Scientific Method - The Traditional View and Popper's View

From: Popper by Bryan Magee pp. 18 -

The word 'law, is ambiguous and anyone who talks of a natural or scientific law being 'broken' is confusing the use of the word. A law of nature, is not prescriptive but descriptive. It tells us what happens - for instance that water boils at 100 degrees Ccntigrade. As such it purports to be nothing more than a statement of what - given certain initial conditions, such as that there is a body of water and that it is heated - occurs. It may be true or false, but it cannot be 'broken', for it is not a command: water is not being ordered to boil at 100 degrees Ccntigrade. The pre-scientific belief that it was (by some god) is the reason for the unfortunate ambiguity: the laws of nature were thought to bc commands of the gods. But nowadays no one would dispute that they are not prescriptions of any kind, to be 'kept' or 'obeyed' or 'broken', but explanatory statements of a general character which purport to be factual and must therefore be modified or abandoned if found to be inaccurate.

Thc search for natural laws has long been seen as the central task of science, at least since Newton. The way scientists were supposed to proceed was first systematically descibed by Francis Bacon. Although his formulation has been much qualified, added to, refined and sophisticated since his day, something in the tradition he pioneered has been accepted by nearly all scientifically minded people from thc seventeenth century to the twentieth. It goes like this, the scientist begins by carrying out experiments whose aim it is to make carefully controlled and meticulously measured observations at some point on the frontier between our knowledge and our ignorance. He systematically records his findings, perhaps publishes them, and in the course of time he and other workers in the field accumulate a lot of shared and reliable data. As this grows, general features begin to emerge, and individuals start to formulate general hypotheses - statements of lawlike character which fit all the known facts and explain how they are causally related to each other. The individual scientist tries to confirm his hypothesis by finding evidence which will support it. If he succeeds in verifying it he has discovered another scientific law which will unlock more of the secrets of nature. The new seam is then worked - that is to say the new discovery is applied wherever it is tbought it might yield fresh information. Thus the existing stock of scientific knowledge is added to, and the frontier of our ignonace pushed back And the process begins again on the new frontier.

The method of basing general statements on accumulated observations of specific instances is known as induction and is seen as the hallmark of science. In other words the use of the inductive method is seen as the criterion of demarcation between science and non-science. Scientific statements, being based on observational and experimental evidence - based, in short, on the facts - are contrasted with statements of all other kinds, whether based on authoity, or emotion, or tradition, or speculation, or prejudice, or habit, or any other foundation, as alone providing sure and certain knowledge. Science is the corpus of such knowledge, and the growth of science consists in the endless process of adding new certainties to the body of existing ones.

Some awkward questions about this were raised by David Hume at the University of Edinburgh, Scotland. He pointed out that no number of singular observation statements, however large, could logically entail an unrestictedly general statement. If I observe that event A is attended by event B on one occasion, it does not logically follow that it will be attended by it on any other occasion. Nor would it follow from two such observations - nor from twenty, nor from two thousand. If it happens often enough, said Hume, I may come to expect that the next A will be attended by a B, but this is a fact of psychology, not of logic. The sun may have risen again after every past day, but this does not entail that it will rise tomorrow.

1f someone says: 'Ah yes, but we can in fact predict the precise time at which the sun will rise tomorrow from the established laws of physics, as applied to conditions as we have them at this moment', we can answer him twice over. First, the fact that the laws of physics have been found to hold good in the past does not logically entail that they will continue to hold good in the future. Second, the laws of physics are themselves general statements which are not logically entailed by the observed instances, however numerous, which are adduced in their support. So this attempt to justify induction begs the question by takin'g the validity of induction for granted. The whole of our science assumes the regularity of nature assumes that the future will be like the past in all these respects in which natural laws are taken to operate - yet there is no way in which this assumption can be secured. It cannot be established by observation, since we cannot observe future events. And it cannot be established by logical argument, since from the fact that all past futures have resembled past pasts it does not follow that all future futures will resemble future pasts. Thc conclusion Hume himself came to was that although there is no way of demonstrating the validity of inductive procedures we are so constituted psychologically that we cannot help thinking in terms of them. And since they seem to work in practice we go along with tbem.

Tbe problem of induction, which has been called Hume's problem', has baffled philosophers from his time to our own. C D. Broad described it as tbe skeleton in tbe cupboard of philosophy. Bertrand Russell wrote in his History of Western Philosophy (pp. 699 - 700): 'Hume has proven that pure empiricism is not a sufficient basis for science. But if this one principle (induction) is admitted, everything else can proceed in accordance with the theory that all our knowledge is based on experience.What these arguments prove- and I do not think the proof can be controverted - Is, that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle, science is impossible.'

