E. Mach and P. Duhem: The Philosophical Significance of the History of Science
Author: Mariano Artigas
Published in: Física y religión en perspectiva. Rialp, pp. 99-119.
Date of publication: 1991
Ernst Mach (1838-1916) and Pierre Duhem (1861-1916) can be seen as parallel figures. Both lived at the same time, died in the same year, were prominent physicists, conducted research into the history of science, and related that work to their ideas about the Philosophy of science. As if this were not enough, both asserted that scientific theories are neither true nor false. It is not surprising, therefore, that their names are commonly associated in the epistemological literature and that they are presented as prominent representatives of conventionalism.
However, there are important differences between them. Mach's ideas are closely related to an evolutionary and empiricist perspective, where science represents a useful tool for survival and there is no place for metaphysics; Mach's influence was naturally prolonged in the neo-positivism of the Vienna Circle. In contrast, Duhem harmonised his epistemology with a realist philosophical perspective, emphasised in his historical research the importance of Christianity in the birth of modern science, and affirmed the coherence between science, Philosophy and Christianity.
Mach is one of the leading empiricist authors of all times. From the beginning of his degree program as a physicist, his interest was polarised around psycho-physical problems, which he considered fundamental to determine the value of knowledge in general and of science in particular. After working in Vienna in his first period (1860-1864), in Graz for 3 years (1864-1867) and in Prague for 28 years (1867-1895), he returned to Vienna in 1895 to take up a Chair position at Philosophy, with the title degree scroll as professor of history and theory of the inductive sciences, position from which he retired in 1901. His influence was felt until the appearance on the same stage of Moritz Schlick, promoter of the Vienna Circle, who gave a strong impulse to the modern Philosophy of science in a distinctly empiricist and anti-metaphysical direction. The association Ernst Mach served as a platform for the constitution of the Circle, whose ideas were inspired by those of Mach.
The Vienna Circle considered one of its main tasks to be the reconstruction of science according to empiricist standards, i.e. scientific ideas should be limited to expressing information from sensible experience. On this basis, the Circle declared meaningless all propositions that could not be formulated and verified by agreement in accordance with empiricist requirements. As is well known, this criterion of significance was the object of numerous criticisms and, despite being subjected to successive reworkings, it was never formulated in an acceptable way. The anti-metaphysical thesis of the Circle was, in such circumstances, deprived of a basis.
It may be surprising at first glance that the trajectory of these ideas might have some point of speech with Duhem, well known for his catholic ideas. However, it was Mach himself who underlined his affinity with Duhem's epistemology. And he did so in unequivocal words, expressed in very significant circumstances. The book The Physical Theory, in which Duhem expounded his main epistemological ideas, was published in German in 1908 with a preface by Mach, which contributed not a little to brand Duhem as a positivist. Moreover, Mach had already referred to Duhem's book in one of his own works.
We find these references in the preface to the second edition of (Mach , XXXV-XXXVI). The first edition of 1905 was quickly sold out. A second edition, almost identical to the first, appeared in 1906. In the foreword, Mach notes that he has added some references, in the form of notes, to works related to his own and published at the same time or shortly after. After briefly mentioning two of them, he devotes the rest of the foreword, which makes up almost half of it, to Duhem's book, published in the same year. He says of it that it has given him great pleasure to read; that he did not expect to find such a broad agreement with any physicist so soon; that he especially values the agreement with Duhem, because both have reached the same conclusions by independent paths; and he adds that Duhem throws new light on the relations between the ordinary and the scientific knowledge , for which he recommends Duhem's work as a complement and illumination of his own book.
What are the coincidences that so pleasantly surprised Mach? In that foreword he mentions the following: Duhem rejects any metaphysical interpretation of the problems of physics; he considers that the goal of physics is to determine the facts in a conceptually economical way; and he affirms that the genetic and historical method of presenting physical theories is the only correct and the most pedagogically effective one. Mach then adds that he has held these same ideas for the previous 30 years.
