Rafe Champion's M Sc thesis on the Duhem problem, Duhem's solution and Conclusions

CHAPTER 5

THE DUHEM SOLUTION

Clearly Duhem himself did not think that the integrity of science and its empirical base were seriously compromised by the problems with falsification which he identified. After all, his book was concerned with the methods employed by physics to make progress. He merely insisted that the relationship between theories and facts was more complicated than the positivists (or, later, the naive falsificationists) wanted to accept. He still considered that scientific theories should strive to account for the facts and consistency with the facts was the primary requirement for theories. He also moved towards a form of realism, with the view that scientific theories could develop towards a natural classification

To grasp his solution to the problems of falsification it is necessary to discern the larger outline of his ideas and to dispel some myths about them. Chief among these is the idea that Duhem's ideas on falsification made him a conventionalist or an instrumentalist, dedicated to the proposition that theories are mere instruments, chosen for their simplicity or their usefulness. For example, Popper referred to 'those who are influenced by a school of thought known as "conventionalism"...The chief representatives of the school are Poincare and Duhem'. (Popper, 1972, 78).

Duhem's alleged conventionalism has been interpreted as a reaction to the turn-of-the-century crisis of mechanistic theories, and to the difficulties of classical science. Maiocchi checked the chronology of Duhem's development and found the main themes of this epistemology in place well before the turn of the century and the alleged crisis in physics.

The study of Duhem's intellectual biography has led me to reach conclusions in many ways diametrically opposed to traditional judgements. These may be synthesised in a formula which is only apparently paradoxical: the main intent of the Theorie physique was to oppose instrumentalism, subjectivism, and the devaluation of the cognitive power of science...In fact, the thematics of crisis are totally absent in Duhem. On the contrary, all of Duhem's historical and epistemological reflections, all of his scientific work, as a researcher reveals the conviction that science was not only undergoing a period of great splendour during the late nineteenth century, but was getting rid of the errors that has accompanied it through the last three centuries! (Maiocchi, 1990, 385-86).

Far from the mood of crisis, Duhem emphasised the continuity of theories, and the way that science advances in an evolutionary rather than a revolutionary manner. His views were backed by his profound studies of the medieval roots of ideas in modern physics, facilitated by his own linguistic skills which gave him easy access to manuscripts in medieval Latin.

In our days, many are being swept by a wave of skepticism but those who force themselves to find in science the continuation of a tradition of a slow but steady progress will see that a theory that disappears, never disappears completely. (quoted in Maiocchi, 1990, 386)

As for the charge of instrumentalism against Duhem, certainly he was steeped in the strong French tradition of scepticism about hypotheses, linked with a phenomenalist view of science. According to Maiocchi, Duhem was personally much influenced by the French chemist-physicist Deville who stated, before Mach, that every scientific theory is merely a device for classification. However Duhem's mission was to praise theory, not to bury it.

Unlike Mach in Germany, Duhem did not have to fight against dogmatic belief in the nascent cognitive power of mechanics or against a tendency to objectify models. The cognitive devaluation of theories and models was already extensively employed as a criticism by French positivism...Duhem had to fight a battle in exactly the opposite direction...he had to avenge the rights of theory...Duhem's epistemology was a defence of theories against positivist pretences to eliminate them by strictly reducing science to pure experience. The positivists considered theories as secondary tools when compared to experience, even as superfluous and therefore, eliminable. Duhem endeavoured to show that theories are the heart of a scientific venture. (Maiocchi, 1990, 387)

Thus the philosophical tendencies that confronted Duhem at the turn of the century were the tides of instrumentalism, anti-intellectualism and subjectivism. A 'bankruptcy of science' debate began, fuelled by Bergsonianism and modernism, radical conventionalism and diverse forms of spiritualism. Duhem embarked on a series of publications to defend science from the skeptical conclusions of the 'revolt of the heart against the head' and to show that his own critique of positivism did not justify any of the desperate moves by conventionalists and others less sympathetic to science.

Duhem attempted to maintain a middle position between skepticism and the dogmas of positivism and empiricism. A central issue was the function of evidence and Duhem maintained a significant role for evidence while distancing himself from the positivists for whom sensory experience represented virtually the totality of reality.

