5.2.4 The problem of induction

How shall we deal with the intractable problem of induction? As a means of predicting future events, it can’t be proved either deductively or inductively, which essentially exhausts opportunities for logical justification. Just because something has always occurred a certain way, you can't deduce that it will continue to do so (unless you take as a premise that the future will resemble the past, which just assumes exactly what you are trying to show). And you can't use induction to show that that future events will resemble events observed so far, because that also is what you are trying to prove. Just because induction has worked in the past doesn't mean that it will continue to work. Hume’s solution was to say that we should not refrain from making inductive inferences, but simply realize that we are not being governed by reason when we do so. As Bertrand Russell pointed out, the turkey believes it will be fed every morning until one day when the farmer comes with an axe instead of grain. It is habit, experience, and custom that allows us to rely on inference. We continue to use it because it is the most reliable technique available, despite having no ready proof.

Pragmatic approach
Pragmatists agree with Hume that there is no epistemic justification for induction. Instead, they present a practical explanation of why one is justified in using this method of inference. For one thing, it works better than any alternative, which is a primary selling point for most pragmatic positions. Induction will work if anything will work! Even though the future cannot be known, we can’t avoid having expectations about it. We would be wise to choose a method that would lead to success. One simple way of conceiving of the problem is in a truth table: The world either is uniform or it isn’t. And we can choose to use induction to predict future events or choose not to. Expanding on this exercise, we have six possibilities:

1. Nature really is uniform and regular:
1. induction would be a very reliable method for predicting future events.
2. using some method other than inductive reasoning would be ineffective.


2. or, nature is “somewhat” uniform, and frequently (but not always) evinces a pattern or connection between past and future:
1. induction is of some help, and works as a tool as often as nature chooses to be regular.
2. Non-inductive inference is as reliable as a wild guess.


3. or, nature really is not uniform at all, and there is no significant pattern or connection between past and future:
1. induction is of no help at all.
2. Non-inductive inference is also of no help at all.

Thus, the non-inductive method is useless no matter whether nature is always uniform, somewhat uniform, or chaotic. As for induction, it will certainly be helpful at least in the case when nature is uniform or mostly uniform. Thus, it is rational for us to prefer this method of inference since it is the only one that has any chance at all of being correct.

Avoiding Induction
Karl Popper attempted to resolve the question of induction and inference in science by abandoning the troublesome problem altogether. He had no issue with our inability to conclusively “prove” the validity of the inductive method. If scientific hypotheses (or even less formal everyday hypotheses) are stated in ways that allows them to be falsified, then we can use deductive techniques rather than induction to test them. This technique employs the logical form called “modus tollens”, which was discussed in the section, Moore’s Proof of an External Reality. Knowledge is gradually advanced as tests are made and failures are accounted for. A typical deductive formation of this argument would be along these lines:

• If (some hypothesis is true), then (we will observe some effect)
• We do not (observe some effect)
• Therefore (some hypothesis is true) is proven wrong

Applied to the sunrise, we would say, “If sunrises follow nighttime, the sun will rise tomorrow morning. We do not see the sun rise in the morning. Therefore theory about when the sun rises has been disproved”. As long as we continue to see sunrises after night has passed, we should not reject the theory. When tested many times in many conditions (for example, watch the sunrise from many spots on Earth), and it is never disproved, our confidence in the theory increases (but never becomes 100%). We tentatively and provisionally accept it, barring evidence to the contrary. We should, then continue having confidence in our theory. This is the essence of “falsifiability”. Science, then, could be thought of as a collection of hypotheses that have not been disproved (yet), but none has been conclusively proved, either.

Popper’s seemingly simple argument has not gone unchallenged, though. Among the professional philosophers of science, his view has never been taken as a serious alternative to the consensus theory of probabilistic induction (which takes into account the relevance and weight of evidence, Bayesian probability, and other mathematical representations originated by Carnap and others).

