EXPERIMENT, IMAGINATION AND MEANING Inductive and Hypothetico-deductive Method in Science D. W. Theobald Dept of Chemistry, UMIST, Monchester I Vision and technique Bacon, Hume and Mill . . Philosophical problems for hypothetico-deduction . . . . . . 59 . . . . . . .. . . . . . . 50 . . . . . . . . .. . . 51 Testing in science . . .. .. . . . . . . . . . . 57 Hypotheses Chemistry and scientific method 65 .. . . .. .. . . . . . . . . 61 . . .. . . . . . . References . . .. . . . . .. . . . . . . . . 66 We had the experience but missed the meaning, And approach to the meaning restores the experience In a different form, ... T. S. Eliot, The Dry Salvages The moment we reflect philosophically upon the knowledge we have of the world about us, two questions emerge.One, how do we acquire such know- ledge? And two, how do we guarantee that what passes for knowledge is in fact knowledge? The first is a question about discovery, the second a question about justification and proof. Of course these are strictly speaking philosophi- cal questions, but the answers to them are of interest, indeed importance, to scientists. To explain this a little further, let us take a simple example, an example which we shall return to frequently throughout this essay. Suppose we are interested in rusting, both from a theoretical point of view and perhaps with the practical aim of preventing its occurrence and the inconvenience it causes. First we shall want to find out the conditions under which rusting occurs so that we can discover its causes, and then we shall require some procedure for establishing or proving that we have found out correctly.And the questions I am asking are-one, what are the procedures we use for discovery, and two, what are our methods of proof? How do we make, and how do we check up on our discoveries ? Various answers have been given to these questions by many philosophers and scientists from Bacon1 in the sixteenth century and Mi112 in the nineteenth, to Popper3 and Hanson4 among others in the present century. Nowadays the discussion usually revolves around the question whether science works inside an inductive mould as Bacon and Mill appeared to believe, or inside an hypothetico-deductive mould as Popper and others maintain. Perhaps I should give the terms ‘inductivd and ‘hypothetico-deductive’ some brief preliminary explanation at once.According to inductive method, causal relationships are claimed to be dis- coverable from the repeated coincidence of certain observable properties. Thus, observational generalizations, such as that rusting is always noticed when water is present, are supposed to entitle us to assert for example, that water is a cause of rust. Induction starts with no causal commitment. The 49 Theobald 4 inductivist is entirely open-minded about the causes of rusting before he starts observing. Causes he believes, will emerge from observations without teasing. Hypothetico-deductive method on the other hand, starts with a causal hypo- thesis about rusting, such as that water is always required, and then proceeds via the deduction of observable consequences to subject this hypothesis to the knock-down argument of designed, experimental test.The hypothetico- deductivist then, is not entirely open-minded about the causes of rust when he starts observing. Causes, he believes, are revealed only by teasing. A good deal of philosophical and scientific opinion nowadays is directed squarely against inductive method, witness Popper’s Logic of scientzjic discovery3 and Meda- war’s more recent attack Induction and intuition in scienti3c thought.5 My own view, which I hope will emerge during the rest of this essay, is that it would be wrong to suppose that there was a single scientific method appro- priate to all stages in the development of a scientific enquiry.Scientific know- ledge is often the product of both induction and hypothetico-deduction, but used at different moments in an investigation. In this essay I want to examine some aspects of both inductive and hypothetico-deductive method to see whether or not they separately constitute adequate methods of discovery and proof. Fuller and more systematic accounts can be found in the works cited in the bibliography.293 I shall also touch upon a few aspects of the debate of wider interest, which as far as I know are not discussed by other recent writers on this subject. VISION AND TECHNIQUE The contrast between induction and hypothetico-deduction reflects the con- trast between the two ways we have of considering our experience of the world.Either we can take experience at its face value, or we can assume it to be the sign of some hidden reality which is not directly observable. Either appearances are reality or they are not. This is recognizable as a very ancient philosophical debate, which some may think is hardly worth attention these days. But such issues have a ghostly habit of reappearing in new guises to trouble us. Which is precisely what has happened here. The first disjunct corresponds roughly to the philosophy behind induction, the second to that behind hypothetico- deduction. The inductivist tries to make sense of the phenomenal surface of the world by establishing observational generalizations which he thinks will allow him inter aka to plan his life at the surface of things more effectively.However, generalizations of this sort, though they usually enable one to predict, do not usually enable one to understand. If I know that iron always rusts in the presence of water, then I can predict the occurrence of rusting. If I change the pressure on a gas, Boyle’s Law enables me to predict the change in its volume under certain conditions. But neither inductive generalization taken alone enables me to understand either the corrosion of iron or the compression of gases, that is, to specify their causes. We do not get to know any more about rusting just by observing more and more examples of it. The scientist has to have some idea or hypothesis about the formation of rust and then test his idea experimentally, if he is to further his understanding of such corrosion. On the other hand, we do not get to know anything whatever about rust unless we do 50 R.I. C. Reviews observe some examples of it to begin with. It looks then as though we may need both induction and hypothetico-deduction to succeed with any scientific problem. The hypothetico-deductivist, on the other hand, usually sees the visible world as a clue to some hidden reality which is not directly observable and which has to be discovered by the trial and error of intelligent and imaginative hypothesis. An hypothesis which stands the test of experiment provides the scientist, for the moment at any rate, with both an explanation for the visible world as it is, and an apparatus for successful prediction.The difference between induction and hypothetico-deduction then lies in this-that the former involves diligent and discriminating perception, while the latter involves this and the exercise of the imagination in formulating hypotheses. Induction needs technique, hypothetico-deduction vision and technique. We should note here that both induction and hypothetico-deduction run risks. Induction runs the risk of being trivial since it may be unable to get beyond the level of commonplace generalization. Per contra hypothetico-deduction runs the risk of being fanciful, of considering hypotheses whose metaphysical and physical implications are hard to accept. I have said that the hypothetico-deductivist often explains the phenomenal world by appealing to descriptions of inscrutable processes of which it is the sign.This immediately raises a number of interesting philosophical questions which do not concern the inductivist. Is the world of inscrutable things and processes really inscrutable ? If not, in what senses can it be observed ? Is it real in the same sense that the visible world is acknowledged real? What is the relation between descriptions of this hidden world and descriptions of the visible world? I shall return to some of these peripheral questions later on in this essay. Science then, taken as an explanation of visible reality, cannot rely upon induction alone. Induction can be a useful method of suggesting that there is a connection between various features of the visible world, but it cannot explain and, as we shall see, neither can it establish that connection.This is a matter for hypothetico-deduction. However we can safely say that a bit of induction is often the excuse for a bit of hypothetico-deduction. BACON, HUME AND MILL Discussions of scientific method are found in Aristotle (Posterior analytics) and various mediaeval philosophers such as Grosseteste and Roger Bacon. Such discussions became increasingly important as mediaeval technology grew more important, and Francis Bacon can be regarded as the Renaissance climax to this interest. So, for the purposes of this essay, I shall consider inductive reasoning as discussed by Francis Bacon in his Novum organum (1620), and then subsequently by Mill in his System of Zogic (1843).Bacon is much the more attractive writer although less thorough than Mill, differences which reflect the very different backgrounds of the two writers. What the sciences stand in need of (wrote Bacon) is a form of induction which shall analyse experience and take it to pieces, and by a due process of exclusion and rejection lead to an inevitable conclusion.6 Theobald 51 Induction (wrote Mill) may be defined as the operation of discovering and proving general propositions.7 Note the emphasis here in both Bacon and Mill on proof and discovery as one and the same operation. We shall come to dispute this in due course. Between the seventeenth century arguments of Bacon and the nineteenth century arguments of Mill on behalf of induction, come the eighteenth century criticisms of Hume in the Treatise (1738)s and the Enquiries (1777).9 I shall consider Hume’s point of view fairly briefly here because I think that it is perhaps of more direct interest to the philosopher than the scientist.Hume was concerned at a very fundamental level with how we could form simple generalizations, with how we could pass from statements about our experience of a limited number of examples of say, rusting, to the assertion of a generaliza- tion about it; from ‘This piece of iron x, y, z, and that piece of iron x, y, z, and . . .’ to ‘All pieces of iron x, y, z’. Hume was therefore concerned with the first stage of induction as a search for causes, namely how we get our observa- tional generalizations in the first place.He regarded any form of argument which was not deductive as specious, and since no inductive argument from particular to general is deductive, he would not allow it as a legitimate source of knowledge. It should be said here in passing that Hume did not make it at all clear in what sense he regarded a deduction as a source of knowledge. But whatever his thoughts on this, he would not consent to induction as a method of discovering true generalizations, nor therefore as a sound method of dis- covering the causes of phenomena. In recent times Russell expressed much the same point of view. What is called induction (he wrote in The principles of mathematics) appears to me to be either disguised deduction, or a mere method of making plausible guesses.In deduction, discovery and proof of the truth of that discovery are one and the same thing, whereas in induction they are not. It was this inter aka that Hume was concerned to point out. But let us be clear exactly what it was that Hume was saying. Hume was saying that induction provides no proof of the correctness of its conclusions, although of course these conclusions may in fact be correct. Induction was neither valid nor invalid argument, because strictly speaking it was no argu- ment at all. Hume would not allow that in an argument a conclusion can be supported by certain premises without following from them, and that argu- ments of this form may be sound or unsound although logically invalid.For soundness and validity are not at all the same thing. A good and persuasive argument can be sound without having deductive validity, although it cannot have deductive validity without being sound.10 Moreover as I hinted above, it is arguable whether a valid deductive argument gives us fresh information, although an inductive argument claims to and often does. All new information is subject to correction by further empirical evidence, and so therefore is any inductive conclusion. A valid deductive con- clusion is not corrigible in this way. But the fact that inductive conclusions are corrigible does not mean that induction can never be a source of knowledge.R.I.C. Reviews 52 All it means is that we have to be prepared to look to other than induction for a proof of the correctness of an inductive conclusion. To this we shall return shortly. I think we need say no more here about Hume’s criticisms of the starting point of inductive method in science, the formation of generalizations. For the problem we are faced with is this. When we have got some inductive generaliza- tions about say, rusting, which we believe to be true, can we get any further along the road to understanding and explaining the incidence of rusting from these alone? It is not difficult to see that the answer to this is that we cannot. Thus suppose pace Hume we do manage to formulate some generalizations about the conditions under which rust seems to occur.A conviction that these are in fact causal conditions is defensible only if there is a theoretical, explana- tory background into which the generalizations fit. What I mean here is that if an inductive generalization can be interpreted within some theoretical frame- work, then the connection it asserts is likely to be causally significant. We no longer have to consider the generalization as merely the expression of a re- markable set of observational coincidences as Hume contended was all we were ever entitled to do. For example the causal implications of generaliza- tions about rusting can be understood in terms of the ionic and molecular theories of chemistry in a way which enables us to see why x, y, z are necessary and sufficient conditions for rusting. Ionic and molecular theory explains because inter alia it asserts that there are such things as molecules and ions which obey the general laws of matter and electricity, and which can be related to the fundamental substratum of chemistry, the elements and their recogniz- able powers of valency.We shall have to bear in mind this question of theoreti- cal backing in what follows, for without it we are thrown back upon Hume’s remarkable series of coincidences. And now for a closer look at Bacon and Mill. Here we shall see just how important theoretical preconceptions actually are in framing generalizations, and why therefore Bacon’s and Mill’s suggestions as to how scientists should proceed are insufficient.Both Bacon and Mill believed that we could acquire the knowledge sufficient to control our environment only if we had no pre- conceptions whatsoever about what we might find. There are good reasons why Bacon and Mill thought like this. Bacon lived at a time when mediaeval habits of mind were slowly being replaced by what we would regard as more modern habits of mind. Thus knowledge from authority was being replaced by knowledge from observation, what Bacon himself called the ‘Presentation