Duhem grants that scientific theories are abandoned with great reluctance, sometimes long after experimental evidence points to their defectiveness; he will not admit, all the same, that they are pure conventions, that no experiment can in principle refute them. His object is to give an account of scientific theories which subjects them to the test of experience, while yet granting that this test is not direct and immediate (Passmore, 1966, 327).

At the same time he had to demarcate his position from that of the genuine conventionalists such as Poincare and Le Roy who also resisted the notion of falsifification but on different grounds and with different conclusions. In another deviation from the conventionalists, Duhem rejected the criterion of simplicity in the choice among rival theories. He considered that the capacity to save the appearances, to account for observations, has historically been the most effective consideration in theoretical developments, and progress has mostly involved more complexity rather than greater simplicity. As was noted in Chapter 2, Lakatos criticised Duhem for advocating a position which could permit the choice of theory to become a ‘matter of taste’ but this claim is clearly far from the mark (even though Duhem did allude to the beauty of natural classifications as theories became fully developed).

Yet another position which Duhem opposed was that which rejected the shallowness of the positivists in favour of metaphysical or deep explanations for natural phenomena. Duhem was concerned at the intrusion of metaphysics into science. He wished to avoid the situation of the mechanistic theories (or the method of Cartesians and atomists) which in his view depended on various kinds of metaphysics and so made the development of physics hostage to various schools of metaphysics. Duhem, in contrast, argued for the autonomy of physics.

The physicist who wishes to follow them [various metaphysical schools of thought] can no longer use the methods proper to physics exclusively...he is carried into the domain of cosmology. He no longer has the right to shut his ears to what metaphysics wishes to teach him with respect to the real nature of matter. Hence physics becomes dependent on metaphysics and subject to the fluctuations of its doctrines. Thus the theories constructed according to the Cartesian or atomist method are condemned to infinite multiplicity as well as perpetual new beginnings; they appear far from being able to insure the general consent and continuous progress of science. (quoted by Ariew, 1984, 319)

Typical of the way that Duhem has been misunderstood and misrepresented is the suggestion that his demarcation between the domains of science and religion was a ploy to protect his own Roman Catholic religious beliefs from any conflict with science. In fact he clearly stated that his physics was 'positivist' in spirit, though not Machian positivism, and he wanted to protect science from an invasion by metaphysics.

FURTHER DEVELOPMENTS OF DUHEM’S THOUGHT

Duhem's ideas steadily evolved towards the notion of a natural classification, thus representing a move towards realism, in contrast with both the positivists and the conventionalists. In view of the label of 'conventionalist' which is generally attached to Duhem, it may be surprising to find that he was a realist, possibly even a naive realist.

A striking feature of Duhem's realism is an anticipation of the concept which Lakatos labelled 'surplus content', following Popper, that is, the capacity of a theory to predict phenomena not yet observed.

Thus physical theory, as we have defined it, gives to a vast group of experimental laws a condensed representation, favourable to intellectual economy.

It classifies these laws and, by classifying them, renders them more easily and safely useable. At the same time, putting order into the whole, it adds to their beauty.

It assumes, while being completed, the characteristics of a natural classification. The groups it establishes permit hints as to the real affinities of things.

This characteristic of natural classifications is marked, above all, by the fruitfulness of the theory which anticipates experimental laws not yet observed, and promotes their discovery.

That sufficiently justifies the search for physical theories, which cannot be called a vain and idle task even though it does not pursue the explanation of phenomena. (Duhem, 1954, 30).

It seems that the label 'conventionalist' is not entirely appropriate for Duhem who is perhaps more appropriately described by Gillies as a modified falsificationist (1993, 104). The conventionalist label may have been attached because Duhem insisted that scientific theories do not provide explanations. His arguments to this effect are designed to keep metaphysics out of science, not to deny the vital, indeed indispensable role of theories as described above.

THE CHOICE OF HYPOTHESES

Bearing in mind both the importance of facing the facts and the limitations of experimental tests, Duhem prescribes three conditions logically imposed on the choice of hypotheses to serve as the base of physical theory.

A hypothesis cannot be a self-contradictory (nonsensical) proposition.

The different hypotheses shall not contradict one another.