That the whole of science, of all things, should rest on foundations whose validity it is impossible to demonstrate has been found uniquely embarrassing. It has turned many empirical philosophers into sceptics, or irrationalists, or mystics. Some it has led to religion. Virtually all have felt, bound to admit that, strictly speaking, scientific laws cannot be proved and are therefore not certain. Even so, their degree of probability is raised by each confirming instance; and in addition to the whole of the known past every moment of the world's continuance brings countless billions of confirming instances - and never ~ single counter example. So, if not certain, they are probable to the highest degree which it is possible to conceive; and in practice, if not in theory, this is indistinguishable from certainty. Nearly all scientists, in so far as they reflect on the logical foundations of what they are doing. go along with this attitude. To them the overwhelmingly important thing is that science delivers the goods - it works, it produces a never-ending stream of useful results: and rather than go on banging their heads against the brick wall of an apparently insoluble logical problem they prefer to get on with doing more science and getting more results. The more philosophically reflective among them, however, have been deeply troubled. For them, and for philosophers generally, induction has presented an unsolved problem at
the very foundations of human knowledge, and until such time as it might be solved the whole of science, however intrinsically consistent and extrinsically useful, must be conceded to be somehow floatng in mid air, unfixed to terra firma.

Popper's seminal achievement has been to offer an acceptable solution to the problem of induction. In doing this he has rejected the whole orthodox view of scientific method outlined so far in this chapter and replaced it with another. Popper's solution begins by pointing to a logical asymmetry between verification and falsification. To express it in terms of the logic of statements: although no number of observation statements reporting observations of white swans allows us logically to derive the universal statement 'All swans are white', one single observation statement, reporting one single observation of a black swan, allows us logically to derive the statement 'Not all swans are white.' In this important logical sense empirical generalizations, though not verifiable. are falsifiable. This means that scientific laws are testable in spite of being unprovable: they can be tested by systematic attempts to refute them.

From the beginning Popper drew the distinction between the logic of the situation and the implied methodology. The Logic is utterly simple: if a single black swan has been observed then it cannot be the case that 'All swans are White'. In logic, if we look at the relation between statements - a scientfic law is conclusively falsifiable although it is not conclusively verifiable.

Popper also says we should not abandon our theories lightly for this would involve too uncritical an attitude towards tests, and would mean that the theories theselves were not tested as rigorously as they should be. So although Popper is what might be called a naive falsificationist at the level of logic he is a highly critical falsificationist at the level of methodology.

Let us now consider falsification in a practical example. Suppose we start by believing. as most of us are taught at school, that it is a scientific law that water boils at 100. Centigrade. No number of confirming instances will prove this, but we can nevertheless test it by searching for circumstances in which it does not hold. This alone challenges us to think of things which, so far as we know, no one else has hit on. If we are at all imaginative we shall soon discover that water does not boil at 100 Centigrade in closed vessels. So what we thought was a scientific law turns out not to be one. Now at this point we could take a wrong turning. We could salvage our original inductive statement by narrowing its empirical content to 'Water boils at 100 Centigrade in open vessels.' And we could then look systematically for a refutation of our second statement. And if we were rather more imaginative than before we should find it at high altitudes: so that to salvage our second statement we would have to narrow its empirical content to 'Water boils at 100 Centigrade in open vessels at sea-level atmospheric pressure' And we could then begin a systematic attempt to refute our third statement. And so on. In this way we might regard ourselves as pinning down ever more and more precisely our knowledge about the boiling point of water. But to proceed in this way, through a series of statements with vanishing empirical content, would be to miss the most important features of the situation. For when we discovered tbat water did not boil at 100 Centigrade in closed vessels we had our foot on the threshold of the most important kind of discovery of all, namely the discovery of a new problem: 'Why not ?' We are challenged now to produce a hypothesis altogether richer than our original. simple statement, a hypothesis which explains both why water boils at 100 Centigrade in open vessels and also why it does not in closed ones: and the richer the hypothesis the more it will telll us about the relationship between the two situations and the more precisely it will enable us to calculate different boiling points. In other words we will now have a second formulation which has not less empirical content than our first but very considerably more and we should proceed to look systematically for a refutadon of that. And if we were to find that this formulation was falsified, we should have to search for a third hypothesis richer still, which would explain why each of our first two hypotheses worked, up to the point it did, but then broke down at that point. This new formulation would have to tell us more about the world than we yet know. This, in a nutshell, is Popper's view of the way knowledge advances.