The primary element to consider in Popper’s view is that he believed that focusing on induction, or characterizing our generalizations about the future as exercises in induction was fundamentally mistaken. With finesse worthy of Wittgenstein, he “vanishes” the problem instead of solving it. Statements about how the future will unfold, according to Popper, do not actually employ induction, but instead rely on a technique that only superficially resembles it – the use of tentative hypotheses about future outcomes of our everyday experiments. We conduct an experiment of this sort every morning we look out the window expecting to see the sunrise. When we see it appear over the horizon, we can’t conclusively state that our theory about sunrises is true, but we can say that it has (once again) passed a well-constructed, though informal, test – that our theory can be retained as tentatively valid, useful, and worthy of further testing. We have strong confidence in it because of the countless confirmations of its predictions, and because it is never disproved. It has high verisimilitude, meaning, it correlates strongly with reality.

Like all scientific theories, it cannot ever be completely verified, but it can be quickly falsified. This may appear to share the structure of induction, but it stops short of the end result of induction in that we don’t use the results of this process to construct a general rule from individual outcomes. Instead, we simply can say that, once again, the theory has been corroborated - that it is a very useful and productive theory. We may also construct other theories that have similar logical structure to it regarding moon rises, the rising of Venus, etc. As they are verified, they each help to validate each other and boost our overall confidence in the set of interrelated theories. Popper referred to this as the “Method of conjectures and refutations”. If the sun were to stop rising and not resume its daily circuit across the sky, we would eventually abandon our theory of sunrises as having been falsified. In his view, we can’t accept any theories about the world as absolutely true, regardless of the amount of confirmation they have accumulated. But, those that are consistently corroborated can be made use of because of their eminent practicality and utility, keeping in mind that those same theories may need to be discarded if “eliminative evidence” accrues against them. Although this may seem like a facile manipulation of emphasis, it isn’t – this is exactly how scientists treat all scientific theories, no matter how well established.

Inference to the best explanation
Just as Popper got around the problem of induction by simply dismissing it, others circumvent its difficulties by getting around the issue in other creative ways. One such argument involves “inference to the best explanation” which was first introduced in the chapter on Modern Philosophy of Science. In this view, when one considers all the possibilities for how the future could unfold based on how the past and present events are manifested, the conclusion that the future will resemble the present requires the fewest assumptions, inventions, and stretches – employing Ockham’s Razor – to select the most likely explanation among any of several possible candidates. For example, if one sees a wet sidewalk it is reasonable to assume that it either rained or that the sprinklers were turned on, and less likely that a wave of water suddenly soaked it. Given experience and our knowledge of cause and effect, we can confidently make predictions (using inference) as to past causes of current events and current causes of future events. Drawing other conclusions would require greater leaps of improbability and would stretch credulity. Those who hold this position assert that it is imminently rational to assume that there is order and structure to the universe and that laws of causality actually work, and it would be highly impractical and wildly irrational to assume otherwise. Given the available choices, reliance on induction is the only one that makes any sense.

In fact, inference to the best explanation is used in everyday life far more frequently than either deduction or standard induction. It is how we draw conclusions from partial information. It is how we evaluate social interactions, judge intents of others, and understand potentially ambiguous statements. It is the primary tool of medicine, science, and all other forms of research and discovery. Deduction, although important, is principally a tool used in mathematics, logic, and philosophy.

In making these types of inference, we infer from the fact that a certain hypothesis would explain the evidence, to the truth of that hypothesis. In general, there will be several hypotheses that could potentially explain the evidence, so we systematically consider each one and reject all the least likely ones, leaving one remaining. In this manner, we are able to infer from the premise that a given hypothesis would provide a "better" explanation for the evidence than would any other hypothesis, to the conclusion that the given hypothesis is true. Accepting one of the less probable ones would simply be perverse.

Relax the burden of deductive proof
Another technique for dismissing the inductive problem is to admit and concede that using the strict rules required for deductive logic can’t be applied to induction, which is a fundamentally different and looser form of reasoning. The truth-preserving nature of deductive reasoning doesn’t work when used to justify a reasoning process in which the conclusions are, by definition, not certain. The conclusions of inductive arguments exceed the content of their premises – individual cases when used to construct a general rule necessarily go beyond themselves. However, with deductive arguments the premises contain everything necessary to systematically arrive at a definitive conclusion – the conclusion is inescapable. According to this argument, it is simply inappropriate to impose the tough standards of deduction on the fuzzier process of inductive logic.

