When we think that we have solved a problem, we naturally adopt our new set of theories in preference to the old set. That is why science, regarded as explanation-seeking and problem-solving, raises no ‘problem of induction’. There is no mystery about why we should feel compelled tentatively to accept an explanation when it is the best explanation we can think of.
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.
problem of induction Since scientific theories cannot be logically justified by observation, what does justify them?
induction A fictitious process by which general theories were supposed to be obtained from, or justified by, accumulated observations.
problem A problem exists when it seems that some of our theories, especially the explanations they contain, seem inadequate and worth trying to improve.
criticism Rational criticism compares rival theories with the aim of finding which of them offers the best explanations according to the criteria inherent in the problem.
science The purpose of science is to understand reality through explanations. The characteristic (though not the only) method of criticism used in science is experimental testing.
experimental test An experiment whose outcome may falsify one or more of a set of rival theories.
In fundamental areas of science, observations of ever smaller, more subtle effects are driving us to ever more momentous conclusions about the nature of reality. Yet these conclusions cannot be deduced by pure logic from the observations. So what makes them compelling? This is the ‘problem of induction’. According to inductivism, scientific theories are discovered by extrapolating the results of observations, and justified when corroborating observations are obtained. In fact, inductive reasoning is invalid, and it is impossible to extrapolate observations unless one already has an explanatory framework for them. But the refutation of inductivism, and also the real solution of the problem of induction, depends on recognizing that science is a process not of deriving predictions from observations, but of finding explanations. We seek explanations when we encounter a problem with existing ones. We then embark on a problem-solving process. New explanatory theories begin as unjustified conjectures, which are criticized and compared according to the criteria inherent in the problem. Those that fail to survive this criticism are abandoned. The survivors become the new prevailing theories, some of which are themselves problematic and so lead us to seek even better explanations. The whole process resembles biological evolution.
Thus we acquire ever more knowledge of reality by solving problems and finding better explanations. But when all is said and done, problems and explanations are located within the human mind, which owes its reasoning power to a fallible brain, and its supply of information to fallible senses. What, then, entitles a human mind to draw conclusions about objective, external reality from its own purely subjective experience and reason?
4
Criteria for Reality
The great physicist Galileo Galilei, who was arguably also the first physicist in the modern sense, made many discoveries not only in physics itself but also in the methodology of science. He revived the ancient idea of expressing general theories about nature in mathematical form, and improved upon it by developing the method of systematic experimental testing, which characterizes science as we know it. He aptly called such tests cimenti, or ‘ordeals’. He was one of the first to use telescopes to study celestial objects, and he collected and analysed evidence for the heliocentric theory, the theory that the Earth moves in orbit around the Sun and spins about its own axis. He is best known for his advocacy of that theory, and for the bitter conflict with the Church into which that advocacy brought him. In 1633 the Inquisition tried him for heresy, and forced him under the threat of torture to kneel and read aloud a long, abject recantation saying that he ‘abjured, cursed and detested’ the heliocentric theory. (Legend has it, probably incorrectly, that as he rose to his feet he muttered the words ‘eppur si muove…’, meaning ‘and yet, it does move…’.) Despite his recantation, he was convicted and sentenced to house arrest, under which he remained for the rest of his life. Although this punishment was comparatively lenient, it achieved its purpose handsomely. As Jacob Bronowski put it:
The result was silence among Catholic scientists everywhere from then on … The effect of the trial and of the imprisonment was to put a total stop to the scientific tradition in the Mediterranean. (The Ascent of Man, p. 218)
How could a dispute about the layout of the solar system have such far-reaching consequences, and why did the participants pursue it so passionately? Because the real dispute was not about whether the solar system had one layout rather than another: it was about Galileo’s brilliant advocacy of a new and dangerous way of thinking about reality. Not about the existence of reality, for both Galileo and the Church believed in realism, the common-sense view that an external physical universe really does exist and does affect our senses, including senses enhanced by instruments such as telescopes. Where Galileo differed was in his conception of the relationship between physical reality on the one hand, and human ideas, observations and reason on the other. He believed that the universe could be understood in terms of universal, mathematically formulated laws, and that reliable knowledge of these laws was accessible to human beings if they applied his method of mathematical formulation and systematic experimental testing. As he put it, ‘the Book of Nature is written in mathematical symbols’. This was in conscious comparison with that other Book on which it was more conventional to rely.
Galileo understood that if his method was indeed reliable, then wherever it was applicable its conclusions had to be preferable to those obtained by any other method. Therefore he insisted that scientific reasoning took precedence not only over intuition and common sense, but also over religious doctrine and revelation. It was specifically that idea, and not the heliocentric theory as such, that the authorities considered dangerous. (And they were right, for if any idea can be said to have initiated the scientific revolution and the Enlightenment, and to have provided the secular foundation of modern civilization, it is that one.) It was forbidden to ‘hold or defend’ the heliocentric theory as an explanation of the appearance of the night sky. But using the heliocentric theory, writing about it, holding it ‘as a mathematical supposition’ or defending it as a method of making predictions were all permitted. That was why Galileo’s book Dialogue of the Two Chief World Systems, which compared the heliocentric theory with the official geocentric theory, had been cleared for printing by the Church censors. The Pope had even acquiesced in advance to Galileo’s writing such a book (though at the trial a misleading document was produced, claiming that Galileo had been forbidden to discuss the issue at all).
It is an interesting historical footnote that in Galileo’s time it was not yet indisputable that the heliocentric theory gave better predictions than the geocentric theory. The available observations were not very accurate. Ad hoc modifications had been proposed to improve the accuracy of the geocentric theory, and it was hard to quantify the predictive powers of the two rival theories. Furthermore, when it comes to details, there is more than one heliocentric theory. Galileo believed that the planets move in circles, while in fact their orbits are very nearly ellipses. So the data did not fit the particular heliocentric theory that Galileo was defending either. (So much, then, for his having been convinced by accumulated observations!) But for all that, the Church took no position in this controversy. The Inquisition did not care where the planets appeared to be; what they cared about was reality. They cared where the planets really were, and they wanted to understand the planets through explanations, just as Galileo did. Instrumentalists and positivists would say that since the Church was perfectly willing to accept Galileo’s observational predictions, further argument between them was pointless, and that his muttering ‘eppur si muove’ was strictly meaningless. But Galileo knew better, and so did the Inquisition. When they denied the reliability of scientific knowledge, it was precisely the explanatory part of that knowledge that they had in mind.