If we leave the preface and examine the notes on Duhem, added by Mach in that second edition of Knowledge and Error, we find that they do not shed much light on the coincidences between the two physicists. There are eight notes. In two of them, Mach points out differences of opinion with respect to Duhem (Mach , 133 and 329). Four others concern rather secondary questions (Mach , 146, 202, 224 and 362). There remain only two which, besides pointing out Mach's coincidences with Duhem, refer to important issues. In the first of these (Mach , 161), it is stated that an experiment without theory would be unintelligible. And the second (Mach , 184) refers to Duhem's famous thesis according to which a crucial experiment cannot be incompatible with isolated hypotheses, and can only contradict a whole set of hypotheses.
If we combine these last two observations with the reasons given in the prologue, we can conclude that Mach's sympathy for Duhem's ideas refers to particular issues which, although important, have little effect on the overall picture of science and the framework in which it is framed. For Mach, science fulfils a purely pragmatic function within a biological perspective, and Mach is as hostile to metaphysics within science as he is to metaphysics in general. Duhem, on the other hand, claims that the progress of science has as its result purpose to bring it ever closer to a truly existing natural order, and he is a strong advocate of spiritual dimensions that go beyond the realm of the biological and even of nature as a whole.
Although there are also very notable differences in methodological aspects and their consequences, the differences between Mach and Duhem concern basic issues. Duhem bases his epistemology on the logical analysis of the theories of physics, and sees the scientific perspective as an aspect of human rationality, which is by no means exhausted in science. On the other hand, Mach approaches the problem of the validity of the knowledge of agreement with a psychologism in which sensations constitute the ultimate point of reference letter, and criticises as illusory any claim to knowledge that does not correspond to his empiricist canons.
The divergences between Mach and Duhem with regard to the history of science and its significance are no less striking. Of course, both seek to confirm their ideas by appealing to history, and one finds in their works constant references to concrete historical examples. And it cannot be denied that, with respect to methodological questions, there is no small amount of overlap. However, Mach sees history as exemplified by the behaviour of leading scientists, attributing to that behaviour a paradigmatic character, whereas Duhem conducted his main historical research in a very different sense.
Indeed, research into the origins of physics took Duhem further and further back in time. And when he began to discover unpublished medieval Materials , he plunged into that new and unexplored world. The stereotypical cliché presented the average Age as an obscurantist epoch which, at most, as Mach believed, could timidly stimulate science through the study of logical subtleties, which, however, were applied to meaningless problems. Duhem discovered a completely different reality. His work staff with medieval manuscripts led him to the conviction that the Age average, especially at the University of Paris but also in other intellectual centres, was a time when the concepts that allowed the systematic birth of modern science in the 17th century were gradually developed.
Duhem's historical thesis constitutes subject for debates that sometimes become passionate and polemical. For example, claiming with Duhem that 7 March 1277 was the founding date of modern science can easily be a matter of dispute. However, there is no doubt that the historiography of medieval science, which was highly developed in the decades following Duhem, has its basic starting point in him.
Equally undoubtedly, Mach's and Duhem's historical conclusions have some commonalities, which, however, compared to their discrepancies, are rather superficial. The instrumentalist perspective has a very different scope in the two authors. According to Mach's instrumentalism, science has a function of biological adaptation in which there is no room for reflections on truth in the strong sense. Duhem's epistemology, on the other hand, is only instrumentalist, let alone positivist, in a very special sense.
What Duhem stresses is that the logical analysis of the theories of physics does not allow us to establish that these theories themselves have a realistic scope. Mach is at agreement in the conclusion, and seems to be enthusiastic about its apparent anti-metaphysical air. But, properly speaking, there is nothing anti-metaphysical there. Duhem's idea is important and valid, and it is also perfectly compatible with a metaphysical attitude. Moreover, this compatibility constitutes an essential part of Duhem's ideas. And that there is nothing anti-metaphysical in Duhem, also on the epistemological level, is evident when one considers his undeveloped but unequivocal assertion that there is a gradual approximation of science to the real natural order.
Epistemology, according to Mach, like science, could only be a description, and not properly an explanation. However, at this point it seems inevitable to run into some contradictions. Indeed, what Mach denies on the one hand, he affirms on the other. He proposes an explanation disguised as a description. His epistemology, to be true to its own precepts, should reflect the actual behaviour of scientists. However, the opposite seems to be the case.
