I have long been a critic of induction. The trouble with the word “induction” is that it is used in many different ways. As part of my continuing series on how science works, I want to explain here what I am criticizing, and what I am not criticizing.

## Baconian induction

Sir Francis Bacon suggested used the term “induction” in his recommendations on investigating the natural world. As described by Wikipedia, his method called for:

procedures for isolating and further investigating the form nature, or cause, of a phenomenon, including the method of agreement, method of difference, and method of concomitant variation.

When I criticize induction, I am not in any way criticizing Baconian induction, as represented in that statement. Indeed, the idea of isolating causes is an important part of the scientific method.

## Philosophic induction

A typical example of induction, as presented in philosophic instruction, goes:

All the many crows I have seen have been black. Therefore all crows are black.

I shall use the expression “philosophic induction” to refer to kind of induction thus suggested. It is this philosophic induction, that I criticize. This is the form of induction that has often been criticized as irrational. It is the form of induction that was defended by David Stove, in his book “The Rationality of Induction“.

The important ingredient of philosophic induction, is that it is supposed to yield true statements.

I have not seen any evidence that scientists use philosophic induction. I’m not sure where the idea of philosophic induction originated. Perhaps philosophers were wanting to provide a simplified statement of induction that got to the core of Bacon’s ideas. But, if that were the intention, then I’m afraid that they have thrown out the baby and kept only the bath water.

## Statistical induction

There’s a statistical version of philosophical induction. An example of that would be:

Almost all of the many crows that I have seen were black. Therefore the next crow that I see will probably be black.

I see this as completely rational. It differs from philosophic induction, in that it does not assert the truth of a general statement. It only asserts the predictive power of a general statement, and assert it as uncertain but probable.

We do often use statistical induction. When we do statistical hypothesis testing, we actually come up with numeric values for the probability of successful predictions. Our ability to deduce probabilities suggests that statistical induction should be considered to be an example of deductive inference rather than an example of inductive inference.

## The “black swan” example

I sometimes see comments about the alleged refutation of “all swans are white”. Here’s an example

To cite a famous example, before the time of Captain Cook’s voyage to Australia, Europeans had observed a great many swans, and every one of them was white. Thus, up to that time Europeans had very strong inductive evidence to support the claim that all swans are white. Then Captain Cook discovered black swans in Australia.

I found that example on p. 216 of “Understanding Arguments: An Introduction to Informal Logic“. Similar examples can be found in other books.

I mention this example, because it could be used to criticize statistical induction, and not just philosophic induction.

I find the argument absurd. Captain Cook did not discover black swans in Australia. He discovered black waterfowl of unknown species that resembled swans. If we are going to say that what Captain Cook saw refuted “swans are white”, then we might just as well say that the sight of a lion refutes the generalization “leopards have spots.” The fact is that the Australian black swan is of a different genus and species from the swans known to Europeans. The members of Captain Cook’s crew could just as easily have decided to call it a “false swan.”

As a side point, I grew up in Perth, Western Australia, within walking distance to the Swan River. And we always referred to those birds as “Black Swans”. We never used only “swan” without the qualifying “black”.

## Bayesian philosophy

Bayes’ Theorem is an uncontroversial theorem in the theory of probability. It is used in statistical inference. Properly done, Bayesian inference is uncontroversial. What is controversial, however, is Bayesian philosophy. This seems to be the view that knowledge of the world is acquired by brain processes doing Bayesian inference on sensory data.

Personally, I consider Bayesian philosophy to be absurd.

## Trial and error

We sometimes make decisions based on trial and error methods. Scientists clearly do this. I do not consider it induction. As described by philosophers, induction is a method of finding true statements about the world. But trial and error is not concerned at all with truth, nor with statements about the world. It is concerned with method, with ways of doing things. And trial methods are evaluated on a pragmatic basis — how well they work — rather than on a truth basis.

Perhaps Popper intended his falsificationism to be an account of trial and error. However, Popper was concerned with questions of truth, rather than with what works. I’m a skeptic of falsificationism, as presented by Popper. However, I strongly favor the use of trial and error methods, where appropriate.

## Scientific laws

The underlying question, that induction is supposed to answer, is the question of how we come up with our scientific laws. And that’s where I find inductionism unpersuasive.

Some laws could be said to have arisen by what I have termed “statistical induction.” Boyle’s law is a good example. Boyle’s law is false, and it is well understood to be false by most physicists. It is important, as one of the ideal gas laws, because it is a good and useful approximation.

Laws that result from statistical induction are probably all false, but useful for making good predictions. However, not all scientific laws are of that kind. Some laws come out of theory. The theory itself has typically been well tested for its usefulness on the basis of trial and error. But the laws that arise from that theory are typically theoretical constructs and have not arisen by induction. Newton’s laws of motion would be examples of such theoretical laws.

## Conclusion

I have presented the general picture of how I see induction. I see science as being based on empirical evidence. However, the way that evidence is used is very different from what is suggested by philosophic induction.

I shall probably have a few more posts related to induction in this series on how science works.