Category Archive: The Fabric of Reality

Penguin: 1998.

Reality kicks back

James Boswell relates in his Life of Johnson how he and Dr Johnson were discussing Bishop Berkeley’s solipsistic theory of the non-existence of the material world. Boswell remarked that although no one believed the theory, no one could refute it either. Dr Johnson kicked a large rock and said, as his foot rebounded, ‘I refute it thus.’ Dr Johnson’s point was that Berkeley’s denial of the rock’s existence is incompatible with finding an explanation of the rebound that he himself felt. Solipsism cannot accommodate any explanation of why that experiment – or any other experiment – should have one outcome rather than another. To explain the effect that the rock had on him, Dr Johnson was forced to take a position on the nature of rocks. Were they part of an autonomous external relaity, or were they figments of his imagination? In the latter case he would have to conclude that ‘his imagination’ was itself a vast, complex, autonomous universe. […]

But Dr Johnson’s idea is more than a refutation of solipsism. It also illustrates the criterion for reality that is used in science, namely, if something can kick back, it exists. ‘Kicking back’ here does not necessraily mean that the alleged object is responding to being kicked – to being pysically affected as Dr Johnson’s rock was. It is enough that when we ‘kick’ something, the object affects us in ways that require independent explanation. For example, Galileo had no means of affecting planets, but he could affect the light that came from them. His equivalent of kicking the rock was refracting that light through the lenses of his telescopes and eyes. That light responded by ‘kicking’ his retina back. The way it kicked back allowed him to conclude not only that the light was real, but that the heliocentric planetary motions required to explain the patterns in which the light arrived were also real.

By the way, Dr Johnson did not directly kick the rock either. A person is a mind, not a body. The Dr Johnson who per­formed the experiment was a mind, and that mind directly ‘kicked’ only some nerves, which transmitted signals to muscles, which propelled his foot towards the rock. Shortly afterwards, Dr Johnson perceived being ‘kicked back’ by the rock, but again only indirectly, after the impact had set up a pressure pattern in his shoe, and then in his skin, and had then led to electrical impulses in his nerves, and so forth. Dr Johnson’s mind, like Galileo’s and everone else’s, ‘kicked’ nerves and was ‘kicked back’ by nerves, and inferred the existence and properties of reality from those interactions alone. What Dr Johnson was entitled to infer about reality depends on how he could best explain what had happened. For example, if the sensation had seemed to depend only on the extension of his leg, and not on external factors, then he would probably have concluded that it was a property of his leg, or of his mind alone. He might have been suffering from a disease which gave him a rebounding sensation whenver he extended his leg in a certain way. But in fact the rebounding depended on what the rock did, such as being in a certain place, which was in turn related to other effects that the rock had, such as being seen, or affecting other people who kicked it. Dr Johnson perceived these effects to be autonomous (independent of himself) and quite complicated. [86-7]

An explanatory gap

An analogous gap exists in Popperian epistemology. Its critics wonder why the scientific method works, or what justifies our reliance on the best scientific theories. This leads them to hanker after a principle of induction or something of the sort (though, as crypto-inductivists, they usually realize that such a principle would not explain or justify anything either). For Popperians to reply that there is no such thing as justification, or that it is never rational to rely on theories, is to provide no explanation. Popper even said that ‘no theory of knowledge should attempt to explain why we are success­ful in our attempts to explain things’ (Objective Knowledge p. 23). But, once we understand that the growth of human knowledge is a physical process, we see that it cannot be illegitimate to try to explain how and why it occurs. Episte­mology is a theory of (emergent) physics. It is a factual theory about the circumstances under which a certain physical quantity (knowledge) will or will not grow. The bare assertions of this theory are largely accepted. But we cannot possibly find an explanation of why they are true solely within the theory of knowledge per se. In that narrow sense, Popper was right. The explanation must involve quantum physics, the Turing principle and, as Popper himself stressed, the theory of evolution. [341]

Free will in the multiverse

Another mental attribute that is somehow associated with consciousness is free will. Free will is also notoriously difficult to understand in the classical world-picture. The difficulty of reconciling free will with physics is often attributed to deter­minism, but it is not determinism that is at fault. It is … classical spacetime. In spacetime, something happens to me at each particular moment in my future. Even if what will happen is unpredictable, it is already there, on the appropriate cross-section of spacetime. It makes no sense to speak of my ‘changing’ what is on that cross-section. Spacetime does not change, therefore one cannot, within spacetime physics, conceive of causes, effects, the openness of the future or free will.