Whether Mach's epistemology is in contradiction with real scientific progress is a matter of debate topic . It is hardly possible to definitively conclude this discussion, if one takes into account that Einstein himself expressly claimed to be intellectually indebted to Mach, and that the orthodox interpretation of quantum mechanics has often been presented as being akin to a phenomenistic Philosophy or, at least, has used expressions that seem to move in that direction.
On the other hand, Mach's supporters are forced to justify why he opposed atomic theory, and it seems difficult for them to make Mach's phenomenalism compatible with the minimum dose of realism that seems necessary for subatomic entities, which have proliferated extraordinarily in recent decades. They even have to explain Mach's civil service examination to the theory of relativity, of which he is supposed to be a precursor.
Hypotheses about atoms and molecules were regarded by Mach as intellectual aids which could have a certain value in achieving concrete aims, and which should not be disregarded in their function as Economics of thought; but he compared their realistic value with that of the symbols of algebra, and added that we can expect no more from them than we put into them ourselves, and certainly no more than we can achieve by experience (Mach , 311).
It is possible to defend Mach's attitude to atomic theory by distinguishing the different formulations and implications of that theory during the nineteenth century (Brush ), and by stressing that the theory grew in progressiveness, explanatory power and testability, so that scientists became increasingly convinced of the reality of atoms (Gardner ). Certainly, Mach was not the only scientist of the time who had misgivings about this theory. But, even in that case, it seems forced to admit that, for Mach, the unreality of atoms or of any other entity that was not subject to sensible observation was a basic axiom (Brush , 210). This is certainly compatible with the Admissions Office of atomic theory as a hypothesis of work. However, it is not enough to present Mach in the line of the later development of physics, let alone as a precursor of that development.
There is no shortage of scholars who suggest that Mach's civil service examination to atoms and Boltzmann's kinetic theory is scientifically justifiable (Clark ; Gardner ; Feyerabend ). Others argue the opposite. In this context, Blackmore states: "it is understandable that philosophers find it hard to admit that scientific progress may collide in its path with philosophical ideas, prior assumptions or prejudices, but sometimes the evidence is too strong to be easily counter-argued or brushed aside", and concludes that "Mach's civil service examination to both the reality of atoms and Boltzmann's kinetic theory of gases was philosophical, and was not even accompanied by a serious scientific argument against either" (Blackmore , 299 and 303-304).
For his part, Capek states that "Mach was convinced that the process of adjustment of human cognitive functions was basically complete and that, apart from minor modifications, no basic revision of the nineteenth-century picture of reality was needed", adding that, for this reason, Mach opposed the theory of relativity, for he did not suspect the enormous enlargement of the scope of our experience and the consequent transformation of our picture of the world that science could provide, and his phenomenalism prevented him from seeing the possibility of the world being very different from what manifests itself to our sensory experience (Capek , 188-189).
On Mach and relativity theory, it has been claimed that Mach's epistemology played a significant role in the genesis of relativity theory, linking this claim with a more general one, according to which positivism would have stimulated the modern scientific revolution (Schaffner ). However, these claims have to be taken, at the very least, with serious reservations. For example, it has been argued that Einstein, in formulating his special theory of relativity, violated cardinal principles of Mach's Philosophy , and that if he had not done so, he would never have formulated that theory, adding, along the same lines, that Mach's epistemology was irrelevant to the development of physics (Zahar ).
That Mach opposed relativity is a fact. And it is not very convincing to justify it, as Feyerabend does, by resorting to some somewhat enigmatic words of Mach, who mentions the increasingly dogmatic character that, in his opinion, the theory was acquiring, and alludes to particular reasons, which he does not make explicit, to explain his rejection (Feyerabend ).
These controversies are not limited to specific aspects. On the contrary, they concern basic questions about the possibility and meaning of the scientific research . Even if one were to admit that Mach's aversion to atomic theory and relativity can be justified in some way, it seems necessary to point out that his image of science is too polarised towards a psychology of sensations which was a function of biological adaptation, and that this results in a conception in which it is not easy to find a place for the understanding of the natural order and not even for the activity of the individual who puts his capacities into play in order to achieve a true knowledge of nature (Cohen ).
