Hi folks,

Roger is currently tied up with a writing project, and being hounded with menaces by some large henchmen sent round by his publisher. Apparently, something about chapters being overdue. As he has gone into hiding I have volunteered to cover the blog for the next few weeks, and so to kick us off with a good weighty topic to frazzle the grey cells. So here we go with the problem of induction.

Although in essence inductive reasoning appears fairly simple (generate a list of probable explanations to explain an observed phenomenon) there are some underlying assumptions that are more problematic, and together these are known as the Problem of Induction. This is quite complex to grasp, so be warned, if you are new to these arguments, the following may give rise to headaches and palpitations. Here is a synopsis of the problem based on my feeble grasp of it:

Firstly there is the assumption of generalization. Induction requires we generalize about the properties of a set of objects based on repeated observations of particular instance. For example, we may infer that all the sheep are white, based on multiple instances of observing only white sheep, but this would later be found to be false, when we discover a black sheep. This would make any proposition derived from this generalization equally invalid (see the famous black sheep joke for a good example).

Secondly we have the assumption of uniformity. In inductive reasoning we presuppose that a sequence of events will occur in the future just as they have in the past (for example, the sun will rise in the east). This assumption itself relies on inductive reasoning, as the only way we can predict the future is by speculation based on past experience. This is circular reasoning by deriving a conclusion from premises that presuppose the conclusion. I.e. we are basically saying that the future will be the same as the past because in the past the future has been the same as the past!

Causality is the third area raised in criticism of inductive reasoning. Causality is a basic assumption of science and although we generally accept the concept of cause and effect, philosophically it is a challenging principle. Aristotle discussed ideas of deliberate (prior) and accidental causation, but the great thinker David Hume (1711-1776) outlined more detailed principles suggesting three basic elements.

If there is a causal link between A and B:

1) One must always precede the other (temporality),

2) The cause and effect must be in contact (spatial contiguity), and

3) There is some power in A to cause B (necessary connection).

This third point is philosophically a little more problematic in that it requires a theoretical element, “something that exists in the mind, not in the objects” (Hume, 2000). That is to say, a mental notion must be established linking the two types of object or event. Hume suggests it is our mind that makes this connection between objects or events when in reality they should be regarded as separate isolated instances. Relativity and quantum mechanics have also forced physicists to abandon their assumptions of causality, as they don’t seem to apply at the sub-atomic particle level. However they seem to remain valid for what happens at the level of human experience.

The major problem identified with inductive reasoning lies in the fact that to justify generalization or causality we use experience and inductive reasoning, creating a kind of circular logic, as we are justifying an inductive argument with more inductive reasoning.

The Raven Paradox

Carl Gustav Hempel (1905-1995) technically described this problem in logical terms with his Raven Paradox. Inductively to describe ravens we can hypothesize “all ravens are black” based on our observation of a subset of all ravens (as we cannot view them all). Over time with no non-black ravens encountered we accept this hypothesis. Therefore, by logical implication we can also state “everything that is not black is not a raven.”  Our hypothesis “all ravens are black” therefore has the equivalent form “all non-black things are non-ravens,” or more precisely, “if an object isn’t black then it is not a raven.” Logically, if every sighting of a black raven confirms our hypothesis, then every sighting of a non-black non-raven should equally confirm our hypothesis. This is where he argues inductive logic falls down, as if I look at my car, and see it is green, and it is not a raven, this confirms my hypothesis that all ravens are black! This of course makes no sense at all, but by the rules of logic, if I accept inductive hypotheses and confirmation by observation, then every observation (except one that refutes my hypothesis) confirms it, even when totally irrelevant.

The problem of induction is an argument frequently used by philosophers to “beat up” science, by suggesting that science is no better than alternative narratives for explaining the world. However, Karl Popper proposed a partial solution to the problem of induction with falsifiability, and  Charles Saunders Pierce gives us a pragmatic framework that appears quite effective at generating effective outcomes in the hypothetio-deductive model. So practically the problem of induction remains more philosophical than practical in its nature.

At worst the problem of induction represents a set of arguments that show inductive reasoning can only suggest a truthful explanation but cannot ensure it. We should certainly accept that there could well be alternative explanations for a phenomenon that we have not considered and be open to them.

Pragmatically, we should also note that we frequently use inductive reasoning everyday in general learning for the real world. For example, in learning to drive we learn how to start a car engine by turning a key, and generalize this technique to use in other models of cars. For science, we still rely on induction, and it is very much part of the creative (and arguably most interesting) part of scientific inquiry. The inductive conjecture about best treatment options is also a central part of the evidence based practice process in healthcare. Of course, scientists also discovered that inductive reasoning becomes much more powerful for systematic inquiry when combined with deductive reasoning.

Anyhow, in order to stimulate some creative thinking Roger and I are offering a fabulous prize (as yet to be determined, but surely some object of unimaginable wealth and beauty) for the most inventive solution to the problem of induction posted below. Go on you know you want to give it a go…

Onwards

Bernie

P.S. I got reunited with my luggage eventually, so take back all those bad thoughts I had about Virgin Atlantic.

References

Hempel, C. G. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: New York Free Press.

Hume, D. (2000). A treatise of human nature (originally published in 1739). Oxford: Oxford Philosophical Texts.

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