Science and Its Limits

The author of this book (What Science Knows) is one of the most interesting philosophers at present working in Australia. He is a Professor of Mathematics at the University of New South Wales. His book The Science of Conjecture was published in 2001. It considers the notions of evidence and probability before Pascal gave the first mathematical treatment of probability. It was immediately recognised as a work of wide and rigorous scholarship that, one might say, created its own field of investigation. Perhaps something of its width can be appreciated by the headings for the first chapter, “The Ancient Law of Proof”: Egypt and Mesopotamia, the Talmud, Roman Law, Proof and Presumption, Indian Law. In later chapters, selecting at random, the contributions of the Witch inquisitors, the Greek Sophists, the thinking about insurance, annuities, bets and dice in the ancient and medieval world, are all passed in review. And there is depth as well as width.

In 2003 Franklin published a history of philosophy in Australia. A worthy subject, but perhaps a little dull? Not quite. He summoned up the shade of Socrates and titled it Corrupting the Youth. It is easily the liveliest history of philosophy ever written. It is true that Melburnians complained that it was really little more than a history of Sydney philosophy, and undoubtedly they had a case. But much may be forgiven this enjoyable book (especially by Sydneysiders as this reviewer is).

Now we have from him a fascinating book, What Science Knows. It is a defence and apology for science (against postmodernists and more subtle opponents). But it should be noticed that he does not think that all our rational belief is science-based. He speaks already in his preface of “the essentially non-scientific character of some of the topics on which we most desire and need knowledge: consciousness and ethics”. (Naturalists such as myself would, of course, not stop at this point.)

A feature of the book is the inserted boxes that serve all sorts of purpose: to follow some interesting historical issues such as the case of the black swans (complete with a picture of such a swan); to give a mathematical treatment of some points of the argument, together with some formulas (optional); quotations from inductive sceptics and critics of inductive scepticism, including David Stove’s wonderfully witty send-up of Popper, Kuhn, Lakatos and Feyerabend’s re-writings of the sentence “Cook discovered Cook Strait”; a physics student’s T-shirt, and much more. The book has some excellent jokes of its own, my favourite being the useful dictum, “Concepts that need to be expressed in German are, in general, dubious.”

Franklin begins at the beginning: the low-level generalisations that must be rational if scientific knowledge is to have any empirical foundation. “All ravens are black” is a traditional example. “It’s in spring that the wheat comes up” is a further example that he gives. One can go on indefinitely with knowledge such as this. If it is not rational to accept such generalisations, the huge edifice of theoretical science lacks a proper observational foundation. Franklin favours logical probability, a notion to which he was introduced by David Stove, the most influential of Franklin’s philosophy teachers. The rather controversial idea is that the evidence of repeated observation of, say, ravens that are black without any counter-instances, creates an objective probability (though no certainty) that unobserved ravens will have the same colour of plumage. The discussion has to get rather technical. But Franklin also draws attention to an idea that many philosophers are currently attracted to: it is inference to the best explanation. (I am strongly attracted myself.) Applied to the case of the ravens it goes like this. The observed constant colour of ravens needs explanation. The best explanation would be that being a raven in some way ensures (or ensures the probability of) blackness of feather. This argument seems to me to be like the (idealised) village maiden: simple and good. The seminal idea that there are laws of nature with universal scope then rather naturally follows.

Logical probability or inference to the best explanation, or both, would seem to be hopeful ways of making progress with the philosophically famous problem of induction, bequeathed to present-day philosophers by David Hume. Franklin then turns to the congenial task of criticising the inductive sceptics and those he labels the Enemies of Science. Hume’s quite complex argument is criticised for simply assuming that probabilistic arguments cannot have weight. His sin is “deductivism” (Stove’s term), that is, the assuming that what is needed is some deductive proof that, for example, the sun will rise tomorrow.

At this point Franklin pauses to refute the canard that in the Middle Ages everybody thought the earth was flat. Aquinas for one, he points out, knew it was spherical. But, he says, the argument for Earth’s sphericity is fairly difficult to mount. It depends on an inference to the best explanation for various facts such as the detailed nature of eclipses. This, by the way, indicates that an inference to the best explanation (or abduction, as it is sometimes called) is not always so easy as it is in the case of the simple generalisations already discussed. It takes ingenuity to think the explanation up, and the explanation then needs, of course, to be tested by controlled experiments.