of instances to the understanding’.ll Bacon was inclined to distrust theorizing on the grounds that whereas nearly everyone could make observations, by no means everyone could invent theories. Theories and hypotheses, ‘the fume of subtile, sublime or delectable speculation’, was open to all the old mediaeval abuses.Moreover, in Bacon’s day there were considerable practical difficulties in following up investigations to any depth, and Bacon no doubt thought that it was better to concentrate in the circumstances upon what could be done easily and effectively, namely observing and reflecting inductively upon the simple surface aspects of things. There is however in Bacon a detectable ambival- ence on this point, but then this is perhaps no more than a reflection of the total ambivalence of his age. Thus he writes apparently in support of induction: Theobald 53 The human understanding is of its own nature prone to abstractions . . . but to resolve nature into abstractions is less to our purpose than to dissect her into parts.12 whereas elsewhere he writes what could be taken to be support for hypothetico- deduction : For like as a man’s disposition is never well-known till he be crossed, nor Proteus ever changed shapes till he was straitened and held fast; so the passages and variations of nature cannot appear so fully in the liberty of nature, as in the trials and vexations of art.13 Mill of course was educated in the philosophical tradition of English empiricism which had not been developed when Bacon was writing.This philosophy supposes that all our knowledge has its source in experience, but more controversially that the content of knowledge can never be logically richer than the content of experience. So it is not surprising that Mill had little time for truths supposedly known by intuition. And one might guess that he had a similar attitude towards the imagination. Like Locke before him, he had no belief in innate ideas or in innate differences between men.It was almost inevitable then that he should decide upon a scientific method which left little room for that in which men clearly do differ, imagination. Besides this, Mill was interested in devising an acceptable scientific method for the developing social sciences,14 and this could only be done, he thought, by con- centrating upon empirical generalization, for it was far too dangerous and provocative to theorize about matters such as these. Mill was not unopposed in his advocacy of inductive method. Among nineteenth century controversial- ists on scientific method, Jevons, Pierce and Whewell all disagreed with him.Whewell for example in his History of the inductive sciences (1 837) formulated a primitive version of hypothetico-deduction later to be elaborated by Popper in his important Logic ofscientijic discovery (1935, 1959). Pierce and Jevons took issue with Mill when he suggested that induction was a method of dis- covering causal connection and at the same time a rigorous method of proving it. But Mill found some support in Pearson who in his Grammar of science (1892) urged that the collection of facts into general bundles was the proper aim of science, that facts ‘were the one thing needful to form the minds of reasoning animals’ .I5 Pearson’s claim raises the question as to what facts are, whether facts are free from all theoretical or conceptual colouring, whether facts are untreated reports of direct experience.Is the assumption of Mill and Pearson following Locke that there is such a thing as pure, naive observation valid? I think that most philosophers nowadays would argue that all observation is theory- loaded at some point;16 and that if we have no theoretical background against which to observe, then our observations will be mechanical acts of sentience, and so meaningless. Kant made this point in his criticisms of empiri- cal philosophy at the end of the eighteenth century. He wrote in the Prolegomena . . . although all judgements of experience are empirical, i.e.have their ground in immediate sense-perception, yet all empirical judgments are not 54 R. I. C. Re views conversely for that reason judgments of experience, but in addition. . . , special concepts which have their origin wholly apriori in pure understand- ing must still be added.. . and it is these which make the judgement of experience objectively valid.17 Let us now look at Mill’s discussion of induction. Mill, like Bacon, discusses four inductive methods in his System of logic (1843). I shall consider only two of them, since the criticisms I shall level at these can be levelled similarly at the others. One method Mill calls ‘the method of agreement’, and it works as follows. We survey all the examples of the phenomenon P we can, and try to see what factor (or factors) F they seem to have in common.This factor Fcan then be taken as the cause or part of the cause of the phenomenon P, as reflected in generalizations of the form ‘For any F, P’ (sufficient condition) or ‘For any P, I;’ (necessary condition). (From exercising the method of agree- ment alone we cannot tell which. As we shall see later-p. 58-we can decide only by attempting to falsify the generalizations.) This seems clear enough, even to conforming with common practice, but upon reflection there are several evident difficulties with it. For example, how in fact shall we hit upon the common factor F, when as far as Mill’s instructions are concerned, we ought to approach the matter with open minds. If we are true to the philosophy of the method we ought to pay attention to every possible causal factor F.Suppose we are trying to find out why iron rusts. According to this Millian method, we ought to examine every aspect of those samples of rusty iron which we have before us-their size, shape, origin, position, purity, history, environment, owner and so on. Clearly this will not do. The only way we can make the method work is to decide what factors are relevant to outbreaks of rusting and what are not. We must have some idea what we are looking for, or we cannot begin to look. We must have some idea about what might be the causes of rusting before we begin; our search in other words, has to be guided by some tentative theory of rust. By itself therefore, the method constitutes an ineffective means of discovery.(The same sorts of criticism can be made of Mill’s complementary ‘method of difference’.)lg Even if we do succeed in discovering some F which seems to be universally correlated with rusting, we cannot rule out the possibility that both P and F may be caused by something else. For example suppose we found that water is always present when iron rusts. We could not say that water was a cause of rust, for as far as we can tell while using the method, the rust might be the cause of the water, or both the rust and the water might be the effects of some third and unidentified influence. This no doubt seems absurd to us, but only because we already have some theory of rusting in mind. If we approach the matter in true Millian manner, it is not at all absurd.Theobald As I have already said, we might be able to tell whether F is sufficient, necessary or necessary and sufficient condition of P by testing our generaliza- tions, but such testing according to Mill is not necessary if we have followed the inductive method properly. But, testing apart, a causal analysis becomes possible only when we have some theory or hypothesis with which we can assess the significance of the correlations we observe, with which we can separate real causal connection from fortuitous conjunction. Mill we must suppose, 55 like Hume before him, read no more into the notion of cause than that of invariable suc~ession.~~ Mill calls the second method I consider ‘the method of concomitant varia- tion’. This at first sight seems close to aspects of contemporary scientific practice, and was indeed close to the aspirations of nineteenth century philo- sophers of science like Mach who wished to limit science to establishing func- tional relationships without further enquiry into their physical significance. The method requires us to find some Fwhich varies in an orderly manner when the phenomenon P in which we are interested varies.This can be formulated in quantitative terms, though of course Bacon in the seventeenth century would have found it difficult to exploit this possibility. But what, we may ask, is meant by ‘orderly’ here? What is an orderly variation? Since there is no such thing as absolute or complete disorder, any set of data will exhibit some order.The question is: is it significant order? Moreover the observation of simultaneous variations in P and F does not of itself establish any causal connection, for both variations may be governed by the variation of a third, unidentified factor. Nor can we tell whether F i s a necessary, sufficient or necessary and sufficient condition of P. Only some theoretical preconceptions can help us to answer these questions. For example we might observe that the more a piece of iron rusts, the less oxygen there is in the immediate surroundings. Yet we cannot infer from this alone that the oxygen causes the iron to rust, though such an inference might be justified if we took our generalization in the light of some hypothesis about rusting.We must conclude then that although Mill’s methods may discover causes to us, they do not prove their discoveries. Mill’s claim that his inductive methods constituted methods of discovery and proof at one and the same time is false. For proof at least, we shall have to turn to the logically more rigorous hypothetico-deduction. The limitation of inductive science then, as I have described it, is that even if we do discover true correlations which may be useful predictively, we shall still be unable to prop up these predictions with satisfactory explanations. Here one is led to think of one of Mill’s primary concerns, the social sciences, where inductive generalization still plays an important part.There are of course difficulties in getting even as far as reliable generalizations in the social sciences for various reasons, generally well known; the fact that human beings may be predisposed to behave in a certain way by external conditions, but they are not usually constrained so to behave; the fact that how they behave will depend upon their evaluation of those conditions; the fact that control experi- ments in the social sciences are not possible as they are in the physical sciences; the fact that society is arguably not a system in the way that a physical system is a system; and so on. It may be that these difficulties rule out the formation of sensible hypotheses in the social sciences, thus confining social scientists to making inductive generalizations with limited predictive usefulness and little real explanatory power.Unless society is a system, it will not be possible to form clear ideas as to what universal forces may be at work within it. It might even be argued that the failure to find such forces suggests increasingly that society is not a system. Ironically therefore Mill seems to have developed his inductive philosophy, which in the event turns out to be inadequate, with R.I.C. Reviews 56 perhaps the most intractable subject matter he could find at the back of his mind. Induction by itself then will not do as a source of explanation and under- standing. The laws of chemical composition do not by themselves help us to understand chemical changes. Hypothetico-deduction on the other hand, according to which we form relevant hypotheses of cause and structure and then attempt to reject them seriatim by appealing to their experimental implications is in some ways nearer the mark.I say in some ways because although it gives us a clear criterion of validity by its emphasis on falsification, it does not help us to understand the generation of hypotheses. And here we may find ourselves back with all the informality of induction. I am inclined to think that in chemical practice for example, scientists work in a variety of ways, which may now be inductive and now hypothetico-deductive. But I shall return to this point later (p. 65). TESTING IN SCIENCE I want now to turn to the important question of how we test scientific claims, because this rather nicely illustrates some of the important differences between induction and hypothetico-deduction.20 It hardly needs saying that some rigorous testing of any empirical claim is a vital part of scientific method.Now there would seem to be two ways of testing a scientific statement; one is to try to confirm or verify it, the other is to try to falsify it. Both are used, though which depends quite a lot upon the science concerned and more than that, upon the context of the testing. Thus physics in contrast perhaps to botany is a full-time matter of looking for trouble. We ought to remember here that testing, whether confirmation or falsifica- tion, has no proper place in inductive method because this method is supposed by its advocates, incorrectly, to supply its own validation.Nevertheless let us suppose we are going to test both an hypothesis and a generalization. As an inductive generalization we may consider (a) ‘All damp iron rusts’; and as an hypothesis (b) ‘If iron is damp, then it rusts’. If we think about rust in terms of the hypothesis (b), then it is, I maintain, more natural to consider testing by falsification rather than by confirmation. On the other hand, if we think of rust in terms of the general statement (a), then I would say that confirmation seems the more appropriate procedure for testing. For if our claim is a properly formed inductive generalization, then we should not be expecting to find any falsifying cases, but merely confirming examples. And if it is an hypothesis, it stands accepted until shown to be false. ‘All damp iron rusts’ suggests then, that we look for further examples of water with rust.