Articles

Induction

This article is a brief summary of a problem I see with the claim that science of itself does not make metaphysical statements - it does not assert, for example, the reality of the things it observes.

Induction.

My "position" is that induction requires an axiom of order in observations which is no less metaphysical than the naive realist's belief in the reality of the objects which are observed. Please bear in mind that this article is something of a draft - and I am unlikely to be capable of re-writing it with more rigour. If it contains significant blunders, I'd like to know. And I apologise for the style - which is more of a rant thant I would like: that's because it started as a response to some things that were said on the 'net!

I started by thinking that since scientists obviously refer to their toys and pets as if they were real, science itself makes realist statements. However it soon became apparent that different people define science differently. It is not very useful to define it as what scientists think, as scientists all think different things. Likewise they all *do* different things - and it's not clear where the science stops and their personal habits begin. The same goes for what they say: there is no obvious dividing line between speaking about a theory and interpreting it. Unfortunately it is also misleading to define it by means of a philosophical model such as d-n, since there is no a priori guarantee that the result is going to be anything recognizable as science. (Experience would suggest this is actually rather unlikely.) So it would seem that the definitions game is not going to get anywhere.

Perhaps, though, it is not necessary. I originally objected to defining science by a philosophical model, but there is still some mileage in seeing what possible ways such a model could be incomplete. The simplistic answer is that science is innately realist, d-n does not explicitly mention reality, thus it is only good as far as it goes: it is not the whole picture. Of course, this argument founders without an independent definition of what science is. However, it occurred to me that there must be a good reason why scientists are often naive realists. If nature turned out to be capricious we might offer sacrifices to placate the energizing spirits but we could hardly investigate the world. Science would be impossible. However, science is possible, nature is not capricious, indeed it is highly ordered. Thus, rather than defining science as a realist pursuit, why not look at this orderliness of nature?

Science certainly finds order in nature. One may distinguish between different types of order. The universe is orderly as a whole - or so scientists tend to assume. It also yields orderly observations in well-defined experiments designed to elucidate particular features of the world: "physical laws". And, of course, there are systems which create order of their own which do not seem to need extra fundamental laws but are just things working in particular ways.

D-n hinges on the creation of laws by induction. Observations yield data; examination of the data suggests a covering law which is then tested against more data. It seems to me that, for this to be a good model of what science does, real observations need to be orderly enough for laws to emerge with reasonable regularity. Specifically a putative law is tested against further data - the assumption being that there is a consistency about nature which allows this. If scientists never discovered anything because their observations were never consistent, d-n would be a bad model. It would merely describe what would happen in a more orderly world. Thus d-n, in so far as it purports to be a model of science, contains a hidden assumption, that order is there and can be discovered. A true assumption, most people would agree, but an assumption nonetheless.

The defenders of d-n may well wish to rebutt the accusation of hidden assumptions. One way is to say "but science has found the world to be consistent" - which, if true, would make d-n a good model after all. However, I dispute the claim! To be more precise, I dispute that science as modelled by d-n could ever find out whether the world is consistent.

Science, as understood by a naive realist, relies on the world being orderly and, of course, finds its expectations fulfilled again and again - to nobody's surprise. But a hard-line d-ner has problems. He/she cannot invoke naive realism to justify expecting the world to be orderly. Instead he/she will invoke the principle of induction. Induction works in science, therefore it will continue to work. This is inductive reasoning applied to the (inductive) methods of science. Of course, the success of this process justifies the belief that the world is orderly. Unfortunately, this is not enough. In order to validate induction, one has to validate the methods for detecting order. In general, arguments are of the form "these observations cannot have arisen by chance, here is a plausible explanation". Such arguments rely on probability theory. Thus the d-n model relies on probability theory a priori.

The next step, then, is to justify probability theory. Recall that the hard-line d-ner has no recourse to naive realism from which probability arises naturally. So, for him/her, probability theory must rest on the data that scientists accumulate. Does it make good predictions? Of course. But can we conclude that it will continue to do so? Yes, if we allow induction. For scientists that is fine - scientists can be realists at this point. For d-ners, probability theory rests on induction, which is what we are trying to justify by induction. This problem can be formulated as question-begging or as an infinite regress: neither is satisfactory.

I believe Quine has addressed this problem.

It remains, then, to see whether the model, d-n, could be shored up with an axiom - that observations are orderly. That is all very well, except that there is no logical reason why they have to be. We could live in an disorderly world. Thus the orderliness of observations is an ad-hoc (though usually hidden) axiom in d-n, just as surely as it is an implicit axiom in naive realist formulations of scientific theories.

My interpretation of this need for ad-hoc axioms is that either

D-n is, of course, powerless to decide *which* metaphysics describes ultimate reality, just as science is. But it very definitely imputes a property of orderliness to observations which is not entailed by either the existence of the observations themselves or by their consistency. Thus d-n does place certain requirements on its concommitant metaphysics. Laws which worked yesterday usually continue to work tomorrow. There is a permanence to laws which is also not entailed by the fact that one can retrodict. If one repeats the process and says "retrodiction confirmed the principle of induction yesterday thus it will continue to do so tomorrow" it leads straight to the infinite regress.

A law about the permanance of laws may, or may not, be significantly different from imputing existence to the entities referred to by the laws, but to my mind they are indistinguishable. There again, although I am realist, it is realism with a caviat - we could all be brains in a vat, or less fancifully, as Einstein noted: science cannot possibly tell what is ultimately real. My argument about d-n is that it is just as metaphysical as my realism.

Derek Potter