Now for the Enemies of Science. The first four are David Stove’s “four modern irrationalists”: Popper, Kuhn, Lakatos and Feyerabend. Popper, correctly I think, gets off relatively lightly. His stress on the importance of attempts to falsify theories is accepted by Franklin, but his deductivism, inherited from Hume, means that Popper cannot consistently claim rational belief for any scientific theory, something that he never seems to grasp. Kuhn’s notion of paradigm shifts that he thinks are involved in scientific advances, with the new ruling paradigm theories incomparable with the displaced theories, begins an unwholesome drift towards relativism about truth. Lakatos and Feyerabend are of less importance, I think.

Kuhn, in particular, unwittingly prepared the way for the intellectual horrors of the postmodernist attack on science. Franklin takes us through the entirely justified Sokal hoax. The physicist Alan Sokal wrote a nonsensical article on physics, lacing it with postmodernist slogans as bait. The article was accepted and published by a postmodernist journal. There were some lines of genuine poetry in the works of Ern Malley, but Sokal’s “paper” is straight garbage.

Franklin then sets himself to discuss the nature of science. He draws the all-important distinction between the empirical (observational) sciences and mathematics (together with logic). The latter may be called the rational sciences. Quite rightly I think, he rejects the very influential view of W.V. Quine that the distinction between the two sorts of discipline is one of degree alone. The mark of the rational sciences is that here we have proof, something that is largely absent in the empirical sciences. A mathematical theorem that, after careful checking, is pronounced proved, stays proved. (Recently illustrated by the long-sought proof of Fermat’s “Last theorem”.) Proof is epistemologically very secure. It is, says Franklin, “the gold standard of knowledge”. (He brushes aside an attempt by Lakatos to re-introduce doubt in this sphere.)

This epistemological security is, I think, not the only, or even the main, reason for the importance of mathematics. The laws of nature have turned out to be susceptible to mathematical modelling, something that has been clear since the work of Galileo, Descartes and Newton. I don’t think anybody knows how, or even has a good suggestion, to explain this. In 1960 the physicist Eugene Wigner published an article with a much quoted title: “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”. Perhaps we will just have to accept this effectiveness with “natural piety”.

Turning to empirical science, Franklin recognises the claim of physics to be the central empirical discipline. The equations of contemporary quantum physics, though probabilistic only, are perhaps more securely reliable under testing than any physical theory that has so far been proposed. There is something strange though. Though the predictions are spectacularly accurate, the interpretation of what they say is a scene of wild disagreement, with tests that would discriminate between views not at present available. Speaking as a philosopher, I’m tempted to say that the metaphysics behind the equations is obscure. What seems to be lacking is some “inference to an explanation” that is then testable. No doubt the mathematics behind it will be very difficult.

What is the subject matter of mathematics? It is, says Franklin, “structure, or pattern”. This view seems to be the answer that many other present philosophers of mathematics give, the word pattern taken from the philosopher of mathematics Michael Resnik. I’d suggest that the field of pure mathematics could be usefully circumscribed a little bit more. Using Gilbert Ryle and Jack Smart’s terminology, we can speak of topic neutral structure or pattern, structure that abstracts from all empirical material. This doesn’t mean, however, that we have to embrace a Platonic heaven of mathematical objects. A mathematical structure or pattern that was nowhere to be found in the space-time world—if such there is—would be a mere possibility that we don’t have to give any ontological credit to.

It remains true, as Franklin says, that “structure” and “pattern” are terms that are “vague, general and colourless”. He immediately remedies this by a most useful discussion of the key mathematical properties of symmetry and ratio that are perfectly abstract, but are imaginatively graspable.

As if this were not enough, as it would be for your ordinary author, there is much else that is of great value in this book. A clear discussion explains why thought experiments are useful in physics and other disciplines. A warning is given that where we have complex working systems, paradigm cases being the human body and still more our brains, deep scientific explanations are hard to come by. (Sleep is a baffling problem, but the studies of cognitive development in babies are praised for their successes.) New semi-mathematical disciplines are explained and assessed. Probability is discussed, and it is argued that the social sciences, while not as powerful as other scientific disciplines, make a real contribution. There is even a useful discussion of “actually existing science” with its grants and its refereeing system.