‘If iron is damp, then it rusts’ suggests rather that we look for cases where damp iron does not rust. I want to take this a little further. The general statement (a) ‘All damp iron rusts’ can be converted into a logical equivalent (al) ‘All rust-free iron is dry’. LogicaZly (al) is equivalent to (a). And so we might think that what confirms (a) ought to confirm (al). But (a) is confirmed by damp, rusty iron, and (al) by dry, rust-free iron. And it must strike us as odd that in order to confirm (a) ‘All damp iron rusts’, it seems that all we need to do is observe dry, rust-free iron (which confirms (al) the logical equivalent of (a)).It strikes us as odd because Theobald 57 such an observation does not seem to bear at all critically upon the original general statement (a). This peculiar situation shows us two important things. One, the fact that two statements such as (a) and (al) are logically equivalent does not mean that they are methodologically equivalent. And two, as long as we think of testing a statement in terms of corroboration, we shall be depen- dent upon the logical form our statement takes. This can be very uneconomi- cal. If we are interested in the properties of a small class of Xs, then it will be extravagant, other things being equal, to divert our interest to what will then be a very large class of non-Xs.Suppose we now try to falsify (a) and (al). In the case of (a) we shall need to observe damp, rust-free iron, and in the case of (al) rust-free, damp iron. In other words, to falsify either (a) or (al) requires the same observation. The falsification of a generalization then does not depend upon the logical form of the generalization. Moreover the observation which falsifies (a) and (al) also falsifies (b). It seems then that as far as the methodology of testing is con- cerned we should concentrate upon the falsification of hypotheses and general statements rather than upon their confirmation. Now we had occasion to note above that falsification is more appropriate to (b), while confirmation is more appropriate to (a) and (al).It seems then that when we are concerned with checking the validity of general statements of inductive origin they are better construed as hypotheticals open to falsification. So although we may acquire general knowledge by some inductive generalizing process, Millian or Baconian, its validity is best established by attempting to falsify related hypo- theses. As far as testing is concerned, we must desert induction for hypothetico- deduction. It might be worth digressing here for a moment to point out that some philosophers of science have argued that general statements and hypotheses are not real statements at all, but merely licences for forming such. For example, ‘All damp iron rusts’ or ‘If iron is damp, then it rusts’ licenses us to assert ‘This sample of iron is damp and so will rust’.The claim in effect is that the meaning of hypotheses and general statements is properly to be found in the meaning of the singular observation statements whose truth or falsity would confirm or falsify them. This is the philosophy of logical positivism, whose faults I cannot go into here,21 except to say that the identification of the meaning of a statement with the procedure for testing it has never been persua- sively established. In particular, for the positivist the meaning of an hypothesis which mentions an entity such as an atom which is not directly observable, is to be found in the meaning of the observation statements which confirm or falsify it. The scene is then set for the positivist to say that such a physical object is nothing more than a collection of observable properties.It is the sort of thing it is because it has the particular properties it has. But it could equally well be argued that an object has the properties it does have because it is the sort of thing it is. Now this is an important move, because it leaves the nature of the object open to be investigated. If an object is nothing but a collection of observable properties, if it has no nature, indeed if there is really no such thing as ‘it’, what reason can we have to investigate it beyond what we have already observed? Indeed what reason can we have even to start investigation? And besides, if an object has R.I.C. Reviews 58 no nature apart from its properties, what sort of properties are we to consider looking for? Any? If so we are back with the problems of inductive method discussed earlier, of not knowing how to start or when to stop.Positivism is not a philosophy for research. In a later development of positivism, instrumentalism, the argument was changed somewhat. A theory, it was contended, was simply a rule for inferring one observation statement from another. A theory asserted nothing whatso- ever about what the world was made of. But the same counter move can be made here-it is because a theory asserts something in fact about the world that it is a successful rule for making inferences. Let us now return to testing. There is a simple reason why falsification is in logic the proper way of bearing critically upon an hypothesis.I have so far merely discussed some methodological reasons why this is so. Suppose a scientific argument is generally of the form ‘Given Tand A , then B’, where Tis a theory from which given A , B may be deduced. Now if B is true, the con- junction Tand A can be true or false. For any true proposition can be implied by either a true proposition or a false proposition. On the other hand, if B is false, then Tand A can be only false. For no true proposition can imply a false proposition. So if B is a deductive consequence of T and A , and if B is observed to be false, then T and A can be inferred to be false also. And if A are observed initial conditions, the theory T must be false. We may conclude therefore that falsification is the proper way to test an hypothesis. ‘The aim of science is not to open a door to infinite wisdom, but to set a limit to infinite error’ as Brecht has Galileo say.22 There is a further point worth making in connection with testing.In ordinary life we are usually content to treat sufficient conditions as causes, whereas in science we usually reserve this description for necessary and sufficient condi- tions. Now the confirmation of (a) tells us nothing about whether dampness is a necessary, sufficient or necessary and sufficient condition of rust. But the falsification of (a) or (b) tells us at least that dampness is not a sufficient condi- tion of rust. If then we were to falsify (c) ‘All rusty iron is damp’, or ( d ) ‘If iron is rusty, it is damp’, this would tell us at least that rust was not a sufficient condition of dampness and therefore that dampness was not a necessary condition of rust.If attempts to falsify (a), (b), (c) and ( d ) fail (which we know in actual fact they would not), then dampness can be taken to be a necessary and sufficient condition of rust, at least until further evidence is forthcoming. PHILOSOPHICAL PROBLEMS FOR HYPOTHETICO-DEDUCTION I have tried to show how, although knowledge may be obtained fortuitously by an inductive method, the critical evaluation of that knowledge proceeds best by trying to falsify relevant hypotheses. I mentioned at the beginning of this essay that induction remains content with the world at its face value, whereas the invention and testing of hypotheses is not limited in this way.The content of an hypothesis is not limited by our ordinary experience of the world. It is in fact difficult to see how many of the most important principles and theories of physical science could have arisen by any generalizing operation alone. How for example could atomic theory have arisen in this way? And how can the role of conservation principles be interpreted inductively ? Theobald 59 Since the content of an hypothesis is not limited by our everyday experi- ence, we soon have to face the question : are atoms, ions, electrons and so on, which are features of many physical hypotheses, simply fictions or are they real existents? Are they merely grammatical ciphers in a scientific language, or do they actually designate bits of the real physical world? Are atoms and ions real in the sense that we take the furniture of our laboratory to be real? Per- haps I should point out that in a logical sense it does not make any difference to the properties of a thing whether it is a real existent or not.I mean by that that logically speaking, existence adds nothing to anything. If I describe a piece of chemical apparatus in detail, and then add ‘But such a piece of apparatus does not exist’, all I do is to lose the attention of my audience. I do not change the properties of the apparatus. So whether atoms or ions are real existents or not makes no difference to the predictive power of any atomic hypothesis, though it must make a difference to its persuasive power of explanation, its power to help us understand.Hypothetico-deduction then raises certain philosophical problems not raised by induction. It is often said that we never observe atoms in that sense of ‘observe’ appropriate to ordinary common-sense observation. But is this so ? I am inclined to think not. I think that observing an atom or an ion or an electron involves a perfectly proper sense of ‘observe’, a sense which I hope to explain. The atomic theory is designed to explain all the visible aspects of macroscopic change, and therefore atoms themselves cannot be invested with ordinary, visible properties. But this does not mean that they cannot be observed. Imagine looking into the clear night sky and seeing a comet.You say to yourself ‘There’s a comet’ or perhaps ‘I can see a comet’. Rather more im- probably you might say ‘I can see the light-track of a comet’, even though in a sense that is what you do see. You can quite properly say these things because you undoubtedly know a little astronomical science and probably also some- thing about the appearance of moving luminous bodies, and because you are confident that astronomers have some sort of astronomical tests up their sleeves to confirm or falsify such claims. The argument ‘I saw an A ; A is B ; so I saw a B’ is generally valid only if you know that A is B. That is, if you saw A , you are entitled to say you saw B, only if you know that A was B.From the fact that you saw a man, you are entitled to say that you saw a laughing man, only if you know the man was laughing. Of course you need not have observed his laughing, someone might have told you. You can be entitled to say you saw a laughing man without being entitled to say that you saw a man laughing. To take another example, if I saw a piece of apparatus, I am entitled to say I saw an ir spectrometer only if I know it is an ir spectrometer. But I need not have seen that it was an ir spectrometer; someone, an expert, may have told me that that was what I was seeing. To return to comets: if we see a light-track in the sky, we are entitled to say we see the light-track of a comet because we know from astronomers that such is in fact the light-track of a comet.And seeing the light-track of a comet is seeing a comet making a light-track. It is in fact seeing a comet. What else could possibly count as seeing it? And no one on this account would dream of saying that comets are not real. The same sort of considerations apply to seeing a-particles in cloud- R.Z. C. Reviews 60 chambers or molecules in electron micro~copes.2~ One reason why these hypothetical entities are bona fide candidates for the description ‘real’ is that like the comet, there is a particular conceptual background which makes certain claims to see them legitimate and significant. There is an accepted reservoir of knowledge which makes the second premise in the argument I outlined above true. To take a chemical example, to see a chemical change occurring is to see an electronic rearrangement going on, once we know all about chemical theory.The important point is that what we say we can see depends upon our know- ledge. As does therefore what we can say is real. Against this some philosophers have argued that to say that we see an electronic rearrangement going on, if taken literally, is to say something mis- leading if not false. It is argued that whereas seeing a chemical change going on in a flask is clear enough, to say that this is to see electrons rearrange is to hide the fact that an inference has been made in accordance with some physical theory, an inference from what goes on in the flask to the fate of the electrons. This has been the view of many instrumentalist and positivist philosophers of science.24 But given the setting of atomic theory, seeing a chemical change in progress just is seeing the electrons rearranging, and moreover that is all there is to seeing the electrons rearranging.The confusion arises from failing to notice the difference between seeing inside a theory and seeing outside it. Both are legitimate seeings, and neither involves making inferences of any sort. Seeing is not just opening one’s eyes-seeing is an achievement. Note how frequently ‘see’ is used with ‘can’ and how rarely if at all in the present tense, ‘I see. . .’ or ‘I am seeing. . .’. For to see is to invest what you notice with some significance. And this is what theories and hypotheses are for.All observation is dyed with theory to a greater or lesser extent, and it was a cardinal and curiously romantic error of Mill, Pearson and others to suppose that there was such a thing as simple, naive observation, and therefore that there was such a thing as a fact which was not charged with some theoretical preconceptions. HYPOTHESES I have argued that although it may suggest correlations between observable properties, induction cannot establish causal connection. And so it cannot supply profound understanding. We need to devise hypotheses and test them critically in order to explain and understand. The actual form any hypothesis takes and the particular suggestions it makes will depend a great deal upon our present knowledge. For any hypothesis which is to extend our present knowledge will begin by suggesting analogies between new physical systems and systems with whose behaviour we are already familiar.Rarely therefore will an hypothesis depart completely from previous ideas. This might be taken to imply that the refutation of an hypothesis will call the whole of the science concerned into question. But this is not necessarily so. As has been said, falsification is the sign only that something has gone wrong, not that every- thing has gone wrong. On the occasions when an hypothesis does depart radically from previous ideas the result is a conceptual revolution in science, examples of which will be very familiar. To the chemist the reorientation of chemical thought by Lavoisier in the eighteenth century, by Dalton in the Theobald 61 nineteenth, and by Bohr and later quantum theorists in the twentieth century are perhaps the most important.Sometimes, metaphysical conviction can lead to the retention of hypotheses even when the evidence is against them, even when they have been technically falsified. Witness the persistence of alchemical ideas despite their many failures,25 and the reluctance of chemists, for example Priestley, to abandon phlogiston theory even after the work of Cavendish and Lavoisier. As another example we may recall that MendelCef persisted with his classification of the elements despite the fact that at the time his periodic arrangement failed in several places. Sometimes metaphysical conviction makes us continue with an hypothesis when there is no clear evidence for or against it.Dalton’s atomic hypothesis was maintained in the face of a great deal of initial quantitative uncertainty, and an inability to see precisely how to put it to conclusive test. In fact there was a gradual decline of interest in atomic theory during the middle of the nineteenth century until the work of Avogadro and Gay-Lussac was re- presented by Cannizzaro, and shown to be compatible with Dalton’s hypo- thesis after some modifications. These few historical points show that dis- covery, justification, judgement, imagination and metaphysical conviction become inextricably mixed during the evolution of scientific ideas. They also show that hypothetico-deduction is not a scientific method which commands the scientist’s unswerving allegiance. As I pointed out in the introduction to this essay, science like any other human activity cannot always be conducted successfully by rule of logic alone. But the most interesting question to do with hypotheses has yet to be asked. How do we form hypotheses ? How does our guided imagination work ?4 There are very difficult questions even to begin to answer.We can certainly make a survey of the sorts of person who have had the necessary imaginative frame of mind to devise hypotheses, and we can certainly make a survey of the physical and intellectual conditions which predispose (but not determine) a man to be imaginative. But I doubt whether any statistical findings of this sort about imaginative thinking will leave us any nearer either predicting or engineering its occurrence.And such a survey would in any case do little to clarify what imagination is or how it works in the business of discovery. And it is to aspects of the philosophy of the imagination I wish to turn now. All our attempts to come to terms with the experienced world depend upon our fitting this experience into an orderly, though flexible matrix of general concepts whose expression is usually verbal. As I have already remarked, scientific knowledge which is linguistic and propositional, requires more than a keen eye for phenomenal incident. To know is to create order and structure in the world by means of language. Knowledge is not something absolute, just ‘out there’ for quick capture, but is, as Coleridge realized, something to be created and recreated because language is subject to constant, creative renewal by philosophers, poets and scientists.