As we have seen, inability to disprove a proposition does not render it true. For example:

• Although the Omphalos and Solipsistic positions are immune from disprove, all reasonable people agree they are beneath consideration.
• Russel's celestial teapot and the Flying Spaghetti Monster (blessed be his name) cannot be successfully defeated through argument. But, all satire aside, they are not really out there.
• The many varieties of supernatural mythology all create beings or histories or forces that are beyond the means of science to disprove. This doesn't make them real.
• There is an astronomical number of other incredible claims that bear similar logical structures to the above examples that also are unsusceptible to the power of logic. They are not, therefore, all true.

Likewise, no one can disprove this claim: "Reliance on induction is unwarranted". That does not automatically render this proposition true. If we can't disprove that "induction is groundless", reliance on induction is not, therefore, groundless. In fact, it is "probably true".

So, as with all assertions about the future (which are what both scientific theories and the inductive process concern themselves), they are beyond positive proof, though their conclusions (when supported by much confirming evidence) are well worth relying on. Interesting.

Probabilistic approach
For all of human history and as far back in time as we can collect evidence, the laws of cause and effect and the uniformity of nature have existed, unchanged. It is completely true that we can't use that past run to make conclusive statements about the future continuation of this consistent track record. However, it would be a gigantic leap of faith to assume that all of this will suddenly change as soon as I finish typing this sentence... See, nothing changed! If these laws were going to change at some time, and that time has not occurred in the last several billion years, there is not a shred of evidence that indicates that it is going to occur in the next few seconds, years, or centuries. From a purely probabilistic framework, the odds of everything being turned topsy-turvy exactly right now are very very very slim when measured against all of the opportunities for change that came and went in the past. For this reason it would be rational to assume the present trend is likely to continue, and highly irrational to assume it will not. For all practical purposes, for all of us, for the rest of our lives and the rest of humanity's existence, the chances of something like this that has never ever occurred and shows no sign of occurring now, are not likely to suddenly happen. Although we can't prove that the continuity of past/present/future will persist, a betting man could reliably count on it.

Even Deduction Cannot Be Proved
The problem that Induction has is that it cannot be proved deductively, and using induction to prove it would be circular. However, the same type of attack could be made on deduction, even though no one serious contemplates abandoning that reasoning technique. Lewis Carroll, the author of Alice in Wonderland, wrote in one of his stories that reaching conclusions by deduction can only be justified by an appeal to deductive inference, yet that doesn't dissuade us from believing that it is a valid methodology. We still consider it to be a rational approach to problem solving, so why would we have a higher standard for induction? If you were to try to convince a person of

• if p then q
• p
• therefore q

and they rejected it how would you respond? They might agree to "if p then q" and also agree to "p", but still not believe "q", because they don't accept the rules of deductive logic. The only response is to tell them that they are not being logical, that you can deductively show them their error, that they are not following the rules of deduction! But that is the issue - they don't accept the rules of deduction, and the only response you can give them is that they really ought to. So, we see that induction can be inductively justified after all, because even deduction can only be given a circular (in other words, deductive) justification.

People still debate the many ways of viewing the inductive process and its legitimacy. There are complex mathematical and probabilistic arguments too intricate to try to try to explain here. However, it is fairly clear that there is no clear cut and unambiguously convincing logical argument in its favor. We are left with one of several responses – to agree with Hume that there is no legitimate rule of inference as induction, and rely either on habit and experience. Or we can agree with Popper that we are mistaken in calling what we do "induction". Or with those who argue that requiring a proof of the validity of induction is not needed, requiring a less rigorous proof of a process that itself is less than purely rigorous. Also there is the argument that we don't require a non-deductive proof of deduction - we think of the rules of logic and deduction as fundamental and intrinsic to our concept of rationality. There is nothing more fundamental that we can use to demonstrate that deduction is justified. The same might also be said of induction - it is just fundamental to what it means to be "rational". It remains an interesting, and still unsolved, problem.

See chapter 2 of James Ladyman's Understanding Philosophy of Science, called "The problem of induction and other problems with inductivism" here for several more responses to the Problem of Induction. I just wish I would have read that before writing this chapter, because he does a much better job than I!