Hypotheses shall be chosen in such a manner that from them taken as a whole mathematical deductions may draw consequences representing with a sufficient degree of approximation the totality of experimental laws. In fact, the proper aim of physical theory is the schematic representation by means of mathematical symbols of the laws established by the experimenter: any theory one of whose consequences is in plain contradiction with an observed law should be mercilessly rejected. But it is not possible to compare an isolated consequence of theory with an isolated experimental law. The two systems must be taken in their integrity; the entire system of theoretical representations on the one hand and the entire system of observed data on the other. As such they are to be compared to each other and their resemblance judged. (ibid, 220)

Beyond the logical considerations 1 and 2 above, logic can do little to resolve the issue of theory choice, or indeed when to give away a theory that has been apparently refuted. As noted elsewhere scientists confronted with falsifying evidence can adopt very different strategies, ranging from fundamental revision of the theory, through modification of auxiliary hypotheses, to denial of the validity of the evidence. Here we must proceed to matters of judgement and good sense.

Duhem has a section in his major book titled 'Good Sense Is the Judge of Hypotheses Which Ought to Be Abandoned'. However he does not have a great deal to say about theory choice, because he believes that, for the most part, scientists do not hasten to make major decisions about theory choice.

We should notice the hesitations, the gropings and the gradual progress obtained by a series of partial retouchings which we have seen during the three half-centuries separating Copernicus from Newton. (ibid, 253)

Duhem argues that good sense is required to supplement falsifications and crucial experiments because these cannot provide decisive logical arguments for one side or the other. Some have regarded the theory of 'le bon sens' as important and promising but nobody has made much of it. Duhem himself makes more sense when he writes of an old system crumbling away beneath the weight of accumulating falsifications. This would have been the case with the Priestley's phlogiston theory which was in deep trouble with internal problems and accumulating ad hoc modifications even without the rapidly developing rival program of Lavoisier. Newton's theory may have been in the same situation, though not to the same extent and not with accumulating falsifications, merely the burden of unsolved problems which were eventually resolved by general relativity.

Scientists certainly do not make unanimous decisions.

Hence, the possibility of lengthy quarrels between the adherents of an old system and the partisans of a new doctrine, each camp claiming to have good sense on its side, each party finding the reasons of its adversary inadequate. (ibid, 217)

It may be that this is a case of the scientific community manifesting ‘good sense’ by keeping alternative theories alive long enough for each to demonstrate its full capacity. No doubt individual good sense needs to be supplemented by appropriate institutions and traditions to maintain an exchange of ideas and criticism.

GOOD SENSE

Duhem's concept of good sense was clearly very important to him although he does not appear to have written very much systematically about it. Possibly his most extended account of good sense is in his lecture series titled German Science (1991), first published in 1915. Unfortunately these four lectures were delivered during 1914 and are likely to be regarded as partisan contributions to the war effort.

The main theme of the lectures is a criticism of various unhelpful practices in science, by no means restricted to German science. One of the defects is a deficiency in the ‘good sense’ which is required to handle situations where logic is inadequate (as in the Duhem-Quine problem) and the evidence in hand is inconclusive or even contradictory. Duhem spelled out in some detail how good sense and the spirit of intuition can become suppressed when sciences reach a state of development where major theoretical innovations have opened the way for ongoing development by merely working out the consequences of well-founded theories.

In proportion as an experimental science is perfected, the hypotheses upon which it rests, at first hesitantly and confusedly, become more precise and firm...From this moment on, these propositions serve as principles in processes of reasoning at the conclusion of which is found the clarification of certain observations or the prediction of certain events...science uses the deductive method more and more. (Duhem, 1991, 27)

According to the mathematical/deductive cast of mind which comes into its own in the situation described above - the period of consolidation of theoretical progress - ‘an experimental science is born the day that it takes deductive form, or better still, the day it becomes clothed in mathematical apparel’ (ibid, 29). Duhem invokes Kant as a majestic expositor of the notion that theories of nature are not properly scientific except for the amount of mathematics which they contain. On this criterion chemistry was ruled out of court as ‘purely empirical’.