‘The relation of language to thought and reality is not a passive ref? ection, but an active and tendentious reaction’ wrote the literary critic and poet Christopher Caudwell.26 This I think is not such a bad definition of scientific practice. We can see this more surely if we reflect upon how we come by the concepts R.I.C. Reviews 62 we have. Let us take the concept ‘chemist’ as an example. A common view of the origin of our concept ‘chemist’ would be this-all we do is to make a survey of all chemical persons we know, and draw up an inventory of what they have in common.As a result we have a concept ‘chemist’ the meaning of which is decided, that is defined, by a collection of common properties. But clearly this will not do, attractively simple as it seems. And it will not do for the same reasons that Mill’s method of agreement will not do. For until we have at least some concept ‘chemist’ in our minds, we can have no idea who are chemical persons, and therefore no idea what common characteristics we are to look for. This is an important point. Suppose we take the concept ‘red’. It is often argued that this concept is acquired by noticing and naming what is common to a set of red objects. But this can be done only if we are quite clear that we are dealing with culuur as opposed to say shape, size or weight.We must be clear what sort of thing we are attending to before we start. Concepts are not acquired independently, but in relation to other concepts. Another way of putting this would be to say that language is a system of concepts, not a collection. We cannot and do not acquire concepts by diligent stock-taking. The concept ‘chemist’ like all other concepts is first and foremost a mental invention, but one whose meaning will change and develop as our experience of the class of objects designated by the concept increases. It is not easy to say precisely why we invent concepts, nor how they and our experience develop side by side. We may feel (inductively) that there is some uniformity in our experience which needs charting, or we may wish to discover whether there is.These are matters clearly for imaginative judgement, for hypothesis and testing, not simply for an inductive logic. What has been said here of the concepts ‘chemist’ and ‘red’ is, I think, true of all concepts. They are first and foremost mental inventions and they designate open classes. Whether or not some particular item of experience falls under a given concept is a matter both for our perception and our judgement, but not for our perception alone. It is a matter of weighing the evidence for or against inclusion. This looseness in the application of language to the world is vitally important, for it allows language to hover over our experience of the world, and settle upon it not only as an instrument of definition, but as an instrument of promise, expectation and revaluation.Concepts are like Axes After whose stroke the wood rings, And the echoes! Echoes travelling Off from the centre like horses.27 In scientific contexts it is this looseness which allows us to overlook disagree- ment between hypothesis and observation without being guilty of logical inconsistency.28 For, as we have seen, theories and hypotheses are not always refuted by such disagreements. Concepts then do not mirror reality; rather in an important way they create the reality we talk about. Experience does not give our concepts meaning; we give them meaning, and by so doing we endow experience with meaning. This Theobald 63 is an extremely important point which explains why I head this essay with some words from Eliot’s Dry Salvages, and which is at the heart of the conflict between induction and hypothetico-deduction.‘Concepts lead us to make in- vestigations ; are the expression of our interest, and direct our interest’ wrote Wittgenstein.29 This can be said equally of any hypothesis in science. My remarks about concepts in the preceding paragraphs, although they need more elaboration and defence than I can give them here, can be directly translated into the terms of the induction/hypothetico-deduction controversy. For hypotheses are not elicited from experience, they are invented to make sense of experience and, like concepts-themselves in some ways hypotheses of persis- tence, identity, resemblance and uniformity-they are modified in the light of it.The object of ordinary language, like its scientific development, is to tie down experience into labelled bundles, to reduce the apparent variety in experience by collecting it into generalities. The scientific imagination tries to simplify, though not, as I have tried to show, exclusively by induction. The poetic imagination as I understand it, tries to complicate. ‘What we have gotten by this revolution is a great deal of good sense. What we have lost is a world of fine fabling’ wrote Richard Hurd, Bishop of Worcester, of the scien- tific enlightenment in the eighteenth century. The poet, the Blake who sees scientists as generalizing idiots, thinks of simplification as restricting the pos- sibilities for seeing the world, as numbing our sensitivity to small but impor- tant differences in things. ‘We have art in order not to die of the truth’ wrote Nietz~che.~~ Scientific imagination is more controlled and has less room for manoeuvre than the artistic imagination, and yet in the long run it may carry more universal conviction. For the fact that the scientific imagination works within the confines of previous knowledge and opinion guards scientific hypotheses against some of the subjective extravagancies which Bacon, Mill and others feared.New ideas in science are either rejected or become accepted as textbook truths, but new ideas from the artistic imagination are always fresh to each generation. They are not assimilable to a body of knowledge.This is because in science the meaning of a term is designed to be independent of the context in which it is used and so becomes the expression of a timeless gener- ality in nature whereas in poetry, say, the meaning depends very much upon that context and requires revaluation when that context changes. I have already mentioned the importance of analogy in science. The scien- tist’s imagination works by seeing in the apparently new much that is like the already familiar. The artist works by seeing in the apparently familiar much that is actually new. The effectiveness of all analogy as Coleridge pointed out31 is a complex and subtle matter of ‘the balance or reconciliation of opposite or discordant qualities; of sameness with difference; of the general with the concrete, the individual with the representative; the sense of novelty and freshness, with old and familiar objects; a more than usual state of order .. .’. Once we have accepted an analogy, once it convinces us, we are necessarily converted to a reconstructed reality. ‘The expression of a change of aspect is the expression of a new perception and zt the same time of the perception’s being ~ n c h a n g e d . ’ ~ ~ We cannot look at gases in the same way once we havesup- posed that they consist of bits of matter in Newtonian motion. We cannot look at human beings and chairs in the same way once we accept that they both R.I.C. Reviews 64 have legs, nor at clouds in the same way once we have seen ‘a cloud that’s dragonish.. .’.33 In science this sort of imaginative move is part and parcel of forming and testing hypotheses. We start by seeing A as B and we then act on this sugges- tion to find out whether in fact A is B, whether the analogy stands up to examination. Imagining is always preliminary to knowing. Imagining a gas as a collection of Newtonian particles is preliminary to knowing that a gas is in fact more or less just that; and also to seeing why it is onZy more or less just that. We can see then that hypothetico-deduction is an extension of aspects of the philosophy of concept formation into the methodology of science. I have tried to show that induction is by itself methodologically inadequate, and in some respects philosophically naive.This does not mean to say however that a Mill- ian approach to a problem is always inappropriate, as some critics seem to suppose. I return to a point I made earlier which was that it is not possible to legislate about how scientists should go about the business of discovery. It is possible to legislate only about how they should check their discoveries, how they should check their claims to know And here the verdict is clearly in favour of hypothetico-deduction. Hypothetico-deduction will evidently find favour with logicians and mathematically-minded physical scientists on account of its logical rigour, but it is not so clear that it will always find favour with the more experimental scientist for whom the chance observation, the remarkable coincidence is of great moment.One is sometimes tempted to think that those scientists who argue often overbearingly for hypothetico-deduction have themselves lost contact with the uncertainties and chances of day to day work in the laboratory. CHEMISTRY AND SCIENTIFIC METHOD I want now to say a few words about the position of the chemist in all this. Many important discoveries have been made in chemistry (as indeed they have in the other physical sciences) from the odd observation, the peculiar coinci- dence, so that although chemists may need the logic of hypothetico-deduction to put their ideas to the test, they often rely upon the informal consequences of induction to generate their ideas in the first place.The chemist is traditionally a scientist who often simply wants to know what occurs when A is mixed with B, besides wanting to produce a theoretical explanation for it. Although admittedly we may wish to explain the reaction once we have mixed A with B, it is inductive curiosity which leads us to the mixing in the first place. In chemistry many more things have been discovered than have been explained, and there is no sign that discovery is dependent for its impetus upon theory and explana- tion as it undoubtedly is in physics. Chemistry is still in many respects an informal science. And as I have already remarked, important discoveries come from such informality. I think that chemical curiosity is much less dis- ciplined than physical curiosity, and it is probably this element of ‘idle curiosity’ which makes chemistry so successful in its relations with technology.For it is the chance rather than the systematic discovery which is often interesting to the technologist. Theobald 65 5 It is a notorious fact that in theoretical physics one experimental result is often all that is necessary, indeed in practice is often all that is available to evaluate an hypothesis and if need be reject it. On the other hand in chemistry there is more often than not a vast array of experimental results which can be brought to bear upon an hypothesis. Usually no single result bears upon a chemical hypothesis in the way a single result can bear upon an hypothesis in physics. This is reflected in the fact that theories and models in chemistry are generally much looser formulations than those in physics.The chemist is concerned with modifying details of a well-authenticated molecular model, not with rejecting it. On the other hand the physicist at his level of physical enquiry is concerned much more with making a conclusive choice between rival models. Accordingly there is not such a tight relationship between hypothesis and observation in chemistry as there seems to be in physics. These things are all a reflection of the fact that chemistry is still in some measure an inductive science. Chemistry then stands between physics on the one hand and the field biological sciences on the other in being an area of inquiry peculiarly appro- priate for the exercise of both inductive and hypothetico-deductive method.However chemists will continue to enjoy this stimulating position only if they resist the temptation to suppose that they must model their science either on physics or biology. This, as I have argued elsewhere,34 is seriously to suppress the imagination besides, as I believe, being logically and methodologically indefensible. There is more I believe in heaven and earth than is comprehended in the philosophy of physics. But fortunately there is no reason to suppose that chemistry must succumb to relations with either of its suitors. Those who would have it do so will I think find relations become very strained, and I suggest they would do well to remember Tristram’s remarks about his father: he was systematical, and, like all systematic reasoners he would move heaven and earth and twist and torture everything in nature to support his hypothesis.In a word he was serious and be content to remain chemists. ACKNOWLEDGMENT The excerpt from T. S . Eliot’s The Dry Salvages is reproduced by permission of Faber and Faber. REFERENCES 1 Novum organum (1 620) ; The advancement of learning (1 605). 2 System of logic (1843). 3 Logic of scientific discovery (1935, 1959). 4 Patterns of discovery (1958); The concept of the positron (1963). 5 Induction and intuition in scientific thought (1969). 6 Thegreat instauration (1607), Plan of (trans. by J. Spedding, R. L. Ellis and D. D. Heath). 7 System of logic, book 3, chapter 1.8 Treatise of human nature (1738). 9 Enquiry concerning human understanding (1 777). 10 See my Introduction to the philosophy of science (1968) for further discussion and references. 11 Novum organum, Aphorisms, book 2, 15 (trans. by J. Spedding, R. L. Ellis and D. D. Heath) . 12 Ibidem, book 1, 51. R . I. C. Reviews 66 13 Advancement of learning, book 2. 14 System of logic, book 6. 15 C. Dickens, Hard times, book 1, chapter 1. 16 See, for example, Hanson, op. cit. 17 Prolcgomena to any future metaphysics (1783), para. 18 (trans. by P. G. Lucas). 18 These methods are discussed more fully in most books on scientific method, e.g. E. Nagel, An introduction to logic and scientific method (1934). 19 System of logic, book 3, chapter 5.20 See my Introduction to the philosophy of science, chapter 4. 21 See J. 0. Urmson, Philosophical analysis (1956), and G. J. Warnock, English philosophy since 1900 (1958, 1969) for useful discussions. 22 Scene 9. 23 See my ‘Observation and reality’, Mind, 1967, 76, 198. 24 See E. Nagel, The structure of science (1961). 25 See my ‘Alchemy; a philosophical reappraisal’, Technology and Society, 1965, 2, 135. 26 Illusion and reality (1 937). 