Quite different is Duhem's perspective. His presumed positivism goes hand in hand with an acceptance of the value of metaphysics. Duhem is convinced that there is a natural order goal, that we have the capacity to know it, and that this knowledge is the goal towards which scientific progress is directed. Recent programs of study agree with Duhem's affirmation of realism (Artigas ; Ramoni ). After an examination of Duhem's scientific and epistemological motivations, studied in relation to his scientific historiography, it has even been affirmed that "the ambition to construct an adequate image of reality - a condition of possibility for any scientific project that wishes to present itself as such - thus leaves a marginal place, confined to the folds of the history of science, to reveal itself as a constitutive factor of Pierre Duhem's entire methodological theory" (Ramoni , 58).
What Duhem underlines is the specific character of scientific procedures. Mathematical physics does not provide us with a knowledge of nature in the manner of a photographic or mirror image. In this sense he states that "physical theory is a purely ideal construction, the elements of which have no relation of nature to concrete objects.... Physics seeks only to construct, by means of notions borrowed from mathematics, a logical system which gives an approximate picture of the laws relating to bodies" (Duhem , 12-13). These statements, which emphasise the constructive aspect of mathematical physics, correspond to the real characteristics of science, and are in line with the most recent scientific progress sample .
Duhem stated unequivocally that to be a positivist is to admit that there is no other logical method but that of the sciences, and that everything that cannot be reached by this method is absolutely unknowable. It is therefore logical to agree with Jaki when he states, in his excellent monograph on Duhem's life and work, that Duhem's positivism was a simple technique and not that philosophical creed that eliminates metaphysics (Jaki , 325). At final, to align Duhem with positivist epistemology, if positivism is understood in its usual sense, is a mistake. To be sure, this misconception has been fostered by judgements, such as Mach's own, which have been repeated in the context of contemporary epistemology; but such judgements only reflect some partial aspects, interpreted out of their proper context, of Duhem's position.
What Duhem stresses is the constructive, symbolic and approximate character of scientific laws. In this sense, he states that laws are neither true nor false, and that they are always relative to concrete historical contexts (Duhem [1906, 260). As for theories, he points out that they do not have an explanatory function in a metaphysical sense, and adds that, through their successive refinements, they tend to synthesise the laws of agreement with an order that is more and more analogous to the real order, so that physical theory gradually moves towards its limit form, which is that of a natural classification (Duhem , 450).
Contemporary epistemology agrees with Duhem's assessments. It makes no sense to accuse him, as was done during his lifetime and has been repeated subsequently, of defending a scientific instrumentalism for apologetic reasons, that is, to leave the field free for metaphysics and religious beliefs. Duhem himself vigorously clarified his thinking in this respect. In fact, Duhem is neither instrumentalist nor positivist; he simply points out the limits that come from the specific method of the mathematical science of nature, but he is far from depriving this science of its real cognitive scope.
Duhem's distance from positivism is even greater if one considers the field of history. He devoted thousands of pages to showing the continuity of scientific progress, especially during medieval times (Duhem [1906-1913] and [1913-1959]). Jaki, who has devoted extensive attention to these programs of study and has followed them up with original works, admits that it is possible to argue that Duhem in some respects attributed too much importance to Buridan, Oresme and other medievalists, but that it is nevertheless impossible to ignore that Duhem's works revealed crucial aspects of the development of science; and adds that, if these perspectives are not only useful for the historiography of science, but also for Christian apologetics, this could only annoy those who seek in the history of science a weapon to combat Christianity (Jaki [1978b], 67-68).
The issue addressed by Mach and Duhem is still alive today. In today's epistemology, the discussion debate about instrumentalism and realism has reached new heights. Strong defences of the instrumentalist and pragmatist perspectives have been formulated, which have been subject to no less severe criticism. It is not possible to go into the details of these controversies here. Suffice it to point out that it is possible to accept a weak version of instrumentalism, which consists in affirming that empirical adequacy is a necessary condition for scientific acceptability, but that it is not sufficient to affirm the real existence of the referents of theories.
