Induction is the idea that the past is a guide to the future. We believe the Sun will rise tomorrow because it has risen in the past.
Unfortunately, attempts to prove that induction is rational have failed. In An Enquiry Concerning Human Understanding, published in 1748, David Hume wrote:
“That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects.”
Hume is the philosopher most closely associated with the problem that induction cannot be logically justified. We cannot look at our past success at using induction as justification for using induction in the future, because such a justification assumes the principle of induction which it is trying to prove.
Usually, if a claim has not be justified by a rational argument, we discount the claim, and tend to think the claim is as likely false as true. For example, if someone claims that the inflation rate will go up above 3% next year, we’re not likely to believe them unless they provide reasons for believing their claim. If the principle of induction cannot be rationally justified, should we drop belief in the principle?
The short answer is no.
The principles of rationality cannot be rationally justified. Any justification one would produce would necessarily involve some sort of circular argument. Thus, some unjustifiable claims are unjustifiable because they aren’t rational, and some unjustifiable claims are unjustifiable because they are the bedrock of rational thought. The trick, of course, is knowing the difference.
The principles of rational thought, this bedrock, are very general principles that make rational thinking possible. One of the principles of rational thought is the principle of non-contradiction that I discussed in my last post. The principle of non-contradiction isn’t the kind of principle that we can give up and still be able to reason. Once we admit contradictory beliefs, we blur the distinctions between truth and falsehood. There literally becomes no distinction to be made between true and false, and so everything is simultaneously true and false. This leads us to a rather strange realization. The principle of non-contradiction cannot be proven true, but it also cannot be false. If the principle is false, then there is no such thing as “false”.
We have compelling reasons (albeit circular ones) to think that induction is one of these special principles. There are many accepted truths that are regarded as deductive, i.e., not dependent on experience. We tend to think that arithmetic is not something dependent upon experience. We typically think that the sum of 345 and 578 is not uncertain. It’s not something that experience will lie to us about. However, this isn’t true, strictly speaking. We don’t learn arithmetic except with plenty of experience. Moreover, if I asked you to multiply three 5 digit numbers, you would probably do the calculation more than once in order to be more likely to have avoided any errors. Even in simple logic problems, we need to rely on our experience to home-in on the correct answer.
If inductive inference is prohibited, then even our knowledge of arithmetic and logic principles goes out the window. Indeed, induction seems at least as vital to the enterprise of knowing things as is logical deduction.
Of course, all of this remains circular, but it fits in very well with what we know about human cognition. Humans are natural inductive reasoners. Neural networks in our brains perform induction at the cellular level, well below the level of consciousness. Neural networks learn from experience, and they automatically treat the past as a guide to the future. We couldn’t stop making inductive inferences if we wanted to.