Tag Archives: induction

Does the problem of induction defeat scientism?

Quillette magazine recently published a piece written by Spencer Hall giving: “The Philosophical Case against Scientism”. He begins:

Scientism is the claim that science is the only source of knowledge.

Let’s accept this definition, though it’s important to note that no-one defending such a thesis would interpret “science” in a narrow sense, but would regard it broadly as including the gathering of empirical evidence and rational analysis and conceptualising about that evidence. Thus, “scientism” would not, for example, deny that historians can generate knowledge, it would instead claim that they are doing so using methods that are pretty much the same as those used also by scientists. The differences in approach then arise from the pragmatics of what sort of evidence is accessible, not from their being distinct and separate “ways of knowing”.

The philosophical case that Hall presents is based on the problem of induction. No amount of observing a regularity proves that it will still hold tomorrow. The supposition that it will requires a “uniformity of nature” thesis that the future will be like the past, and since we cannot obtain empirical evidence from the future, that thesis — it is claimed — cannot be proven by science.

Hall then argues that science finds this “Past–Future Thesis” indispensable, but declares:

… either the PFT can be justified on non-empirical grounds, or it cannot be justified at all. If we accept the first horn, then we are conceding that scientific observation is not the only source of knowledge, and thus that scientism is false.

Hall then declares that the PFT is indeed true, and says:

… since there is no empirical way of defending PFT, we are forced to conclude that defending the assumption — and ultimately defending science itself — must rest on a philosophical foundation rather than an empirical one. And, thus, it follows that the claim that science is the only source of knowledge is false.

He then, rather derisively, declares this to be basic stuff akin to “remedial pre-algebra”, and finishes with: “If popular science writers wish to defend scientism, they would do well to demonstrate a modicum of understanding of the best arguments against their position”.

So, according to Hall’s argument, science is not the only source of knowledge because: (1) we know that the PFT is true, and (2) we know that from philosophy rather than from science.

But strikingly absent from Hall’s article is any philosophical defence of PFT. If one wants to use this example to show that philosophy can produce knowledge where science cannot, one first has to show that philosophy proves the PFT true. Yet Hall does not do this.

So this refutation of scientism fails right there. Showing that science cannot answer a question is only halfway to a refutation of scientism, since one then needs to show that some “other way of knowing” can produce a reliable answer.

But can the use of induction be defended? Personally I think it can, though as a matter of probability and likelihood, not of rigorous proof. (But then it is accepted that science never produces absolute proof, but only provisional, most-likely models that are better than any known alternatives.)

Hall indeed considers this, suggesting that: “… if we look at the past, we see that the future resembles the past all the time, so there’s an overwhelming probabilistic case for the PFT”, but then objecting that: “in appealing to what’s happened in the past as a guide to what will happen in the future, the would-be defender is assuming the very thing in question”.

But, we can consider the set of all events, past and future. And we can consider picking from that set, and encountering a sequence of picking one thousand white balls in a row and then the next ball being black. Obviously, the likelihood of that happening will depend on the probability distribution governing picking from the set, and — ex hypothesi — we don’t know that, since we don’t know about future events. But, that sequence will have some probability, and so we can consider the ensemble of all possible probability distributions.

If there are long periods of stasis of unknown length, it is more probable that one is somewhere within the period of stasis rather than exactly at its end. That follows simply because there is only one “slot” at the end of the sequence but lots of slots that are not at the end. Given a long sequence of normality, and picking our location on that sequence at random, it is more likely that we will be somewhere boring in the midst of the sequence, rather than at the highly particular “last day of normality” right at its end. In essence, we’re not using the past as a guide to the future, we’re using it as a guide to the present time, and asking whether it is unusual.

This analysis requires as to conceptualise a birds-eye overview of the timeline, but it doesn’t require any assumption about the future and it doesn’t require knowing the probability distribution of future events.

Of course it is no guarantee, and for all we know the probabilities could be such that normality is coming to an imminent end. But, the sub-set of probability distributions that make it likely that, after having picked a thousand white balls in a row, the next is a black, is much smaller than the set of all possible probability distributions. Only a very special and particular probability distribution could make it more likely that we are exactly at the end of such a sequence, rather than anywhere else along it. And, given that we don’t know the probability distribution, that is unlikely. So it is more likely than not that a sequence of stasis will continue with the next pick.

Again, this argument does not depend on assuming a uniform probability distribution, it only depends on their being a probability distribution, and on considering the super-set of all possible such probability distributions.

This line of reasoning has been proposed by Ray Solomonoff, who formalised and developed it into his “Formal Theory of Inductive Inference”. I’m not aware of any refutation of the argument and so I currently regard it as a sufficient resolution of the problem of induction. (Though part of the point of writing a blog piece about it is that, if it’s wrong, someone might tell me why!)

As regards scientism, a last question arises as to whether the above argument counts as “science” or as “philosophy”. It is certainly a rational analysis involving mathematical reasoning. It is not a rebuttal that can be observed empirically with a pair of binoculars or a microscope. But then no sensible account limits science to what can be directly observed. That’s only the half of it. Science is just as much about the concepts and rational analysis that make sense of the empirical world. Thus the above rebuttal is squarely within the domain of science, and so the attempt to defeat scientism fails.


Tools of science: Induction and Occam’s razor

As philosophers are fond of pointing out, induction is logically unsound: no track record, however lengthy, of observing that swans are white can validate the conclusion that all swans are certainly white and that no-one will ever encounter a black swan. Yet science uses induction every day, and it works. Our sampling of information is always partial, and yet that partial information tells us enough about the world around us to generate highly successful predictions and to produce engineering and technology that works. One can thus ask on what basis science uses the principle of induction.

Some would argue that induction is an example of a basic assumption of science that cannot be further justified. They might claim that all “ways of knowing” depend on such unverified assumptions, that science is just one example of such a system, and that other assumptions can lead to equally valid domains of understanding, such as theology.

A scientist, though, would argue that tools of science such as induction are not arbitrary, but are themselves justified by science. The scientific method is itself the product of science, deriving from a long historical process of working out what works. Thus, by bootstrapping, science arrives at methods that produce good predictions about the world, and produce engineering and technology that works. Continue reading