Category: .Deutsch, David

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]

What makes life special

We can see that the ancient idea that living matter has special physical properties was almost true: it is not living matter but knowledge-bearing matter that is physically special. Within one universe it looks irregular; across universes it has a regular structure, like a crystal in the multiverse. [190]

A theory’s mark of Cain

In general, perverse but unrefuted theories which one can propose off the cuff fall roughly into two categories. There are theories that postulate unobservable entities, such as particles that do not interact with any other matter. They can be rejected for solving nothing (‘Occam’s razor’, if you like). And there are theories, like yours, that predict unexplained observable anomalies. They can be rejected for solving nothing and spoiling existing solutions. It is not, I hasten to add, that they conflict with existing observations. It is that they remove the explanatory power from existing theories by asser­ting that the predictions of those theories have exceptions, but not explaining how. [160-1]

On the shoulders of giants

The reverence that philosophers show for the historical sources of ideas is very perverse, you know. In science we do not consider the discoverer of a theory to have any special insight into it. On the contrary, we hardly ever consult original sources. They invariably become obsolete, as the problem-situations that prompted them are transformed by the discoveries themselves. For example, most relativity theorists today understand Einstein’s theory better than he did. The founders of quantum theory made a complete mess of understanding their own theory. Such shaky beginnings are to be expected; and when we stand upon the shoulders of giants, it may not be all that hard to see further than they did. But in any case, surely it is more interesting to argue about what the truth is, than about what some particular thinker, however great, did or did not think. [157]

Corroboration and refutation

Well, Popperians might speak of a theory being the best available for use in practice, given a certain problem-situation. And the most important features of a problem-situation are: what theories and explanations are in contention, what arguments have been advanced, and what theories have been refuted. ‘Corroboration’ is not just the confirmation of the winning theory. It requires the experimental refutation of rival theories. Confirming instances in themselves have no significance. …

Under inductivism, observation was supposed to be primary. One imagined a mass of past observations from which the theory was supposed to be induced, and observations also constituted the evidence which somehow justified the theory. In the Popperian picture of scientific progress, it is not observations but problems, controversies, theories and criticism that are primary. Experiments are designed and performed only to resolve controversies. Therefore only experimental results that actually do refute a theory – and not just any theory, it must have been a genuine contender in a rational controversy – constitute ‘corroboration’. And so it is only those experiments that provide evidence for the reliability of the winning theory. …

And even then, the ‘reliability’ that corroboration confers is not absolute but only relative to the other contending theories. That is, we expect the strategy of relying on corroborated theories to select the best theories from those that are proposed. That is a sufficient basis for action. We do not need (and could not validly get) any assurance about how good even the best proposed course of action will be. Furthermore, we may always be mistaken, but so what? We cannot use theories that have yet to be proposed; nor can we correct errors that we cannot yet see. [148-9]

It’s all about argument

Only argument ever justifies anything – tentatively, of course. All theorizing is subject to error, and all that. But still, argu­ment can sometimes justify theories. That is what argument is for. [146]