The Beginning of Infinity: Explanations That Transform the World (2 page)

Scientific theories are
explanations
: assertions about what is out there and how it behaves. Where do these theories come from? For
most of the history of science, it was mistakenly believed that we ‘derive’ them from the evidence of our senses – a philosophical doctrine known as
empiricism
:

Empiricism

For example, the philosopher John Locke wrote in 1689 that the mind is like ‘white paper’ on to which sensory experience writes, and that that is where all our knowledge of the physical world comes from. Another empiricist metaphor was that one could
read
knowledge from the ‘Book of Nature’ by making observations. Either way, the discoverer of knowledge is its passive recipient, not its creator.

But, in reality, scientific theories are not ‘derived’ from anything. We do not read them in nature, nor does nature write them into us. They are guesses – bold conjectures. Human minds create them by rearranging, combining, altering and adding to existing ideas with the intention of improving upon them. We do not begin with ‘white paper’ at birth, but with inborn expectations and intentions and an innate ability to improve upon them using thought and experience. Experience is indeed essential to science, but its role is different from that supposed by empiricism. It is not the source from which theories are derived. Its main use is to choose between theories that have already been guessed. That is what ‘learning from experience’ is.

However, that was not properly understood until the mid twentieth century with the work of the philosopher Karl Popper. So historically it was empiricism that first provided a plausible defence for experimental science as we now know it. Empiricist philosophers criticized and rejected traditional approaches to knowledge such as deference to the authority of holy books and other ancient writings, as well as human authorities such as priests and academics, and belief in traditional lore, rules of thumb and hearsay. Empiricism also contradicted the opposing and surprisingly persistent idea that the senses are little more than sources of error to be ignored. And it was optimistic, being all about
obtaining new knowledge, in contrast with the medieval fatalism that had expected everything important to be known already. Thus, despite being quite wrong about where scientific knowledge comes from, empiricism was a great step forward in both the philosophy and the history of science. Nevertheless, the question that sceptics (friendly and unfriendly) raised from the outset always remained: how can knowledge of what has
not
been experienced possibly be ‘derived’ from what
has
? What sort of thinking could possibly constitute a valid derivation of the one from the other? No one would expect to deduce the
geography
of Mars from a map of Earth, so why should we expect to be able to learn about
physics
on Mars from experiments done on Earth? Evidently, logical deduction alone would not do, because there is a logical gap: no amount of deduction applied to statements describing a set of experiences can reach a conclusion about anything other than those experiences.

The conventional wisdom was that the key is
repetition
: if one repeatedly has similar experiences under similar circumstances, then one is supposed to ‘extrapolate’ or ‘generalize’ that pattern and predict that it will continue. For instance, why do we expect the sun to rise tomorrow morning? Because in the past (so the argument goes) we have seen it do so whenever we have looked at the morning sky. From this we supposedly ‘derive’ the theory that under similar circumstances we shall always have that experience, or that we probably shall. On each occasion when that prediction comes true, and provided that it never fails, the probability that it will always come true is supposed to increase. Thus one supposedly obtains ever more reliable knowledge of the future from the past, and of the general from the particular. That alleged process was called ‘inductive inference’ or ‘induction’, and the doctrine that scientific theories are obtained in that way is called
inductivism
. To bridge the logical gap, some inductivists imagine that there is a principle of nature – the ‘principle of induction’ – that makes inductive inferences likely to be true. ‘The future will resemble the past’ is one popular version of this, and one could add ‘the distant resembles the near,’ ‘the unseen resembles the seen’ and so on.

But no one has ever managed to formulate a ‘principle of induction’ that is usable in practice for obtaining scientific theories from experiences. Historically, criticism of inductivism has focused on that
failure, and on the logical gap that cannot be bridged. But that lets inductivism off far too lightly. For it concedes inductivism’s two most serious misconceptions.

First, inductivism purports to explain how science obtains
predictions about experiences
. But most of our theoretical knowledge simply does not take that form. Scientific explanations are about reality, most of which does not consist of anyone’s experiences. Astrophysics is not primarily about
us
(what we shall see if we look at the sky), but about what stars are: their composition and what makes them shine, and how they formed, and the universal laws of physics under which that happened. Most of that has never been observed: no one has experienced a billion years, or a light year; no one could have been present at the Big Bang; no one will ever touch a law of physics – except in their minds, through theory. All our predictions of how things will
look
are deduced from such explanations of how things
are
. So inductivism fails even to address how we can know about stars and the universe, as distinct from just dots in the sky.

The second fundamental misconception in inductivism is that scientific theories predict that ‘the future will resemble the past’, and that ‘the unseen resembles the seen’ and so on. (Or that it ‘probably’ will.) But in reality the future is unlike the past, the unseen very different from the seen. Science often predicts – and brings about – phenomena spectacularly different from anything that has been experienced before. For millennia people dreamed about flying, but they experienced only falling. Then they discovered good explanatory theories about flying, and then they flew – in that order. Before 1945, no human being had ever observed a nuclear-fission (atomic-bomb) explosion; there may never have been one in the history of the universe. Yet the first such explosion, and the conditions under which it would occur, had been accurately predicted – but not from the assumption that the future would be like the past. Even sunrise – that favourite example of inductivists – is not always observed every twenty-four hours: when viewed from orbit it may happen every ninety minutes, or not at all. And that was known from theory long before anyone had ever orbited the Earth.