Thus, replacing deterministic laws of motion by indeterministic (random) ones would do nothing to solve the problem of free will, so long as the laws remained classical. Freedom has nothing to do with randomness. We value our free will as the ability to express, in our actions, who we as individuals are. Who would value being random? What we think of as our free actions are not those that are random or undetermined but those that are largely determined by who we are, and what we think, and what is at issue. (Although they are largely determined, they may be highly unpredictable in practice for reasons of complexity.) [338]

Futile refutations

Dawkins has somehow become the public defender of scientific rationality against, of all things, creationism, and more generally against a pre-scientific world-view that has been obsolete since Galileo. The frustrating thing about all this is that, so long as the proponents of our best theories of the fabric of reality have to expend their intellectual energies in futile refutation and re-refutation of theories long known to be false, the state of our deepest knowledge cannot im­prove. [335]

Popper prevails

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. [331-2]

The scientific ideal

I have sometimes found myself on the minority side of fundamental scientific controversies. But I have never come across anything like a Kuhnian situation. Of course, as I have said, the majority of the scientific community is not always quite as open to criticism as it ideally should be. Nevertheless, the extent to which it adheres to ‘proper scientific prac­tice’ in the conduct of scientific research is nothing short of remarkable. You need only attend a research seminar in any fundamental field in the ‘hard’ sciences to see how strongly people’s behaviour as researchers differs from human behaviour in general. …

A senior politician might say in response to criticism from an obscure but ambitious party worker, ‘Whose side are you on, anyway?’ Even our professor, away from the research context (while delivering an undergraduate lecture, say) might well reply dismissively, ‘You’d better learn to walk before you can run. Read the textbook, and meanwhile don’t waste your time and ours.’ But in the research seminar any such response to criticism would cause a wave of embar­rassment to pass through the seminar room. People would avert their eyes and pretend to be diligently studying their notes. There would be smirks and sidelong glances. Everyone would be shocked by the sheer impropriety of such an attitude. In this situation, appeals to authority (at least, overt ones) are simply not acceptable, even when the most senior person in the entire field is addressing the most junior.

So the professor takes the student’s point seriously, and responds with a concise but adequate argument in defence of the disputed equation. The professor tries hard to show no sign of being irritated by criticism from so lowly a source. Most of the questions from the floor will have the form of criticisms which, if valid, would diminish or destroy the value of the professor’s life’s work. But bringing vigorous and diverse criticism to bear on accepted truths is one of the very pur­poses of the seminar. Everyone takes it for granted that the truth is not obvious, and that the obvious need not be true; that ideas are to be accepted or rejected according to their content and not their origin; that the greatest minds can easily make mistakes; and that the most trivial-seeming objection may be the key to a great new discovery. [325-6]

Objective growth of knowledge

So the growth of objective scientific knowledge cannot be explained in the Kuhnian picture. It is no good trying to pre­tend that successive explanations are better only in terms of their own paradigm. There are objective differences. We can fly, whereas for most of human history people could only dream of this. The ancients would not have been blind to the efficacy of our flying machines just because, within their paradigm, they could not conceive of how they work. The reason why we can fly is that we understand ‘what is really out there’ well enough to build flying machines. The reason why the ancients could not is that their understanding was objectively inferior to ours. [324]

The subject-matter of mathematics

Abstract entities that are complex and autonomous exist objectively and are part of the fabric of reality. There exist logically necessary truths about these entities, and these comprise the subject-matter of mathematics. However, such truths cannot be known with certainty. Proofs do not confer certainty upon their conclusions. The validity of a particular form of proof depends on the truth of our theories of the behaviour of the objects with which we perform the proof. Therefore mathematical knowledge is inherently derivative, depending entirely on our knowledge of physics. [256-7]

No, not even maths is certain

Thanks to Gödel, we know that there will never be a fixed method of determining whether a mathematical proposition is true, any more than there is a fixed way of determining whether a scientific theory is true. Nor will there ever be a fixed way of generating new mathematical knowledge. Therefore progress in mathematics will always depend on the exer­cise of creativity. It will always be possible, and necessary, for mathematicians to invent new types of proof. They will validate them by new arguments and by new modes of explanation depending on their ever improving understanding of the abstract entities involved. Gödel’s own theorems were a case in point: to prove them, he had to invent a new method of proof. I said the method was based on the ‘diagonal argument’, but Gödel extended that argument in a new way. Nothing had ever been proved in this way before; no rules of inference laid down by someone who had never seen Gödel’s method could possibly have been prescient enough to designate it as valid. Yet it is self-evidently valid. Where did this self-evidentness come from? It came from Gödel’s understanding of the nature of proof. Gödel’s proofs are as compelling as any in mathematics, but only if one first understands the explanation that accompanies them.

So explanation does, after all, play the same paramount role in pure mathematics as it does in science. Explaining and understanding the world – the physical world and the world of mathematical abstractions – is in both cases the object of the exercise. Proof and observation are merely means by which we check our explanations. [235-6]

Mere word usage

Do abstract, non-physical entities exist? Are they part of the fabric of reality? I am not interested here in issues of mere word usage. It is obvious that numbers, the laws of physics, and so on do ‘exist’ in some senses and not in others. The substantive question is this: how are we to understand such entities? Which of them are merely convenient forms of words, referring ultimately only to ordinary, physical reality? Which are merely ephemeral features of our culture? Which are arbitrary, like the rules of a trivial game that we need only look up? And which, if any, can be explained only in a way that attributes an independent existence to them? Things of this last type must be part of the fabric of reality as defined in this book, because one would have to understand them in order to understand everything that is understood. [222-3]

Older posts «