To the extent that a concept capable of being constructed shall not have been found for the chemical action of matter, chemistry cannot be anything but a systematic art or an experimental doctrine, but in no case a science properly speaking, for the principles of chemistry [in that case] are purely empirical and do not allow of being represented a priori in intuition. They do not in the least make the possibility of fundamental laws of chemical phenomena conceivable for they are not capable of being worked on by mathematics. (Kant, quoted in Duhem, 1991, 30)

Duhem noted how various disciplines arose in some countries (such as France) and later became institutionalised at the mathematico-deductive stage in Germany where ‘research factories’ churned out results without need of intuition or originality. At the same time the fruits of these labours can pay off handsomely through practical applications in industry and technology. Despite the potential for scientific progress and technological developments under these conditions Duhem located two dangerous features that were likely to emerge. One is a tendency to impose mathematics and the deductive form on developing sciences before intuition and experiment have had time to deliver the foundations of well-tested theories required to support extended mathematical and deductive development. The other is the neglect of the need for rigorous testing to ensure that first principles remain open to development by error-elimination. Duhem's comments on this point read a little like an anticipation of some critiques of "normal science".

There, each student punctually, scrupulously, carried out the small bit of work which the chief has entrusted to him. He does not discuss the task which he has received. He does not criticize the thought that dictated this task. He does not get tired of always doing the same measurement with the same instrument (Duhem, 1991, 122).

According to Duhem, Pasteur provides a model of the kind of mind which avoids those defects, blending rigorous thinking with the spirit of intuition. Duhem's account of Pasteur is based on stories from assistants in the great man's laboratory.

Pasteur began with a preconceived idea and prepared experiments which were expected to produce certain results. Often the expected results did not appear, whereupon Pasteur would have the experiments repeated with greater care. Often, again, they did not work.

My friends the laboratory assistants were often astonished at the obstinacy of "the boss", intoxicated by the pursuit of the consequences of what was obviously an erroneous preconception. Finally a day came when Pasteur announced an idea different from the one which experiment condemned. One then realised with admiration that none of the contradictions to which the latter had led had been in vain; for each of them had been taken into account in the formation of the new hypothesis...In this work of successive improvements upon an initial necessarily rash and often false idea which finally leads to a fruitful hypothesis, the deductive method and intuition each play their role. But how much more complex and difficult it is to define their roles than it is in a science of reasoning. (ibid 22-23

In the complex process of deducing consequences from preconceived ideas, there is a need for the rules of syllogistic logic to ‘be assisted by a certain sense of soundness that is one of the forms of good sense’. (ibid 23)

In another way, again, good sense will intervene at the moment at which one realises that the consequences of a preconceived idea are either contradicted or confirmed by the experiment. This realization is in fact far from being entirely simple; the confirmation or contradiction is not always explicit and straightforward, like a simple 'yes' or 'no'. We stress this point a bit, for it is important. (ibid 23)

For example, some of Pasteur's trials involved injecting rabbits with potentially lethal doses of a toxic substance. The death rates had to be carefully examined to take account of the fact that animals could die for reasons other than the experimental treatment (false positive results). Also, and more importantly, some animals could survive due to mistakes in the dose or defects in the method of injection of the substance, or to their greater constitutional strength.

While judgements on these matters are constantly required in scientific researech, Duhem considered that good sense would not return its verdict until the pros and cons of the situation were carefully weighed. It should be noted that the precise moment when a particular scientist makes a verdict is not especially significant in the larger historical perspective, though it may be important for individual people or teams if there is a race for priority under way (pace the double helix). So far as the progress of science is concerned (as opposed to the reputations of scientists) a few months, years or even decades of delay in a blind alley is no great matter, provided that eventually the caravan begins to move onwards.

Returning to the matter of eliminating hypotheses, Duhem argued that it is not enough to eliminate the preconceived idea which did not stand up to tests, there is a need for a replacement.

Here it is necessary (Pasteur excelled in doing this) to pay attention to what each of the observations which have condemned the initial idea suggests, to interpret each of the failures which destroyed that idea, and to synthesise all these lessons for the purpose of fabricating a new thought which will pass once again under the scrutiny of the actual results. What a delicate task, concerning which no precise rule can guide the mind! It is essentially a matter of insight and ingenuity. (ibid 24, my emphasis)

Duhem went on to argue that good sense must transcend itself to become ‘what Pascal called the intuitive mind [esprit de finesse]’. (Duhem, 1991, 25) Presumably the intuitive mind is richly endowed with good sense and Duhem went on to identify various departures from good sense. One of these is the practice of mechanically following particular methods, especially mathematical methods, starting from premises which are held to be beyond criticism. In this situation the theory is being used to test the results rather than the other way about. Admittedly there are situations where results may be challenged on theoretical grounds; the point is to employ enough good sense to ensure that good evidence is given adequate weight and to be at least prepared to reconsider the underlying theory. It is one thing to reject particular falsifications (presumably with reasons) but it is a very different thing to insist that the theory is in principle not open to falsification.