For those who are Christians, as Franklin is, the topic of evolution is a little delicate. He says that in this field his discussion is not comprehensive, nor does he seek to establish conclusions. But, he says: “The logical complexity of the theory itself makes it hard to establish the theory definitively.” He accepts that there is good evidence for “a common descent from primitive forms”. It is the Darwinian mechanism of evolution where intelligent dissent can be entertained. Can natural selection (along with sexual selection that seems to explain such a phenomenon as the peacock’s tail) explain the whole of evolutionary change? Franklin discusses one of the cases brought up by Michael Behe, the case of the flagellum, an organism that has evolved a propeller. This, Behe argues in detail, is something that Darwinian theory cannot explain. Franklin thinks Behe has quite a strong case.

I had the good fortune some years ago to hear Behe talk, at a symposium on evolution at the University of Notre Dame. I thought at the time that Darwinians were lucky to have such an informed and resourceful critic as Behe. Let the chips fall where they may. I’d myself look for some naturalistic explanation for the whole process of evolution, but let us not regard the case as closed.

A glutton for punishment, Franklin takes on the climate change debate as well. His summing up on the two topics is worth quoting in full:

In both evolution and climate change, the majority view of the scientific experts is well ahead. In neither case is there any known coherent alternative. But the complexities of the evidence are such that a higher standard of politeness to sceptics who raise serious problems would be well-advised.

(I have just now been reading Ian Plimer’s newly appeared book Heaven + Earth, which seems to show that the case for the global warming hypothesis is very weak indeed.)

I do have one difference with Franklin in connection with evolutionary theory, and that is his rather dim view of socio-biological theories. He is no doubt right to say that such theories are hypotheses, and are difficult to test. But I think what some have called “just so stories” are interesting and exciting intellectually. They show the empirical possibility of explanations of various matters. A case in point is the recently published book by Denis Dutton, The Art Instinct. Art is a very puzzling phenomenon to capture the lineaments of, and to explain its origin and continued relevance. Dutton gives us a Darwinian theory of art that seems to explain these things in a plausible naturalist manner. It came as a revelation to me. It is true that it is difficult to see how such a theory can be tested at present. But that may come in the future. In the meanwhile it is a suggested “inference to the best explanation” that a naturalist view of human nature should not be without.

This brings me to the last chapter of this book. Franklin argues that science has its limits. It cannot explain consciousness and it cannot explain morality. I will start by conceding that these are very difficult matters, where dogmatism should not be allowed to dictate the answer. The mind, and in particular the human mind, is very puzzling affair. The view I favour is that the mind can be identified with the working of the brain, and that working is a physical process obeying the same physical laws as the rest of nature. We are introspectively aware of our own mind, that much can be conceded to Descartes, who Franklin appeals to. But we are not directly aware what the mind is. It is not the sort of direct knowledge that would be likely to be thrown up in the course of evolution. It does not matter when one is engaged in practical tasks. But it seems a good scientific hypothesis that the mind’s complexity is a physical complexity, dauntingly complex but still physical. I’d agree, though, that the so-called secondary qualities, such as colour, sound, taste and smell, pose a difficult problem for my position. But they don’t seem to be the sort of phenomena on which we can base a worldview.

In discussing morality Franklin appeals to Hume’s view that no ought can be deduced from what is. This is indeed a clever attempt to turn the tables on the naturalist, using the great naturalist’s great weapon. But is Hume a reliable ally for Franklin? Can one not say that here Hume is still a deductivist as he was when he was thinking about induction? Franklin points out that there is some evidence that humans seem to have a moral sense. One might hope to link this sense, if it exists, with the conditions of human flourishing. But why should we be too worried about the fact that moral principles cannot be deduced from human nature?

Regardless of these metaphysical disputes, here is an apology for science that is intelligent, informed, yet nuanced and engagingly presented. It deserves to be widely read.

D.M. Armstrong is Emeritus Professor of Philosophy at the University of Sydney.