We are now in a position to see why it is inherent in Popper's view that what we call our knowledge is of its nature provisional, and permanently so. At no stage are we able to prove that what we now 'know' is true, and it is always possible that it will turn out to be false. Indeed, it is an elementary fact about the intellectual history of mankind that most of what has been 'known' at one time or another has eventually turned out to be not the case. So it is a profound mistake to try to do what scientists and philosophers have almost always tried to do, namely prove the truth of a theory, or justify our belief in a theory. since it is to attempt the logically impossible. What we can do, however, and this is of the highest possible importance, is to justify our preference for one theory over another. In our successive examples about the boiling of water we were never able to show that our current theory was true, but we were at each stage able to show that it was preferable to our preceding theory. This is the characteristic situation in any of the sciences at any given time. The popular notion that the sciences are bodies of established fact is entirely mistaken. Nothing in science is permanently established, nothing unalterable, and indeed science is quite clearly changing all the time and not through the accretion of new certainties. If we are rational we shall always base our decisions and expectations on 'the best of our knowledge', as the popular phrase so rightly has it, and provisionally assume the 'truth' of that knowledge for practical purposes because it is the least insecure foundation available, but we shall never lose sight of the fact that at any time experience may show it to be wrong and require us to revise it.

Popper's notion of 'the truth' is very like this: our concern in the pursuit of knowledge is to get closer and closer to the truth. and we may even know that we have made an advance, but we can never know if we have reached our goal. 'We cannot identify science with truth, for we think that both Newton's and Einstein's theories belong to science, but they cannot both be true and they may well both be false." One of his favourite quotations is from the pre-Socratic philosopher Xenophanes, which he translates as follows:

The gods did not reveal from the beginning,
All things to us. but in the course of time
Through seeking we may learn and know things better.
But as for certain truth, no man has known it
Nor shall he know it, neither of the gods
Nor yet of all the things of which I speak.
For even if by chance he were to utter
The final truth, he would himself not know it:
For all is but a woven web of guesses.

Popper's view of science slides on to its history like a glove. But the particular event which brought home to him the permanently conjectural nature of scientific knowledge was Einstein's challenge to Newton. Newtonian physics was the most successful and important scientific theory ever to be advanced and accepted. Everything in the observable world seemed to confirm it: for more than two centuries its laws were corroborated not just by observation but by creative use, for they became the foundation of Westerr science and technology, yielding marvellously accurate predictions of everything from the existence of new planets down to the movements of the tides and the workings of machinery. If anything was knowledge, this was: the most secure and certain knowledge man had ever acquired about his physical envtronment. If any sdentific laws had been verified inductively as Laws of Nature, these had, by countless billions of observations and experiments. To generation after generation of Western man they were taught as definitivc incorrigible fact. Yet after all this, at the beginning of our own century, a theory different from Newton's was put forward by Einstein. Opinions about the truth of Einstein's theory varied, but its claims to serious attention could not be denied, nor its claim to go beyond Newton's theory in the range of its applications. And this itself is the point. All the observational evidence which fitted Newton s theory (and some about which Newton's theory said nothing) also fitted Einstein's. (In fact it can be logically demonstrated - and had been long ago, by Leibniz - that any finite number of observations can be accommodated within an indefimtely large number of different explanations.) The world had simply been wrong in believing that all that untold evidence proved Newton's theory. (Yet a whole era of civilization had been based on it, with unprecedented material success. If this amount of verification and inductive support did not prove the truth of a theory. what ever could?) And Popper realized that nothing could. He saw that no theory could ever be relied on to be the final truth The most we can ever say is that it is supported by every observation so far and yields more and more precise, predictions than any known alternative.

Popper's moral sentiments about political matters lie with the assumption in our century (20th) that rationality, logic and science should guide leaders into choosing for a society one which is centrally organized, and planned and ordered as a whole. Popper has suggested that this, besides being authoritarian, rests on a mistaken and superior conception of science.

In addition, falsificationism would point to a society which is 'open' and pluralistic, within which incompatible views are expressed and conflicting aims pursued; a society in which everyone is free to investigate problem situations and propose solutions; a society in which everyone is free to criticize the proposed solutions of others, and most importantly, those of the government, whether in prospect or application; and above all a society in which the government's policies are changed in light of the criticism.