Pursuing the theme of inappropriate use of mathematical methods, Duhem deplores the separation of pure mathematics from science, emphasising the value of feeding 'real' problems to maths and science (and to philosophy?)

Nothing is more dangerous than acting in such a fashion [setting up problems of pure mathematics without making any attempt to apply them]. Not only does it deprive the sciences of observation of the indispensable means of research without which they would fall into pragmatic fact-collecting; but, further, in isolating the mathematical sciences it renders them sterile. Most questions which have proved to be fecund, which engendered broad theories of geometry or algebra, have been posed to the mathematician by the physicist or the astronomer. (ibid 60)

Duhem's advice to young scientists is to read the masters, ‘Without respite, give over the care of forming your thought to those who were our precursors and our masters’ (ibid 71). For mathematicians and physicists he nominates Newton, Huyghens, Delambert, Euler, Clairaut, Lagrange, Laplace, Pascal, Poisson, Ampere, Carnot and Foucault. He also suggests various chemists, physiologists and historians.

Nourish your mind with works in which the author has been able to make the proper distinction between the intuitive and the mathematical minds, where penetrating intuition has sensed the principles and a rigorous deduction concluded to the consequences. ( ibid 71)

He proceeds from consideration of the masters to laud the virtue of clarity, with hearty criticism of the fashion of incoherence.

People claimed the right to speak obscurely about obscure things. No! A thousand times, no! There is no right to peak of an obscure thing except to clarify it. If the only effect of your verbiage must be to confuse things further, be still!...My friend, if you do not succeed in making us understand what you are talking about, it is because you yourself do not understand it at all! ( ibid 73-4)

He suggests that clarity is one of the signs of good sense, and so should be defended along with good sense, from those who are inclined to denigrate one or the other or both. He argued against the proposition that good sense is the enemy of originality, drawing on the example of Pasteur who was in appearance and habits entirely commonplace but whose science was revolutionary.

He also rejected the notion that good sense drives out poetry: his counter-example in this case was a venerable neighbour in the countryside of Provence, a man of simple and harmonious language, ‘neat and sober images’ as he spoke of ordinary country things, a man who was, in another capacity, hailed as the great epic poet of Provence, Frederic Mistral.

CONCLUDING COMMENTS

Duhem did not see his exposition of the ambiguity of falsification as a major problem for the progress of science. His aim was to rehabilitate the role of theory at a time when positivists and subjectivists were trying to avoid the complexities of abstract theories and the problems of interpreting experimental results in theoretically advanced sciences. At the same time he wanted to protect the less abstract sciences such as biology (at that time) from premature attempts to force it into the abstract and mathematical mould of physics.

Duhem would surely have appreciated the Popperian rejection of the quest for justified belief because he was prepared to allow time for systems to evolve under the influence of criticism and experimental tests. It is unlikely that he perceive a need for any special solution to the problem that came to bear his name, merely a need for scientists to keep working with 'good sense'. For Duhem, good sense meant using logic and mathematics allied to experimentation with a spirit of criticism and ingenuity, realising that logic and mathematics could not deliver the answer to all scientfic problems. At the highest level, good sense evolves into a form of creative ingenuity, exemplified in the work of Pasteur.

CHAPTER 6

CONCLUSIONS

This thesis has surveyed the Duhem-Quine problem in its classical formulation by Duhem, its radical revision by Quine and its extension by Gillies. This problem, firmly rooted in the logic of the modus tollens, stands as a reproach to positivists and naive falsificationists alike. The logic of the situation is that the conjunction of several hypotheses in any logical deduction preclude the unambiguous attribution of error to any one of them if a prediction fails. This undermines the attractive logic of the crucial experiment as a means of choosing between rival theories.