It is no defence of inductivism to point out that in all those cases the future still does ‘resemble the past’ in the sense that it obeys the
same underlying laws of nature. For that is an empty statement:
any
purported law of nature – true or false – about the future and the past is a claim that they ‘resemble’ each other by both conforming to that law. So that version of the ‘principle of induction’ could not be used to derive any theory or prediction from experience or anything else.

Even in everyday life we are well aware that the future is unlike the past, and are selective about which aspects of our experience we expect to be repeated. Before the year 2000, I had experienced thousands of times that if a calendar was properly maintained (and used the standard Gregorian system), then it displayed a year number beginning with ‘19’. Yet at midnight on 31 December 1999 I expected to have the experience of seeing a ‘20’ on every such calendar. I also expected that there would be a gap of 17,000 years before anyone experienced a ‘19’ under those conditions again. Neither I nor anyone else had ever observed such a ‘20’, nor such a gap, but our explanatory theories told us to expect them, and expect them we did.

As the ancient philosopher Heraclitus remarked, ‘No man ever steps in the same river twice, for it is not the same river and he is not the same man.’ So, when we remember seeing sunrise ‘repeatedly’ under ‘the same’ circumstances, we are tacitly relying on explanatory theories to tell us which combinations of variables in our experience we should interpret as being ‘repeated’ phenomena in the underlying reality, and which are local or irrelevant. For instance, theories about geometry and optics tell us not to expect to see a sunrise on a cloudy day, even if a sunrise is really happening in the unobserved world behind the clouds. Only from those explanatory theories do we know that failing to see the sun on such days does not amount to an experience of its not rising. Similarly, theory tells us that if we see sunrise reflected in a mirror, or in a video or a virtual-reality game, that does not count as seeing it twice. Thus the very idea that an experience has been repeated is not itself a sensory experience, but a theory.

So much for inductivism. And since inductivism is false, empiricism must be as well. For if one cannot derive predictions from experience, one certainly cannot derive explanations. Discovering a new explanation is inherently an act of creativity. To interpret dots in the sky as white-hot, million-kilometre spheres, one must first have thought of the idea of such spheres. And then one must explain why they look small and
cold and seem to move in lockstep around us and do not fall down. Such ideas do not create themselves, nor can they be mechanically derived from anything: they have to be guessed – after which they can be criticized and tested. To the extent that experiencing dots ‘writes’ something into our brains, it does not write explanations but only dots. Nor is nature a book: one could try to ‘read’ the dots in the sky for a lifetime – many lifetimes – without learning anything about what they really are.

Historically, that is exactly what happened. For millennia, most careful observers of the sky believed that the stars were lights embedded in a hollow, rotating ‘celestial sphere’ centred on the Earth (or that they were holes in the sphere, through which the light of heaven shone). This
geocentric
– Earth-centred – theory of the universe seemed to have been directly derived from experience, and repeatedly confirmed: anyone who looked up could ‘directly observe’ the celestial sphere, and the stars maintaining their relative positions on it and being held up just as the theory predicts. Yet in reality, the solar system is
heliocentric
– centred on the sun, not the Earth – and the Earth is not at rest but in complex motion. Although we first noticed a daily rotation by observing stars, it is not a property of the stars at all, but of the Earth, and of the observers who rotate with it. It is a classic example of the deceptiveness of the senses: the Earth looks and feels as though it is at rest beneath our feet, even though it is really rotating. As for the celestial sphere, despite being visible in broad daylight (as the sky), it does not exist at all.

The deceptiveness of the senses was always a problem for empiricism – and thereby, it seemed, for science. The empiricists’ best defence was that the senses cannot be deceptive in themselves. What misleads us are only the false interpretations that we place on appearances. That is indeed true – but only because our senses themselves do not say anything. Only our interpretations of them do, and those are very fallible. But the real key to science is that our explanatory theories – which include those interpretations – can be
improved
, through conjecture, criticism and testing.

Empiricism never did achieve its aim of liberating science from authority. It denied the legitimacy of traditional authorities, and that was salutary. But unfortunately it did this by setting up two other false
authorities: sensory experience and whatever fictitious process of ‘derivation’, such as induction, one imagines is used to extract theories from experience.

The misconception that knowledge needs authority to be genuine or reliable dates back to antiquity, and it still prevails. To this day, most courses in the philosophy of knowledge teach that knowledge is some form of
justified, true belief
, where ‘justified’ means designated as true (or at least ‘probable’) by reference to some authoritative source or touchstone of knowledge. Thus ‘how do we
know
. . . ?’ is transformed into ‘by what authority do we claim . . . ?’ The latter question is a chimera that may well have wasted more philosophers’ time and effort than any other idea. It converts the quest for truth into a quest for certainty (a feeling) or for endorsement (a social status). This misconception is called
justificationism.

The opposing position – namely the recognition that there are no authoritative sources of knowledge, nor any reliable means of justifying ideas as being true or probable – is called
fallibilism
. To believers in the justified-true-belief theory of knowledge, this recognition is the occasion for despair or cynicism, because to them it means that knowledge is unattainable. But to those of us for whom creating knowledge means understanding better what is really there, and how it really behaves and why, fallibilism is part of the very means by which this is achieved. Fallibilists expect even their best and most fundamental explanations to contain misconceptions in addition to truth, and so they are predisposed to try to change them for the better. In contrast, the logic of justificationism is to seek (and typically, to believe that one has found) ways of securing ideas
against
change. Moreover, the logic of fallibilism is that one not only seeks to correct the misconceptions of the past, but hopes in the future to find and change mistaken ideas that no one today questions or finds problematic. So it is fallibilism, not mere rejection of authority, that is essential for the initiation of unlimited knowledge growth – the beginning of infinity.