27 Sylvia Plath, ‘Words’ in Ariel(l948). 28 T. S. Kuhn, The structure of scientific revolutions (1962). 29 Philosophical investigations (1 958), part 1, 570. 30 Goethe is an excellent example of a man torn in the two directions. See E. Heller, The disinherited mind (1952). 31 Biographia literaria 1817, 2, 12.32 Philosophical investigations, part 2, xi. 33 Antony and Cleopatra, act 4, sc. 12. 34 See my Introduction to the philosophy of science, chapter 6. 67 Theobald EXPERIMENT, IMAGINATION AND MEANINGInductive and Hypothetico-deductive Method in ScienceD. W. TheobaldDept of Chemistry, UMIST, Monchester IVision and technique . . . . . . .. . . . . . . 50Bacon, Hume and Mill . . . . . . . . . . .. . . 51Testing in science . . .. .. . . . . . . . . . . 57Philosophical problems for hypothetico-deduction . . . . . . 59Hypotheses .. . . .. .. . . . . . . . . 61Chemistry and scientific method . . .. . . . . . . 65References . . .. . . . . .. . . . . . . . . 66We had the experience but missed the meaning,And approach to the meaning restores the experienceIn a different form, ...T.S. Eliot, The Dry SalvagesThe moment we reflect philosophically upon the knowledge we have of theworld about us, two questions emerge. One, how do we acquire such know-ledge? And two, how do we guarantee that what passes for knowledge is infact knowledge? The first is a question about discovery, the second a questionabout justification and proof. Of course these are strictly speaking philosophi-cal questions, but the answers to them are of interest, indeed importance, toscientists. To explain this a little further, let us take a simple example, anexample which we shall return to frequently throughout this essay. Suppose weare interested in rusting, both from a theoretical point of view and perhaps withthe practical aim of preventing its occurrence and the inconvenience it causes.First we shall want to find out the conditions under which rusting occurs sothat we can discover its causes, and then we shall require some procedure forestablishing or proving that we have found out correctly.And the questionsI am asking are-one, what are the procedures we use for discovery, and two,what are our methods of proof? How do we make, and how do we check up onour discoveries ? Various answers have been given to these questions by manyphilosophers and scientists from Bacon1 in the sixteenth century and Mi112 inthe nineteenth, to Popper3 and Hanson4 among others in the present century.Nowadays the discussion usually revolves around the question whether scienceworks inside an inductive mould as Bacon and Mill appeared to believe, orinside an hypothetico-deductive mould as Popper and others maintain.Perhaps I should give the terms ‘inductivd and ‘hypothetico-deductive’ somebrief preliminary explanation at once.According to inductive method, causal relationships are claimed to be dis-coverable from the repeated coincidence of certain observable properties.Thus, observational generalizations, such as that rusting is always noticedwhen water is present, are supposed to entitle us to assert for example, thatwater is a cause of rust.Induction starts with no causal commitment. TheTheobald 49inductivist is entirely open-minded about the causes of rusting before he startsobserving.Causes he believes, will emerge from observations without teasing.Hypothetico-deductive method on the other hand, starts with a causal hypo-thesis about rusting, such as that water is always required, and then proceedsvia the deduction of observable consequences to subject this hypothesis to theknock-down argument of designed, experimental test. The hypothetico-deductivist then, is not entirely open-minded about the causes of rust when hestarts observing. Causes, he believes, are revealed only by teasing. A good dealof philosophical and scientific opinion nowadays is directed squarely againstinductive method, witness Popper’s Logic of scientzjic discovery3 and Meda-war’s more recent attack Induction and intuition in scienti3c thought.5My own view, which I hope will emerge during the rest of this essay, is thatit would be wrong to suppose that there was a single scientific method appro-priate to all stages in the development of a scientific enquiry.Scientific know-ledge is often the product of both induction and hypothetico-deduction, butused at different moments in an investigation. In this essay I want to examinesome aspects of both inductive and hypothetico-deductive method to seewhether or not they separately constitute adequate methods of discovery andproof. Fuller and more systematic accounts can be found in the works cited inthe bibliography.293 I shall also touch upon a few aspects of the debate ofwider interest, which as far as I know are not discussed by other recent writerson this subject.VISION AND TECHNIQUEThe contrast between induction and hypothetico-deduction reflects the con-trast between the two ways we have of considering our experience of the world.Either we can take experience at its face value, or we can assume it to be thesign of some hidden reality which is not directly observable.Either appearancesare reality or they are not. This is recognizable as a very ancient philosophicaldebate, which some may think is hardly worth attention these days. But suchissues have a ghostly habit of reappearing in new guises to trouble us. Which isprecisely what has happened here. The first disjunct corresponds roughly tothe philosophy behind induction, the second to that behind hypothetico-deduction. The inductivist tries to make sense of the phenomenal surface of theworld by establishing observational generalizations which he thinks will allowhim inter aka to plan his life at the surface of things more effectively. However,generalizations of this sort, though they usually enable one to predict, do notusually enable one to understand.If I know that iron always rusts in thepresence of water, then I can predict the occurrence of rusting. If I change thepressure on a gas, Boyle’s Law enables me to predict the change in its volumeunder certain conditions. But neither inductive generalization taken aloneenables me to understand either the corrosion of iron or the compression ofgases, that is, to specify their causes. We do not get to know any more aboutrusting just by observing more and more examples of it. The scientist has tohave some idea or hypothesis about the formation of rust and then test his ideaexperimentally, if he is to further his understanding of such corrosion.On theother hand, we do not get to know anything whatever about rust unless we do50 R. I. C. Reviewobserve some examples of it to begin with. It looks then as though we mayneed both induction and hypothetico-deduction to succeed with any scientificproblem.The hypothetico-deductivist, on the other hand, usually sees the visibleworld as a clue to some hidden reality which is not directly observable andwhich has to be discovered by the trial and error of intelligent and imaginativehypothesis. An hypothesis which stands the test of experiment provides thescientist, for the moment at any rate, with both an explanation for the visibleworld as it is, and an apparatus for successful prediction.The differencebetween induction and hypothetico-deduction then lies in this-that the formerinvolves diligent and discriminating perception, while the latter involves thisand the exercise of the imagination in formulating hypotheses. Inductionneeds technique, hypothetico-deduction vision and technique. We should notehere that both induction and hypothetico-deduction run risks. Induction runsthe risk of being trivial since it may be unable to get beyond the level ofcommonplace generalization. Per contra hypothetico-deduction runs the riskof being fanciful, of considering hypotheses whose metaphysical and physicalimplications are hard to accept.I have said that the hypothetico-deductivist often explains the phenomenalworld by appealing to descriptions of inscrutable processes of which it is thesign.This immediately raises a number of interesting philosophical questionswhich do not concern the inductivist. Is the world of inscrutable things andprocesses really inscrutable ? If not, in what senses can it be observed ? Is it realin the same sense that the visible world is acknowledged real? What is therelation between descriptions of this hidden world and descriptions of thevisible world? I shall return to some of these peripheral questions later on inthis essay.Science then, taken as an explanation of visible reality, cannot rely uponinduction alone.Induction can be a useful method of suggesting that there is aconnection between various features of the visible world, but it cannot explainand, as we shall see, neither can it establish that connection. This is a matterfor hypothetico-deduction. However we can safely say that a bit of inductionis often the excuse for a bit of hypothetico-deduction.BACON, HUME AND MILLDiscussions of scientific method are found in Aristotle (Posterior analytics)and various mediaeval philosophers such as Grosseteste and Roger Bacon.Such discussions became increasingly important as mediaeval technologygrew more important, and Francis Bacon can be regarded as the Renaissanceclimax to this interest. So, for the purposes of this essay, I shall considerinductive reasoning as discussed by Francis Bacon in his Novum organum(1620), and then subsequently by Mill in his System of Zogic (1843).Bacon ismuch the more attractive writer although less thorough than Mill, differenceswhich reflect the very different backgrounds of the two writers.What the sciences stand in need of (wrote Bacon) is a form of inductionwhich shall analyse experience and take it to pieces, and by a due process ofexclusion and rejection lead to an inevitable conclusion.6Theobald 5Induction (wrote Mill) may be defined as the operation of discovering andproving general propositions.7Note the emphasis here in both Bacon and Mill on proof and discovery as oneand the same operation. We shall come to dispute this in due course.Between the seventeenth century arguments of Bacon and the nineteenthcentury arguments of Mill on behalf of induction, come the eighteenth centurycriticisms of Hume in the Treatise (1738)s and the Enquiries (1777).9 I shallconsider Hume’s point of view fairly briefly here because I think that it isperhaps of more direct interest to the philosopher than the scientist. Humewas concerned at a very fundamental level with how we could form simplegeneralizations, with how we could pass from statements about our experienceof a limited number of examples of say, rusting, to the assertion of a generaliza-tion about it; from ‘This piece of iron x, y, z, and that piece of iron x, y, z,and .. .’ to ‘All pieces of iron x, y, z’.Hume was therefore concerned with thefirst stage of induction as a search for causes, namely how we get our observa-tional generalizations in the first place. He regarded any form of argumentwhich was not deductive as specious, and since no inductive argument fromparticular to general is deductive, he would not allow it as a legitimate sourceof knowledge. It should be said here in passing that Hume did not make it atall clear in what sense he regarded a deduction as a source of knowledge. Butwhatever his thoughts on this, he would not consent to induction as a methodof discovering true generalizations, nor therefore as a sound method of dis-covering the causes of phenomena. In recent times Russell expressed much thesame point of view.What is called induction (he wrote in The principles of mathematics) appearsto me to be either disguised deduction, or a mere method of making plausibleguesses.In deduction, discovery and proof of the truth of that discovery are one andthe same thing, whereas in induction they are not.It was this inter aka thatHume was concerned to point out.But let us be clear exactly what it was that Hume was saying. Hume wassaying that induction provides no proof of the correctness of its conclusions,although of course these conclusions may in fact be correct. Induction wasneither valid nor invalid argument, because strictly speaking it was no argu-ment at all. Hume would not allow that in an argument a conclusion can besupported by certain premises without following from them, and that argu-ments of this form may be sound or unsound although logically invalid.Forsoundness and validity are not at all the same thing. A good and persuasiveargument can be sound without having deductive validity, although it cannothave deductive validity without being sound.10Moreover as I hinted above, it is arguable whether a valid deductiveargument gives us fresh information, although an inductive argument claims toand often does. All new information is subject to correction by further empiricalevidence, and so therefore is any inductive conclusion. A valid deductive con-clusion is not corrigible in this way. But the fact that inductive conclusions arecorrigible does not mean that induction can never be a source of knowledge.52 R.I.C.ReviewAll it means is that we have to be prepared to look to other than induction for aproof of the correctness of an inductive conclusion. To this we shall returnshortly.I think we need say no more here about Hume’s criticisms of the startingpoint of inductive method in science, the formation of generalizations. For theproblem we are faced with is this. When we have got some inductive generaliza-tions about say, rusting, which we believe to be true, can we get any furtheralong the road to understanding and explaining the incidence of rusting fromthese alone? It is not difficult to see that the answer to this is that we cannot.Thus suppose pace Hume we do manage to formulate some generalizationsabout the conditions under which rust seems to occur.A conviction that theseare in fact causal conditions is defensible only if there is a theoretical, explana-tory background into which the generalizations fit. What I mean here is that ifan inductive generalization can be interpreted within some theoretical frame-work, then the connection it asserts is likely to be causally significant. We nolonger have to consider the generalization as merely the expression of a re-markable set of observational coincidences as Hume contended was all wewere ever entitled to do. For example the causal implications of generaliza-tions about rusting can be understood in terms of the ionic and moleculartheories of chemistry in a way which enables us to see why x, y, z are necessaryand sufficient conditions for rusting.Ionic and molecular theory explainsbecause inter alia it asserts that there are such things as molecules and ionswhich obey the general laws of matter and electricity, and which can be relatedto the fundamental substratum of chemistry, the elements and their recogniz-able powers of valency. We shall have to bear in mind this question of theoreti-cal backing in what follows, for without it we are thrown back upon Hume’sremarkable series of coincidences.And now for a closer look at Bacon and Mill. Here we shall see just howimportant theoretical preconceptions actually are in framing generalizations,and why therefore Bacon’s and Mill’s suggestions as to how scientists shouldproceed are insufficient. Both Bacon and Mill believed that we could acquirethe knowledge sufficient to control our environment only if we had no pre-conceptions whatsoever about what we might find.There are good reasonswhy Bacon and Mill thought like this. Bacon lived at a time when