us any closer to deciding whether induction or rational or not.
Philosophers have provided many responses to Hume’s problem. One such response is Nelson Goodman’s ‘New Riddle of Induction’ (1955). Goodman argues that our ordinary inductive practices can lead us to draw inconsistent conclusions from the very same observational evidence. If induction does licence inconsistent conclusions in this way, then it can hardly be a good form of argument and can be seen to be irrational.
Consider the following, bearing in mind that the current time is ‘t’;
- All emeralds examined before t were green
- So, all emeralds are green
This looks like a perfectly good inductive inference; and the larger the number of past observations, the better the inference will be. However, let us introduce a new predicate ‘grue’;
X is grue if and only if either;
- x was examined before t and is green or
- x was not examined before t and is blue.
Whatever observational experience justifies premise (i) also justifies premise (i.i), that all emeralds examined before t were grue. If green is a good inductive inference, the following should also be a good inductive inference:
i.i) All emeralds examined before t were grue
ii.i) Therefore, all emeralds are grue
However, the conclusion of grue is inconsistent with the conclusion of green. (ii) implies that the next emerald we examine, or any emerald that we examine in the future, will be green, whereas (ii.i) implies that the next emerald we examime, or any emerald that we examine in the future, will be blue. It appears that induction of this kindcan support an infinite number of inconsistent predictions about the properties of the next emerald to be examined. If Goodman is correct, then induction cannot be a justified method of inference. Unsurprisingly, responses to Goodman have also been put forward. A first thought might be that ‘grue’ is not projectable (a predicate which is suitable for induction) because it is a complex predicate which can be defined in terms of green and blue. This suggests that a predicate is projectable if and only if it is not complex, in other words, it cannot be defined in terms of other predicates. This gives rise to two problems. Firstly, it is hard to see why being complex should make a predicate unsuitable for induction. Secondly, this notion of complexity doesn't yield the right results anyway. We can define a new predicate, bleen, as follows;
X is bleen if and only if either;
- x was examined before t and is blue
- x was not examined before t and is green
Bleen appears, like grue, to be another complex predicate which can be defined in terms of other predicates, and so our proposal says that it is not suitable for induction. However, not only can we define grue and bleen in terms of blue and green, but we also define blue and green in terms of grue and bleen. So according to our current proposal, blue and green are not projectable predicates either. Goodman has shown that induction licenses inconsistent conclusions, which may lead us to believe that induction is not rational.
P.F. Strawson also responded to Hume’s problem in his ‘Introduction to Logical Theory’ (1952), with the idea that beliefs are reasonable or rational if they are inductively well-supported (well-supported according to the normal, everyday standards embedded in our actual inductive practices). Referring back to my previous example, the fact that the sun has risen every day without exception provides very good inductive support for the claim that the sun will rise tomorrow; whereas the fact that I know one person called Mary, and she has brown hair, provides only weak inductive support for the claim that the next person that I meet called Mary will have brown hair. According to Strawson, to say that a belief is rational just means that it has good inductive support in this sense. However, as with most, if not all, of the responses to Hume, there is a problem with this approach. Is a belief which is rational in the sense of having good inductive support one that is backed by evidence which gives us reason to think that the belief is true? To clarify, are rational beliefs epistemically justified? Strawson gives us no reason to believe that they are and hence I do not believe that he has proved that induction can be rational.
In conclusion, I cannot honestly say that any of the philosophers I have examined have proved to my satisfaction that induction is rational. Hume puts forward interesting and plausible ideas to suggest that it cannot be rational due to the uniformity principle. It seems that there is no possible way of being sure that the sun will rise tomorrow, even if it has risen every day for millions of years. However, I would say that I am much more rational in believing in such an event that has occurred millions of times previously, than in believing that something will happen today just because I saw it for the first time yesterday. Expecting something to occur based on experiencing it only once may even be described as irrational. Evidently, there are degrees of rationality attached to induction. Instinctively, I wish to believe that induction is rational. If I did not believe that eating bread would give me nourishment and stop my hunger, based on the fact that it was done so hundreds of times before, I fear that I would not eat at all. If people could not rely on certain actions having similar outcomes to those they have observed and experienced before, no one would ever do anything and people would starve. We must to some degree believe that the knowledge we induce from our senses is rational, or we would not act in the way that we do. Therefore, although I have been offered no strong proof of the rationality of induction, I am satisfied that induction is rational to some degree, depending on the number of cases on which we are basing our inference.
Bibliography
David Hume – An Enquiry Concerning Human Understanding
Nelson Goodman – ‘The New Riddle of Induction’; Fact, Fiction and Forecast
Bertrand Russell – The Problems of Philosophy
P.F. Strawson – Introduction to logical theory
