Successive explanations of the motions of planets have played an important role in the history of science. Copernicus’s heliocentric theory placed the planets and the Earth in circular orbits round the Sun. Kepler discovered that the orbits are ellipses rather than circles. Newton explained the ellipses through his inverse-square law of gravitational forces, and his theory was later used to predict that the mutual gravitational attraction of planets would cause small deviations from elliptical orbits. The observation of such deviations led to the discovery in 1846 of a new planet, Neptune, one of many discoveries that spectacularly corroborated Newton’s theory. Nevertheless, a few decades later Einstein’s general theory of relativity gave us a fundamentally different explanation of gravity, in terms of curved space and time, and thereby predicted slightly different motions again. For instance, it correctly predicted that every year the planet Mercury would drift by about one ten-thousandth of a degree away from where Newton’s theory said it should be. It also implied that starlight passing close to the Sun would be deflected twice as much by gravity as Newton’s theory would predict. The observation of this deflection by Arthur Eddington in 1919 is often deemed to mark the moment at which the Newtonian world-view ceased to be rationally tenable. (Ironically, modern reappraisals of the accuracy of Eddington’s experiment suggest that this may have been premature.) The experiment, which has since been repeated with great accuracy, involved measuring the positions of spots (the images of stars close to the limb of the Sun during an eclipse) on a photographic plate.
As astronomical predictions became more accurate, the differences between what successive theories predicted about the appearance of the night sky diminished. Ever more powerful telescopes and measuring instruments have had to be constructed to detect the differences. However, the explanations underlying these predictions have not been converging. On the contrary, as I have just outlined, there has been a succession of revolutionary changes. Thus observations of ever smaller physical effects have been forcing ever greater changes in our world-view. It may therefore seem that we are inferring ever grander conclusions from ever scantier evidence. What justifies these inferences? Can we be sure that just because a star appeared millimetrically displaced on Eddington’s photographic plate, space and time must be curved; or that because a photodetector at a certain position does not register a ‘hit’ in weak light, there must be parallel universes?
Indeed, what I have just said understates both the fragility and the indirectness of all experimental evidence. For we do not directly perceive the stars, spots on photographic plates, or any other external objects or events. We see things only when images of them appear on our retinas, and we do not perceive even those images until they have given rise to electrical impulses in our nerves, and those impulses have been received and interpreted by our brains. Thus the physical evidence that directly sways us, and causes us to adopt one theory or world-view rather than another, is less than millimetric: it is measured in thousandths of a millimetre (the separation of nerve fibres in the optic nerve), and in hundredths of a volt (the change in electric potential in our nerves that makes the difference between our perceiving one thing and perceiving another).
However, we do not accord equal significance to all our sensory impressions. In scientific experiments we go to great lengths to bring to our perceptions those aspects of external reality that we think might help us to distinguish between rival theories we are considering. Before we even make an observation, we decide carefully where and when we should look, and what we should look for. Often we use complex, specially constructed instruments, such as telescopes and photomultipliers. Yet however sophisticated the instruments we use, and however substantial the external causes to which we attribute their readings, we perceive those readings exclusively through our own sense organs. There is no getting away from the fact that we human beings are small creatures with only a few inaccurate, incomplete channels through which we receive all information from outside ourselves. We interpret this information as evidence of a large and complex external universe (or multiverse). But when we are weighing up this evidence, we are literally contemplating nothing more than patterns of weak electric current trickling through our own brains.
What justifies the inferences we draw from these patterns? It is certainly not a matter of logical deduction. There is no way of proving from these or from any other observations that the external universe, or multiverse, exists at all, let alone that the electric currents received by our brains stand in any particular relationship to it. Anything or everything that we perceive might be an illusion or a dream. Illusions and dreams are, after all, common. Solipsism, the theory that only one mind exists and that what appears to be external reality is only a dream taking place in that mind, cannot be logically disproved. Reality might consist of one person, presumably you, dreaming a lifetime’s experiences. Or it might consist of just you and me. Or just the planet Earth and its inhabitants. And if we dreamed evidence — any evidence — of the existence of other people, or other planets, or other universes, that would prove nothing about how many of those things there really are.
Since solipsism, and an infinity of related theories, are logically consistent with your perceiving any possible observational evidence, it follows that you can logically deduce nothing about reality from observational evidence. How, then, could I say that the observed behaviour of shadows ‘rules out’ the theory that there is only one universe, or that eclipse observations make the Newtonian world-view ‘rationally untenable’? How can that be so? If ‘ruling out’ does not mean ‘disproving’, what does it mean? Why should we feel compelled to change our world-view, or indeed any opinion at all, on account of something being ‘ruled out’ in that sense? This critique seems to cast doubt on the whole of science — on any reasoning about external reality that appeals to observational evidence. If scientific reasoning does not amount to sequences of logical deductions from the evidence, what does it amount to? Why should we accept its conclusions?
This is known as the ‘problem of induction’. The name derives from what was, for most of the history of science, the prevailing theory of how science works. The theory was that there exists, short of mathematical proof, a lesser but still worthy form of justification called induction. Induction was contrasted, on the one hand, with the supposedly perfect justification provided by deduction, and on the other hand with supposedly weaker philosophical or intuitive forms of reasoning that do not even have observational evidence to back them up. In the inductivist theory of scientific knowledge, observations play two roles: first, in the discovery of scientific theories, and second, in their justification. A theory is supposed to be discovered by ‘extrapolating’ or ‘generalizing’ the results of observations. Then, if large numbers of observations conform to the theory, and none deviates from it, the theory is supposed to be justified — made more believable, probable or reliable. The scheme is illustrated in Figure 3.1.
The inductivist analysis of my discussion of shadows would therefore go something like this: ‘We make a series of observations of shadows, and see interference phenomena (stage 1). The results conform to what would be expected if there existed parallel universes which affect one another in certain ways. But at first no one notices this. Eventually (stage 2) someone forms the generalization that interference will always be observed under the given circumstances, and thereby induces the theory that parallel universes are responsible. With every further observation of interference (stage 3) we become a little more convinced of that theory. After a sufficiently long sequence of such observations, and provided that none of them ever contradicts the theory, we conclude (stage 4) that the theory is true. Although we can never be absolutely sure, we are for practical purposes convinced.’