mediaevalhabits of mind were slowly being replaced by what we would regard as moremodern habits of mind. Thus knowledge from authority was being replaced byknowledge from observation, what Bacon himself called the ‘Presentation ofinstances to the understanding’.ll Bacon was inclined to distrust theorizing onthe grounds that whereas nearly everyone could make observations, by nomeans everyone could invent theories. Theories and hypotheses, ‘the fume ofsubtile, sublime or delectable speculation’, was open to all the old mediaevalabuses.Moreover, in Bacon’s day there were considerable practical difficultiesin following up investigations to any depth, and Bacon no doubt thought thatit was better to concentrate in the circumstances upon what could be doneeasily and effectively, namely observing and reflecting inductively upon thesimple surface aspects of things. There is however in Bacon a detectable ambival-ence on this point, but then this is perhaps no more than a reflection of the totalambivalence of his age. Thus he writes apparently in support of induction:Theobald 5The human understanding is of its own nature prone to abstractions . . . butto resolve nature into abstractions is less to our purpose than to dissect herinto parts.12whereas elsewhere he writes what could be taken to be support for hypothetico-deduction :For like as a man’s disposition is never well-known till he be crossed, norProteus ever changed shapes till he was straitened and held fast; so thepassages and variations of nature cannot appear so fully in the liberty ofnature, as in the trials and vexations of art.13Mill of course was educated in the philosophical tradition of Englishempiricism which had not been developed when Bacon was writing.Thisphilosophy supposes that all our knowledge has its source in experience, butmore controversially that the content of knowledge can never be logicallyricher than the content of experience. So it is not surprising that Mill had littletime for truths supposedly known by intuition.And one might guess that hehad a similar attitude towards the imagination. Like Locke before him, hehad no belief in innate ideas or in innate differences between men. It wasalmost inevitable then that he should decide upon a scientific method whichleft little room for that in which men clearly do differ, imagination. Besidesthis, Mill was interested in devising an acceptable scientific method for thedeveloping social sciences,14 and this could only be done, he thought, by con-centrating upon empirical generalization, for it was far too dangerous andprovocative to theorize about matters such as these. Mill was not unopposedin his advocacy of inductive method. Among nineteenth century controversial-ists on scientific method, Jevons, Pierce and Whewell all disagreed with him.Whewell for example in his History of the inductive sciences (1 837) formulateda primitive version of hypothetico-deduction later to be elaborated by Popperin his important Logic ofscientijic discovery (1935, 1959).Pierce and Jevonstook issue with Mill when he suggested that induction was a method of dis-covering causal connection and at the same time a rigorous method of provingit. But Mill found some support in Pearson who in his Grammar of science(1892) urged that the collection of facts into general bundles was the properaim of science, that facts ‘were the one thing needful to form the minds ofreasoning animals’ .I5Pearson’s claim raises the question as to what facts are, whether facts arefree from all theoretical or conceptual colouring, whether facts are untreatedreports of direct experience.Is the assumption of Mill and Pearson followingLocke that there is such a thing as pure, naive observation valid? I think thatmost philosophers nowadays would argue that all observation is theory-loaded at some point;16 and that if we have no theoretical background againstwhich to observe, then our observations will be mechanical acts ofsentience, and so meaningless. Kant made this point in his criticisms of empiri-cal philosophy at the end of the eighteenth century. He wrote in theProlegomena. . . although all judgements of experience are empirical, i.e. have theirground in immediate sense-perception, yet all empirical judgments are notR.I. C. Re views 5conversely for that reason judgments of experience, but in addition. . . ,special concepts which have their origin wholly apriori in pure understand-ing must still be added.. . and it is these which make the judgement ofexperience objectively valid.17Let us now look at Mill’s discussion of induction. Mill, like Bacon, discussesfour inductive methods in his System of logic (1843). I shall consider only twoof them, since the criticisms I shall level at these can be levelled similarly at theothers. One method Mill calls ‘the method of agreement’, and it works asfollows. We survey all the examples of the phenomenon P we can, and try tosee what factor (or factors) F they seem to have in common. This factor Fcanthen be taken as the cause or part of the cause of the phenomenon P, asreflected in generalizations of the form ‘For any F, P’ (sufficient condition) or‘For any P, I;’ (necessary condition). (From exercising the method of agree-ment alone we cannot tell which.As we shall see later-p. 58-we can decideonly by attempting to falsify the generalizations.) This seems clear enough,even to conforming with common practice, but upon reflection there areseveral evident difficulties with it. For example, how in fact shall we hit uponthe common factor F, when as far as Mill’s instructions are concerned, weought to approach the matter with open minds. If we are true to the philosophyof the method we ought to pay attention to every possible causal factor F.Suppose we are trying to find out why iron rusts. According to this Millianmethod, we ought to examine every aspect of those samples of rusty ironwhich we have before us-their size, shape, origin, position, purity, history,environment, owner and so on.Clearly this will not do. The only way we canmake the method work is to decide what factors are relevant to outbreaks ofrusting and what are not. We must have some idea what we are looking for, orwe cannot begin to look. We must have some idea about what might be thecauses of rusting before we begin; our search in other words, has to be guidedby some tentative theory of rust. By itself therefore, the method constitutes anineffective means of discovery. (The same sorts of criticism can be made ofMill’s complementary ‘method of difference’.)lgEven if we do succeed in discovering some F which seems to be universallycorrelated with rusting, we cannot rule out the possibility that both P and Fmay be caused by something else.For example suppose we found that water isalways present when iron rusts. We could not say that water was a cause ofrust, for as far as we can tell while using the method, the rust might be thecause of the water, or both the rust and the water might be the effects of somethird and unidentified influence. This no doubt seems absurd to us, but onlybecause we already have some theory of rusting in mind. If we approach thematter in true Millian manner, it is not at all absurd.As I have already said, we might be able to tell whether F is sufficient,necessary or necessary and sufficient condition of P by testing our generaliza-tions, but such testing according to Mill is not necessary if we have followedthe inductive method properly. But, testing apart, a causal analysis becomespossible only when we have some theory or hypothesis with which we can assessthe significance of the correlations we observe, with which we can separatereal causal connection from fortuitous conjunction.Mill we must suppose,Theobald 5like Hume before him, read no more into the notion of cause than that ofinvariable suc~ession.~~Mill calls the second method I consider ‘the method of concomitant varia-tion’. This at first sight seems close to aspects of contemporary scientificpractice, and was indeed close to the aspirations of nineteenth century philo-sophers of science like Mach who wished to limit science to establishing func-tional relationships without further enquiry into their physical significance.The method requires us to find some Fwhich varies in an orderly manner whenthe phenomenon P in which we are interested varies.This can be formulated inquantitative terms, though of course Bacon in the seventeenth century wouldhave found it difficult to exploit this possibility. But what, we may ask, is meantby ‘orderly’ here? What is an orderly variation? Since there is no such thing asabsolute or complete disorder, any set of data will exhibit some order. Thequestion is: is it significant order? Moreover the observation of simultaneousvariations in P and F does not of itself establish any causal connection, forboth variations may be governed by the variation of a third, unidentifiedfactor.Nor can we tell whether F i s a necessary, sufficient or necessary andsufficient condition of P. Only some theoretical preconceptions can help us toanswer these questions. For example we might observe that the more a piece ofiron rusts, the less oxygen there is in the immediate surroundings. Yet wecannot infer from this alone that the oxygen causes the iron to rust, thoughsuch an inference might be justified if we took our generalization in the light ofsome hypothesis about rusting.We must conclude then that although Mill’s methods may discover causesto us, they do not prove their discoveries.Mill’s claim that his inductivemethods constituted methods of discovery and proof at one and the same timeis false. For proof at least, we shall have to turn to the logically more rigoroushypothetico-deduction.The limitation of inductive science then, as I have described it, is that even ifwe do discover true correlations which may be useful predictively, we shall stillbe unable to prop up these predictions with satisfactory explanations. Here oneis led to think of one of Mill’s primary concerns, the social sciences, whereinductive generalization still plays an important part. There are of coursedifficulties in getting even as far as reliable generalizations in the socialsciences for various reasons, generally well known; the fact that human beingsmay be predisposed to behave in a certain way by external conditions, but theyare not usually constrained so to behave; the fact that how they behave willdepend upon their evaluation of those conditions; the fact that control experi-ments in the social sciences are not possible as they are in the physical sciences;the fact that society is arguably not a system in the way that a physical systemis a system; and so on.It may be that these difficulties rule out the formationof sensible hypotheses in the social sciences, thus confining social scientists tomaking inductive generalizations with limited predictive usefulness and littlereal explanatory power. Unless society is a system, it will not be possible toform clear ideas as to what universal forces may be at work within it.It mighteven be argued that the failure to find such forces suggests increasingly thatsociety is not a system. Ironically therefore Mill seems to have developed hisinductive philosophy, which in the event turns out to be inadequate, with56 R.I.C. Reviewperhaps the most intractable subject matter he could find at the back of hismind.Induction by itself then will not do as a source of explanation and under-standing. The laws of chemical composition do not by themselves help us tounderstand chemical changes. Hypothetico-deduction on the other hand,according to which we form relevant hypotheses of cause and structure andthen attempt to reject them seriatim by appealing to their experimentalimplications is in some ways nearer the mark.I say in some ways becausealthough it gives us a clear criterion of validity by its emphasis on falsification,it does not help us to understand the generation of hypotheses. And here wemay find ourselves back with all the informality of induction. I am inclined tothink that in chemical practice for example, scientists work in a variety ofways, which may now be inductive and now hypothetico-deductive. But I shallreturn to this point later (p. 65).TESTING IN SCIENCEI want now to turn to the important question of how we test scientific claims,because this rather nicely illustrates some of the important differencesbetween induction and hypothetico-deduction.20 It hardly needs saying thatsome rigorous testing of any empirical claim is a vital part of scientific method.Now there would seem to be two ways of testing a scientific statement; one isto try to confirm or verify it, the other is to try to falsify it.Both are used,though which depends quite a lot upon the science concerned and more thanthat, upon the context of the testing. Thus physics in contrast perhaps tobotany is a full-time matter of looking for trouble.We ought to remember here that testing, whether confirmation or falsifica-tion, has no proper place in inductive method because this method is supposedby its advocates, incorrectly, to supply its own validation. Nevertheless let ussuppose we are going to test both an hypothesis and a generalization. As aninductive generalization we may consider (a) ‘All damp iron rusts’; and as anhypothesis (b) ‘If iron is damp, then it rusts’.If we think about rust in terms ofthe hypothesis (b), then it is, I maintain, more natural to consider testing byfalsification rather than by confirmation. On the other hand, if we think of rustin terms of the general statement (a), then I would say that confirmation seemsthe more appropriate procedure for testing. For if our claim is a properlyformed inductive generalization, then we should not be expecting to find anyfalsifying cases, but merely confirming examples. And if it is an hypothesis, itstands accepted until shown to be false. ‘All damp iron rusts’ suggests then,that we look for further examples of water with rust. ‘If iron is damp, then itrusts’ suggests rather that we look for cases where damp iron does not rust.I want to take this a little further. The general statement (a) ‘All damp ironrusts’ can be converted into a logical equivalent (al) ‘All rust-free iron is dry’.LogicaZly (al) is equivalent to (a).And so we might think that what confirms(a) ought to confirm (al). But (a) is confirmed by damp, rusty iron, and (al) bydry, rust-free iron. And it must strike us as odd that in order to confirm (a) ‘Alldamp iron rusts’, it seems that all we need to do is observe dry, rust-free iron(which confirms (al) the logical equivalent of (a)). It strikes us as odd becauseTheobald 5such an observation does not seem to bear at all critically upon the originalgeneral statement (a).This peculiar situation shows us two important things.One, the fact that two statements such as (a) and (al) are logically equivalentdoes not mean that they are methodologically equivalent. And two, as long aswe think of testing a statement in terms of corroboration, we shall be depen-dent upon the logical form our statement takes. This can be very uneconomi-cal. If we are interested in the properties of a small class of Xs, then it will beextravagant, other things being equal, to divert our interest to what will thenbe a very large class of non-Xs.Suppose we now try to falsify (a) and (al). In the case of (a) we shall need toobserve damp, rust-free iron, and in the case of (al) rust-free, damp iron. Inother words, to falsify either (a) or (al) requires the same observation.Thefalsification of a generalization then does not depend upon the logical form ofthe generalization. Moreover the observation which falsifies (a) and (al) alsofalsifies (b). It seems then that as far as the methodology of testing is con-cerned we should concentrate upon the falsification of hypotheses and generalstatements rather than upon their confirmation. Now we had occasion to noteabove that falsification is more appropriate to (b), while confirmation is moreappropriate to (a) and (al). It seems then that when we are concerned withchecking the validity of general statements of inductive origin they are betterconstrued as hypotheticals open to falsification. So although we may acquiregeneral knowledge by some inductive generalizing process, Millian orBaconian, its validity is best established by attempting to falsify related hypo-theses. As far as testing is concerned, we must desert induction for hypothetico-deduction.It might be worth digressing here for a moment to point out that somephilosophers of science have argued that general statements and hypothesesare not real statements at all, but merely licences for forming such.Forexample, ‘All damp iron rusts’ or ‘If iron is damp, then it rusts’ licenses us toassert ‘This sample of iron is damp and so will rust’. The claim in effect is thatthe meaning of hypotheses and general statements is properly to be found inthe meaning of the singular observation statements whose truth or falsitywould confirm or falsify them.This is the philosophy of logical positivism,whose faults I cannot go into here,21 except to say that the identification of themeaning of a statement with the procedure for testing it has never been persua-sively established.In particular, for the positivist the meaning of an hypothesis which mentionsan entity such as an atom which is not directly observable, is to be found in themeaning of the observation statements which confirm or falsify it. The scene isthen set for the positivist to say that such a physical object is nothing more thana collection of observable properties. It is the sort of thing it is because it hasthe particular properties it has. But it could equally well be argued that anobject has the properties it does have because it is the sort of thing it is.Nowthis is an important move, because it leaves the nature of the object open to beinvestigated. If an object is nothing but a collection of observable properties,if it has no nature, indeed if there is really no such thing as ‘it’, what reason canwe have to investigate it beyond what we have already observed? Indeed whatreason can we have even to start investigation? And besides, if an object has58 R.I.C. Reviewno nature apart from its properties, what sort of properties are we to considerlooking for? Any? If so we are back with the problems of inductive methoddiscussed earlier, of not knowing how to start or when to stop. Positivism isnot a philosophy for research.In a later development of positivism, instrumentalism, the argument waschanged somewhat.A theory, it was contended, was simply a rule for inferringone observation statement from another. A theory asserted nothing whatso-ever about what the world was made of. But the same counter move can bemade here-it is because a theory asserts something in fact about the worldthat it is a successful rule for making inferences.Let us now return to testing. There is a simple reason why falsification is inlogic the proper way of bearing critically upon an hypothesis. I have so farmerely discussed some methodological reasons why this is so. Suppose ascientific argument is generally of the form ‘Given Tand A , then B’, where Tisa theory from which given A , B may be deduced.Now if B is true, the con-junction Tand A can be true or false. For any true proposition can be impliedby either a true proposition or a false proposition. On the other hand, if B isfalse, then Tand A can be only false. For no true proposition can imply a falseproposition. So if B is a deductive consequence of T and A , and if B is observedto be false, then T and A can be inferred to be false also. And if A areobserved initial conditions, the theory T must be false. We may concludetherefore that falsification is the proper way to test an hypothesis. ‘The aim ofscience is not to open a door to infinite wisdom, but to set a limit to infiniteerror’ as Brecht has Galileo say.22There is a further point worth making in connection with testing. In ordinarylife we are usually content to treat sufficient conditions as causes, whereas inscience we usually reserve this description for necessary and sufficient condi-tions. Now the confirmation of (a) tells us nothing about whether dampness isa necessary, sufficient or necessary and sufficient condition of rust.But thefalsification of (a) or (b) tells us at least that dampness is not a sufficient condi-tion of rust. If then we were to falsify (c) ‘All rusty iron is damp’, or ( d ) ‘If ironis rusty, it is damp’, this would tell us at least that rust was not a sufficientcondition of dampness and therefore that dampness was not a necessarycondition of rust. If attempts to falsify (a), (b), (c) and ( d ) fail (which we knowin actual fact they would not), then dampness can be taken to be a necessaryand sufficient condition of rust, at least until further evidence is forthcoming.PHILOSOPHICAL PROBLEMS FOR HYPOTHETICO-DEDUCTIONI have tried to show how, although knowledge may be obtained fortuitously byan inductive method, the critical evaluation of that knowledge proceeds bestby trying to falsify relevant hypotheses.I mentioned at the beginning of thisessay that induction remains content with the world at its face value, whereasthe invention and testing of hypotheses is not limited in this way. The contentof an hypothesis is not limited by our ordinary experience of the world. It is infact difficult to see how many of the most important principles and theories ofphysical science could have arisen by any generalizing operation alone.Howfor example could atomic theory have arisen in this way? And how can therole of conservation principles be interpreted inductively ?Theobald 5Since the content of an hypothesis is not limited by our everyday experi-ence, we soon have to face the question : are atoms, ions, electrons and so on,which are features of many physical hypotheses, simply fictions or are they realexistents? Are they merely grammatical ciphers in a scientific language, or dothey actually designate bits of the real physical world? Are atoms and ionsreal in the sense that we take the furniture of our laboratory to be real? Per-haps I should point out that in a logical sense it does not make any differenceto the properties of a thing whether it is a real existent or not.I mean by thatthat logically speaking, existence adds nothing to anything. If I describe a pieceof chemical apparatus in detail, and then add ‘But such a piece of apparatusdoes not exist’, all I do is to lose the attention of my audience. I do not changethe properties of the apparatus. So whether atoms or ions are real existents ornot makes no difference to the predictive power of any atomic hypothesis,though it must make a difference to its persuasive power of explanation, itspower to help us understand.Hypothetico-deduction then raises certain philosophical problems notraised by induction. It is often said that we never observe atoms in that sense of‘observe’ appropriate to ordinary common-sense observation.But is this so ?I am inclined to think not. I think that observing an atom or an ion or anelectron involves a perfectly proper sense of ‘observe’, a sense which I hope toexplain. The atomic theory is designed to explain all the visible aspects ofmacroscopic change, and therefore atoms themselves cannot be invested withordinary, visible properties. But this does not mean that they cannot beobserved.Imagine looking into the clear night sky and seeing a comet. You say toyourself ‘There’s a comet’ or perhaps ‘I can see a comet’. Rather more im-probably you might say ‘I can see the light-track of a comet’, even though in asense that is what you do see. You can quite properly say these things becauseyou undoubtedly know a little astronomical science and probably also some-thing about the appearance of moving luminous bodies, and because you areconfident that astronomers have some sort of astronomical tests up theirsleeves to confirm or falsify such claims.The argument ‘I saw an A ; A is B ; soI saw a B’ is generally valid only if you know that A is B. That is, if you saw A ,you are entitled to say you saw B, only if you know that A was B. From the factthat you saw a man, you are entitled to say that you saw a laughing man, onlyif you know the man was laughing. Of course you need not have observed hislaughing, someone might have told you. You can be entitled to say you saw alaughing man without being entitled to say that you saw a man laughing. Totake another example, if I saw a piece of apparatus, I am entitled to say I sawan ir spectrometer only if I know it is an ir spectrometer.But I need not haveseen that it was an ir spectrometer; someone, an expert, may have told me thatthat was what I was seeing. To return to comets: if we see a light-track in thesky, we are entitled to say we see the light-track of a comet because we knowfrom astronomers that such is in fact the light-track of a comet. And seeing thelight-track of a comet is seeing a comet making a light-track. It is in fact seeinga comet. What else could possibly count as seeing it? And no one on thisaccount would dream of saying that comets are not real.The same sort of considerations apply to seeing a-particles in cloud-60 R.Z. C. Reviewchambers or molecules in electron micro~copes.2~ One reason why thesehypothetical entities are bona fide candidates for the description ‘real’ is thatlike the comet, there is a particular conceptual background which makes certainclaims to see them legitimate and significant.There is an accepted reservoir ofknowledge which makes the second premise in the argument I outlined abovetrue. To take a chemical example, to see a chemical change occurring is to seean electronic rearrangement going on, once we know all about chemical theory.The important point is that what we say we can see depends upon our know-ledge. As does therefore what we can say is real.Against this some philosophers have argued that to say that we see anelectronic rearrangement going on, if taken literally, is to say something mis-leading if not false.It is argued that whereas seeing a chemical change going onin a flask is clear enough, to say that this is to see electrons rearrange is to hidethe fact that an inference has been made in accordance with some physicaltheory, an inference from what goes on in the flask to the fate of the electrons.This has been the view of many instrumentalist and positivist philosophers ofscience.24 But given the setting of atomic theory, seeing a chemical change inprogress just is seeing the electrons rearranging, and moreover that is all thereis to seeing the electrons rearranging. The confusion arises from failing tonotice the difference between seeing inside a theory and seeing outside it.Bothare legitimate seeings, and neither involves making inferences of any sort.Seeing is not just opening one’s eyes-seeing is an achievement. Note howfrequently ‘see’ is used with ‘can’ and how rarely if at all in the present tense,‘I see. . .’ or ‘I am seeing. . .’. For to see is to invest what you notice withsome significance. And this is what theories and hypotheses are for. Allobservation is dyed with theory to a greater or lesser extent, and it was acardinal and curiously romantic error of Mill, Pearson and others to supposethat there was such a thing as simple, naive observation, and therefore thatthere was such a thing as a fact which was not charged with some theoreticalpreconceptions.HYPOTHESESI have argued that although it may suggest correlations between observableproperties, induction cannot establish causal connection.And so it cannotsupply profound understanding. We need to devise hypotheses and test themcritically in order to explain and understand. The actual form any hypothesistakes and the particular suggestions it makes will depend a great deal uponour present knowledge. For any hypothesis which is to extend our presentknowledge will begin by suggesting analogies between new physical systemsand systems with whose behaviour we are already familiar. Rarely thereforewill an hypothesis depart completely from previous ideas. This might be takento imply that the refutation of an hypothesis will call the whole of the scienceconcerned into question. But this is not necessarily so. As has been said,falsification is the sign only that something has gone wrong, not that every-thing has gone wrong.On the occasions when an hypothesis does departradically from previous ideas the result is a conceptual revolution in science,examples of which will be very familiar. To the chemist the reorientation ofchemical thought by Lavoisier in the eighteenth century, by Dalton in theTheobald 6nineteenth, and by Bohr and later quantum theorists in the twentieth centuryare perhaps the most important.Sometimes, metaphysical conviction can lead to the retention of hypotheseseven when the evidence is against them, even when they have been technicallyfalsified. Witness the persistence of alchemical ideas despite their manyfailures,25 and the reluctance of chemists, for example Priestley, to abandonphlogiston theory even after the work of Cavendish and Lavoisier.As anotherexample we may recall that MendelCef persisted with his classification of theelements despite the fact that at the time his periodic arrangement failed inseveral places.Sometimes metaphysical conviction makes us continue with an hypothesiswhen there is no clear evidence for or against it. Dalton’s atomic hypothesiswas maintained in the face of a great deal of initial quantitative uncertainty,and an inability to see precisely how to put it to conclusive test. In fact therewas a gradual decline of interest in atomic theory during the middle of thenineteenth century until the work of Avogadro and Gay-Lussac was re-presented by Cannizzaro, and shown to be compatible with Dalton’s hypo-thesis after some modifications.These few historical points show that dis-covery, justification, judgement, imagination and metaphysical convictionbecome inextricably mixed during the evolution of scientific ideas. They alsoshow that hypothetico-deduction is not a scientific method which commandsthe scientist’s unswerving allegiance. As I pointed out in the introduction tothis essay, science like any other human activity cannot always be conductedsuccessfully by rule of logic alone.But the most interesting question to do with hypotheses has yet to be asked.How do we form hypotheses ? How does our guided imagination work ?4There are very difficult questions even to begin to answer.We can certainlymake a survey of the sorts of person who have had the necessary imaginativeframe of mind to devise hypotheses, and we can certainly make a survey of thephysical and intellectual conditions which predispose (but not determine) aman to be imaginative. But I doubt whether any statistical findings of this sortabout imaginative thinking will leave us any nearer either predicting orengineering its occurrence. And such a survey would in any case do little toclarify