Duhem restricted the scope of his thesis to parts of physics and chemistry but it appears, following Gillies, that any and indeed all sciences will be liable to the problem as their theories become more abstract and their experimental equipment becomes more sophisticated. Quine promulgated a more radical version of the thesis which threatened to introduce an element of unrestrained conventionalism into science with the notion that selected statements could be held 'come what may' by adjusting other theories, even the principles of logic. He subsequently returned to a more orthodox and pragmatic view of experimental testing. This move was assisted by Grunbaum's argument that if apparently falsified hypotheses are to be held by modifying previously accepted theories or inventing new ones, then the modifications or inventions need to be scientifically useful, not just playthings of logicians. He concedes the legalistic logical point that there is always the logical possibility of evading a refutation, but to contribute to the scientific debate these 'evasive' innovations need to be testable and they need to lead to worthwhile advances in the field.

Popper's contribution to the debate is disappointing in confusing Duhem's formulation of the problem through his efforts to distance himself from it. At bottom his depiction of the modus tollens and its implications for falsification is so close to Duhem that one is tempted to speak of the Duhem-Popper problem. On the positive side, Popper noted the importance of confirmations (as well as refutations), a point pursued by Mayo and Lakatos. The contribution of Mayo is helpful in showing how science can handle anomalies because there is usually a background of well-tested and reliable knowledge - knowledge which is routinely subjected to testing in normal science. Lakatos offered a complex and sophisticated approach to recruit the ambiguity of falsification as a strength rather than a weakness, to maintain theoretical pluralism and allow time for rival theories to show their mettle.

Bayesian subjectivism has been presented as the answer and in one particular case it revealed a great deal of power, especially as a support to Lakatos. The other case examined is less impressive and the requirement that there should not be a major rival theory on the scene is a great disadvantage. In the absence of a serious alternative program scientists have little option but to keep working on the existing theoretical system, even if anomalies persist or even multiply. Where the serious option exists it appears that the Bayesians do not help us to make a choice.

Internal disagreements call for solutions before the Bayesians can hope to command wider assent; perhaps the most important of these is the difference between the 'betting' and the 'belief' schools of thought in the allocation of subjective probabilities. There is also the worrying aspect of betting behaviour which is adduced as a possible way of allocating priors but, as we have seen, this is a highly misleading model of scientific choice.

The 'new experimentalism' has similarly offered the promise (or threat) of rendering the Duhem-Quine problem irrelevant. Indeed there appears to be some truth in this claim, to the extent that experiments can take on a life of their own, partly by preceding deduction from theories, partly through the impact of noteworthy observations and partly through the dynamism of experimental programs which permit effective manipulation and intervention, in advance of theoretical explanation. However theory has a life of its own as well, and the Duhem-Quine problem persists whenever there is a desire to obtain theoretical explanations. But still, of course, experimentation plays a vital role, sometimes by way of genuinely crucial experiments and more usually by the steady accumulation of confirmations (or refutations) which build the credibility of a theory (or undermine its rivals).

The Duhem-Quine problem has not stopped the progress of science and neither Duhem nor Quine anticipated that it would do so. It has provoked a spirited debate and a healthy re-examination of the limits of logic and the pitfalls of simplistic views of the impact of evidence. As Passmore noted, Duhem did not dispute the potential for experiments to refute theories, rather he asserted that refutations fall upon systems of theories and the test of experience is not direct and immediate.

It appears that the diversity of situations which arise in scientific decision-making preclude any single or simple answer to the ambiguity of falsification. As we have seen, there are experimental situations in normal science where the problem does not arise to any significant extent because there is sufficent well-founded background knowledge to allow some security to experimental results. And even in a potentially revolutionary situation, Franklin has illuminated an episode where the experimental results were so convincing that the ambiguity of falsification was not exploited. On other occasions the issue is less clear-cut and decades of work may be required to find a solution.

One finding which emerges from this survey is that the Duhem-Quine problem is too often posed in an unhelpful manner, as though the integrity of science depends on 'instant' verifications or refutations. A more realistic stance can be found in Duhem himself (echoed in Lakatos with his dismissal of 'instant rationality'), with the realisation that scientists do not need to make hasty decisions in a choice between theoretical systems.

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Introduction and Some Popperians Bayes and the New Experimentalism