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Pragmatic instrumentalism has been feasible only because, in most branches of physics, quantum theory is not applied in its explanatory capacity. It is used only indirectly, in the testing of other theories, and only its predictions are needed. Thus generations of physicists have found it sufficient to regard interference processes, such as those that take place for a thousand-trillionth of a second when two elementary particles collide, as a ‘black box’: they prepare an input, and they observe an output. They use the equations of quantum theory to predict the one from the other, but they neither know nor care how the output comes about as a result of the input. However, there are two branches of physics where this attitude is impossible because the internal workings of the quantum-mechanical object constitute the entire subject-matter of that branch. Those branches are the quantum theory of computation, and quantum cosmology (the quantum theory of physical reality as a whole). After all, it would be a poor ‘theory of computation’ that never addressed issues of how the output is obtained from the input! And as for quantum cosmology, we can neither prepare an input at the beginning of the multiverse nor measure an output at the end. Its internal workings are all there is. For this reason, quantum theory is used in its full, multiverse form by the overwhelming majority of researchers in these two fields.

So Everett’s story is indeed that of an innovative young, researcher challenging a prevailing consensus and being largely ignored until, decades later, his view gradually becomes the new consensus. But the basis of Everett’s innovation was not a claim that the prevailing theory is false, but that it is true! The incumbents, far from being able to think only in terms of their own theory, were refusing to think in its terms, and were using it only instrumentally. Yet they had dropped the previous explanatory paradigm, classical physics, with scarcely a complaint as soon as a better theory was available.

Something of the same strange phenomenon has also occurred in the other three theories that provide the main strands of explanation of the fabric of reality: the theories of computation, evolution and knowledge. In all cases the theory that now prevails, though it has definitely displaced its predecessor and other rivals in the sense that it is being applied routinely in pragmatic ways, has nevertheless failed to become the new ‘paradigm’. That is, it has not been taken on board as a fundamental explanation of reality by those who work in the field.

The Turing principle, for instance, has hardly ever been seriously doubted as a pragmatic truth, at least in its weak forms (for example, that a universal computer could render any physically possible environment). Roger Penrose’s criticisms are a rare exception, for he understands that contradicting the Turing principle involves contemplating radically new theories in both physics and epistemology, and some interesting new assumptions about biology too. Neither Penrose nor anyone else has yet actually proposed any viable rival to the Turing principle, so it remains the prevailing fundamental theory of computation. Yet the proposition that artificial intelligence is possible in principle, which follows by simple logic from this prevailing theory, is by no means taken for granted. (An artificial intelligence is a computer program that possesses properties of the human mind including intelligence, consciousness, free will and emotions, but runs on hardware other than the human brain.) The possibility of artificial intelligence is bitterly contested by eminent philosophers (including, alas, Popper), scientists and mathematicians, and by at least one prominent computer scientist. But few of these opponents seem to understand that they are contradicting the acknowledged fundamental principle of a fundamental discipline. They contemplate no alternative foundations for the discipline, as Penrose does. It is as if they were denying the possibility that we could travel to Mars, without noticing that our best theories of engineering and physics say that we can. Thus they violate a basic tenet of rationality — that good explanations are not to be discarded lightly.

But it is not only the opponents of artificial intelligence who have failed to incorporate the Turing principle into their paradigm. Very few others have done so either. The fact that four decades passed after the principle was proposed before anyone investigated its implications for physics, and a further decade passed before quantum computation was discovered, bears witness to this. People were accepting and using the principle pragmatically within computer science, but it was not integrated with their overall world-view.

Popper’s epistemology has, in every pragmatic sense, become the prevailing theory of the nature and growth of scientific knowledge. When it comes to the rules for experiments in any field to be accepted as ‘scientific evidence’ by theoreticians in that field, or by respectable journals for publication, or by physicians for choosing between rival medical treatments, the modern watchwords are just as Popper would have them: experimental testing, exposure to criticism, theoretical explanation and the acknowledgement of fallibility in experimental procedures. In popular accounts of science, scientific theories tend to be presented more as bold conjectures than as inferences drawn from accumulated data, and the difference between science and (say) astrology is correctly explained in terms of testability rather than degree of confirmation. In school laboratories, ‘hypothesis formation and testing’ are the order of the day. No longer are pupils expected to ‘learn by experiment’, in the sense that I and my contemporaries were — that is, we were given some equipment and told what to do with it, but we were not told the theory that the results were supposed to conform to. It was hoped that we would induce it.

Despite being the prevailing theory in that sense, Popperian epistemology forms part of the world-view of very few people. The popularity of Kuhn’s theory of the succession of paradigms is one illustration of this. More seriously, very few philosophers agree with Popper’s claim that there is no longer a ‘problem of induction’ because we do not in fact obtain or justify theories from observations, but proceed by explanatory conjectures and refutations instead. It is not that many philosophers are inductivists, or have much disagreement with Popper’s description and prescription of scientific method, or believe that scientific theories are actually unsound because of their conjectural status. It is that they do not accept Popper’s explanation of how it all works. Here, again, is an echo of the Everett story. The majority view is that there is a fundamental philosophical problem with the Popperian methodology, even though science (wherever it was successful) has always followed it. Popper’s heretical innovation takes the form of a claim that the methodology has been valid all along.

Darwin’s theory of evolution is also the prevailing theory in its field, in the sense that no one seriously doubts that evolution through natural selection, acting on populations with random variations, is the ‘origin of species’ and of biological adaptation in general. No serious biologist or philosopher attributes the origin of species to divine creation or to Lamarckian evolution. (Lamarckism, an evolutionary theory that Darwinism superseded, was the analogue of inductivism. It attributed biological adaptations to the inheritance of characteristics that the organism had striven for and acquired during its life.) Yet, just as with the other three strands, objections to pure Darwinism as an explanation of the phenomena of the biosphere are numerous and widespread. One class of objections centres on the question whether in the history of the biosphere there has been enough time for such colossal complexity to have evolved by natural selection alone. No viable rival theory has been advanced to substantiate such objections, except conceivably the idea, of which the astronomers Fred Hoyle and Chandra Wickramasinghe are recent proponents, that the complex molecules on which life is based originated in outer space. But the point of such objections is not so much to contradict the Darwinian model as to claim that something fundamental remains unexplained in the matter of how the adaptations we observe in the biosphere came into being.