what imagination is or how it works in the business of discovery. And itis to aspects of the philosophy of the imagination I wish to turn now.All our attempts to come to terms with the experienced world depend uponour fitting this experience into an orderly, though flexible matrix of generalconcepts whose expression is usually verbal.As I have already remarked,scientific knowledge which is linguistic and propositional, requires more thana keen eye for phenomenal incident. To know is to create order and structure inthe world by means of language. Knowledge is not something absolute, just‘out there’ for quick capture, but is, as Coleridge realized, something to becreated and recreated because language is subject to constant, creative renewalby philosophers, poets and scientists. ‘The relation of language to thought andreality is not a passive ref? ection, but an active and tendentious reaction’ wrotethe literary critic and poet Christopher Caudwell.26 This I think is not such abad definition of scientific practice.We can see this more surely if we reflect upon how we come by the concepts62 R.I.C.Reviewwe have. Let us take the concept ‘chemist’ as an example. A common view ofthe origin of our concept ‘chemist’ would be this-all we do is to make asurvey of all chemical persons we know, and draw up an inventory of whatthey have in common. As a result we have a concept ‘chemist’ the meaning ofwhich is decided, that is defined, by a collection of common properties. Butclearly this will not do, attractively simple as it seems. And it will not do for thesame reasons that Mill’s method of agreement will not do. For until we have atleast some concept ‘chemist’ in our minds, we can have no idea who arechemical persons, and therefore no idea what common characteristics we areto look for. This is an important point.Suppose we take the concept ‘red’. It isoften argued that this concept is acquired by noticing and naming what iscommon to a set of red objects. But this can be done only if we are quite clearthat we are dealing with culuur as opposed to say shape, size or weight. Wemust be clear what sort of thing we are attending to before we start. Conceptsare not acquired independently, but in relation to other concepts. Another wayof putting this would be to say that language is a system of concepts, not acollection. We cannot and do not acquire concepts by diligent stock-taking.The concept ‘chemist’ like all other concepts is first and foremost a mentalinvention, but one whose meaning will change and develop as our experienceof the class of objects designated by the concept increases.It is not easy to sayprecisely why we invent concepts, nor how they and our experience developside by side. We may feel (inductively) that there is some uniformity in ourexperience which needs charting, or we may wish to discover whether there is.These are matters clearly for imaginative judgement, for hypothesis and testing,not simply for an inductive logic.What has been said here of the concepts ‘chemist’ and ‘red’ is, I think, trueof all concepts. They are first and foremost mental inventions and they designateopen classes. Whether or not some particular item of experience falls under agiven concept is a matter both for our perception and our judgement, but notfor our perception alone.It is a matter of weighing the evidence for or againstinclusion. This looseness in the application of language to the world is vitallyimportant, for it allows language to hover over our experience of the world,and settle upon it not only as an instrument of definition, but as an instrumentof promise, expectation and revaluation. Concepts are likeAxesAfter whose stroke the wood rings,And the echoes!Echoes travellingOff from the centre like horses.27In scientific contexts it is this looseness which allows us to overlook disagree-ment between hypothesis and observation without being guilty of logicalinconsistency.28 For, as we have seen, theories and hypotheses are not alwaysrefuted by such disagreements.Concepts then do not mirror reality; rather in an important way they createthe reality we talk about.Experience does not give our concepts meaning; wegive them meaning, and by so doing we endow experience with meaning. ThisTheobald 6is an extremely important point which explains why I head this essay with somewords from Eliot’s Dry Salvages, and which is at the heart of the conflictbetween induction and hypothetico-deduction. ‘Concepts lead us to make in-vestigations ; are the expression of our interest, and direct our interest’ wroteWittgenstein.29 This can be said equally of any hypothesis in science. Myremarks about concepts in the preceding paragraphs, although they need moreelaboration and defence than I can give them here, can be directly translatedinto the terms of the induction/hypothetico-deduction controversy.Forhypotheses are not elicited from experience, they are invented to make sense ofexperience and, like concepts-themselves in some ways hypotheses of persis-tence, identity, resemblance and uniformity-they are modified in the light of it.The object of ordinary language, like its scientific development, is to tiedown experience into labelled bundles, to reduce the apparent variety inexperience by collecting it into generalities. The scientific imagination tries tosimplify, though not, as I have tried to show, exclusively by induction. Thepoetic imagination as I understand it, tries to complicate. ‘What we havegotten by this revolution is a great deal of good sense.What we have lost is aworld of fine fabling’ wrote Richard Hurd, Bishop of Worcester, of the scien-tific enlightenment in the eighteenth century. The poet, the Blake who seesscientists as generalizing idiots, thinks of simplification as restricting the pos-sibilities for seeing the world, as numbing our sensitivity to small but impor-tant differences in things. ‘We have art in order not to die of the truth’ wroteNietz~che.~~ Scientific imagination is more controlled and has less room formanoeuvre than the artistic imagination, and yet in the long run it may carrymore universal conviction. For the fact that the scientific imagination workswithin the confines of previous knowledge and opinion guards scientifichypotheses against some of the subjective extravagancies which Bacon, Milland others feared.New ideas in science are either rejected or become acceptedas textbook truths, but new ideas from the artistic imagination are always freshto each generation. They are not assimilable to a body of knowledge. This isbecause in science the meaning of a term is designed to be independent of thecontext in which it is used and so becomes the expression of a timeless gener-ality in nature whereas in poetry, say, the meaning depends very much uponthat context and requires revaluation when that context changes.I have already mentioned the importance of analogy in science. The scien-tist’s imagination works by seeing in the apparently new much that is like thealready familiar.The artist works by seeing in the apparently familiar muchthat is actually new. The effectiveness of all analogy as Coleridge pointed out31is a complex and subtle matter of ‘the balance or reconciliation of opposite ordiscordant qualities; of sameness with difference; of the general with theconcrete, the individual with the representative; the sense of novelty andfreshness, with old and familiar objects; a more than usual state of order . . .’.Once we have accepted an analogy, once it convinces us, we are necessarilyconverted to a reconstructed reality. ‘The expression of a change of aspect is theexpression of a new perception and zt the same time of the perception’s being~ n c h a n g e d . ’ ~ ~ We cannot look at gases in the same way once we havesup-posed that they consist of bits of matter in Newtonian motion.We cannot lookat human beings and chairs in the same way once we accept that they both64 R.I.C. Reviewhave legs, nor at clouds in the same way once we have seen ‘a cloud that’sdragonish. . .’.33In science this sort of imaginative move is part and parcel of forming andtesting hypotheses. We start by seeing A as B and we then act on this sugges-tion to find out whether in fact A is B, whether the analogy stands up toexamination. Imagining is always preliminary to knowing. Imagining a gas asa collection of Newtonian particles is preliminary to knowing that a gas is infact more or less just that; and also to seeing why it is onZy more or less justthat.We can see then that hypothetico-deduction is an extension of aspects of thephilosophy of concept formation into the methodology of science.I have triedto show that induction is by itself methodologically inadequate, and in somerespects philosophically naive. This does not mean to say however that a Mill-ian approach to a problem is always inappropriate, as some critics seem tosuppose. I return to a point I made earlier which was that it is not possible tolegislate about how scientists should go about the business of discovery. It ispossible to legislate only about how they should check their discoveries, howthey should check their claims to know And here the verdict is clearly infavour of hypothetico-deduction.Hypothetico-deduction will evidently find favour with logicians andmathematically-minded physical scientists on account of its logical rigour,but it is not so clear that it will always find favour with the more experimentalscientist for whom the chance observation, the remarkable coincidence is ofgreat moment.One is sometimes tempted to think that those scientists whoargue often overbearingly for hypothetico-deduction have themselves lostcontact with the uncertainties and chances of day to day work in thelaboratory.CHEMISTRY AND SCIENTIFIC METHODI want now to say a few words about the position of the chemist in all this.Many important discoveries have been made in chemistry (as indeed they havein the other physical sciences) from the odd observation, the peculiar coinci-dence, so that although chemists may need the logic of hypothetico-deductionto put their ideas to the test, they often rely upon the informal consequences ofinduction to generate their ideas in the first place.The chemist is traditionallya scientist who often simply wants to know what occurs when A is mixed with B,besides wanting to produce a theoretical explanation for it. Although admittedlywe may wish to explain the reaction once we have mixed A with B, it isinductive curiosity which leads us to the mixing in the first place. In chemistrymany more things have been discovered than have been explained, and there isno sign that discovery is dependent for its impetus upon theory and explana-tion as it undoubtedly is in physics. Chemistry is still in many respects aninformal science. And as I have already remarked, important discoveriescome from such informality. I think that chemical curiosity is much less dis-ciplined than physical curiosity, and it is probably this element of ‘idlecuriosity’ which makes chemistry so successful in its relations with technology.For it is the chance rather than the systematic discovery which is ofteninteresting to the technologist.Theobald 65It is a notorious fact that in theoretical physics one experimental result isoften all that is necessary, indeed in practice is often all that is available toevaluate an hypothesis and if need be reject it. On the other hand in chemistrythere is more often than not a vast array of experimental results whichcan be brought to bear upon an hypothesis. Usually no single result bearsupon a chemical hypothesis in the way a single result can bear upon anhypothesis in physics. This is reflected in the fact that theories and models inchemistry are generally much looser formulations than those in physics. Thechemist is concerned with modifying details of a well-authenticated molecularmodel, not with rejecting it. On the other hand the physicist at his level ofphysical enquiry is concerned much more with making a conclusive choicebetween rival models. Accordingly there is not such a tight relationshipbetween hypothesis and observation in chemistry as there seems to be inphysics. These things are all a reflection of the fact that chemistry is still insome measure an inductive science.Chemistry then stands between physics on the one hand and the fieldbiological sciences on the other in being an area of inquiry peculiarly appro-priate for the exercise of both inductive and hypothetico-deductive method.However chemists will continue to enjoy this stimulating position only if theyresist the temptation to suppose that they must model their science either onphysics or biology. This, as I have argued elsewhere,34 is seriously to suppressthe imagination besides, as I believe, being logically and methodologicallyindefensible. There is more I believe in heaven and earth than is comprehendedin the philosophy of physics. But fortunately there is no reason to suppose thatchemistry must succumb to relations with either of its suitors. Those whowould have it do so will I think find relations become very strained, andI suggest they would do well to remember Tristram’s remarks about his father:he was systematical, and, like all systematic reasoners he would moveheaven and earth and twist and torture everything in nature to support hishypothesis. In a word he was seriousand be content to remain chemists.ACKNOWLEDGMENTThe excerpt from T. S . Eliot’s The Dry Salvages is reproduced by permissionof Faber and Faber.REFERENCES1 Novum organum (1 620) ; The advancement of learning (1 605).2 System of logic (1843).3 Logic of scientific discovery (1935, 1959).4 Patterns of discovery (1958); The concept of the positron (1963).5 Induction and intuition in scientific thought (1969).6 Thegreat instauration (1607), Plan of (trans. by J. Spedding, R. L. Ellis and D. D. Heath).7 System of logic, book 3, chapter 1.8 Treatise of human nature (1738).9 Enquiry concerning human understanding (1 777).10 See my Introduction to the philosophy of science (1968) for further discussion and11 Novum organum, Aphorisms, book 2, 15 (trans. by J. Spedding, R. L. Ellis and D. D.12 Ibidem, book 1, 51.66 R . I. C. Reviewsreferences.Heath) 13 Advancement of learning, book 2.14 System of logic, book 6.15 C. Dickens, Hard times, book 1, chapter 1.16 See, for example, Hanson, op. cit.17 Prolcgomena to any future metaphysics (1783), para. 18 (trans. by P. G. Lucas).18 These methods are discussed more fully in most books on scientific method, e.g. E. Nagel,19 System of logic, book 3, chapter 5.20 See my Introduction to the philosophy of science, chapter 4.21 See J. 0. Urmson, Philosophical analysis (1956), and G. J. Warnock, English philosophy22 Scene 9.23 See my ‘Observation and reality’, Mind, 1967, 76, 198.24 See E. Nagel, The structure of science (1961).25 See my ‘Alchemy; a philosophical reappraisal’, Technology and Society, 1965, 2, 135.26 Illusion and reality (1 937).27 Sylvia Plath, ‘Words’ in Ariel(l948).28 T. S. Kuhn, The structure of scientific revolutions (1962).29 Philosophical investigations (1 958), part 1, 570.30 Goethe is an excellent example of a man torn in the two directions. See E. Heller, The31 Biographia literaria 1817, 2, 12.32 Philosophical investigations, part 2, xi.33 Antony and Cleopatra, act 4, sc. 12.34 See my Introduction to the philosophy of science, chapter 6.An introduction to logic and scientific method (1934).since 1900 (1958, 1969) for useful discussions.disinherited mind (1952).Theobald 6