This is the line of Duhem's epistemology. He stresses that scientific theories, by themselves, seek to save phenomena, and tries to justify this idea by showing his development since antiquity (Duhem ). As for the problem of realism, he limits himself to pointing out the realistic tendency of scientific progress, without explaining how the approximation between theories and reality takes place.
This perspective can be completed by showing that it is legitimate to admit the existence of a scientific truth that is contextual, partial and authentic (Artigas , 209-307). Empirical adequacy is a necessary condition or minimum requirement that scientific constructs must fulfil, but it does not exhaust their significance. Certainly, these constructions have a very abstract character, and this is especially evident when studying aspects of reality that are far removed from our possibilities of immediate observation. The abstract and formal level reached by present-day physics would have greatly satisfied Duhem, since it coincides with the line of his scientific work and with his epistemological ideas. However, it is possible to show that, through highly abstract and sophisticated constructions, we refer to reality and, in fact, know it better and better. Although this is only hinted at in Duhem's work, it corresponds to his basic ideas.
Quite different is the case of Mach. His fundamental intention, aimed at constructing a psycho-physics where scientific constructs refer to phenomena observable through sensory experiences, is far removed from the results of contemporary science. The episodic connections between Mach's programme and some scientific achievements such as relativity and quantum mechanics are superficial and do not reach the real core of the problem. And the development of current epistemology has little to do with Mach's proposals.
It is not difficult to identify the reason for these discrepancies. Duhem's epistemology, precisely because it is framed in a general perspective in which science coexists peacefully with metaphysics and religion, is a realistic and open epistemology, which can easily be completed with the opportune developments of a scientific realism that Duhem only hints at. In contrast, Mach's epistemology regards the scientific knowledge , and the whole of human knowledge in general, simply as a useful instrument for biological adaptation. For this reason, Mach's epistemology does not admit realist complements, unless its fundamental intention is changed. It is a closed epistemology, where the scope of science is inevitably reduced to a much less important function than it actually possesses, and where it is not easy to find room for acknowledging the legitimacy of metaphysical and religious perspectives.
It is paradoxical that these assessments have to face a difficulty, stemming from the idiosyncrasies of the respective authors. Duhem was polemical and blunt in his assessments, both in the scientific field and in others, to the extent that, from the beginning of his scientific degree program , he did nothing to avoid clashing with the opinions of other scientists, which had a negative influence on his professional status and on the appreciation of his work. On the contrary, Mach appears as an open temperament, and this is recognised even by those who negatively underline his civil service examination to progressive scientific work lines.
One possible answer to this difficulty is to distinguish between a person's temperament and the value of his or her ideas. This is certainly a valid response. A psychic portrait of a person can help us to understand his ideas by placing them in their proper context, but it is of little use if we try to assess the ideas themselves. However, something else must be added. Mach's criticisms of ideas contrary to his own are no less severe than those of Duhem. And above all, Duhem's realism is related to his conviction that we can attain truth, whereas Mach's instrumentalism seems to correspond to a scepticism about the scope of our knowledge. Therefore, if Mach's thought is qualified as open-minded in comparison with Duhem's, this may be due to the affinity of the ideas of the person making this judgement with Mach's scepticism.
From an objective perspective, both in reference letter to science and to the other modalities of knowledge, Duhem's thought is sample as open and integrative, and Mach's as closed and exclusivist. This is compatible with the fact that some of Mach's ideas may be useful in both the scientific and philosophical realms, and that Mach was right in pointing out that scientific concepts must always be open to the results of testing them against experience (Mach , 289-290).
The comparative analysis of Mach's and Duhem's work leads to two general reflections on the relationship between science, metaphysics and religion.
The first concerns the limitations of positivism. Duhem's work on medieval science may have been motivated by religious concerns, even of an apologetic subject nature. But, apart from the fact that this intention is in itself legitimate, this work has contributed decisively to show the falsity of the historical clichés of positivism. sample that Christianity played an important role in the progressive development of the ideas that led to the systematic birth of modern science.
The pursuit of this line of work, subsequently carried out by researchers of the most varied tendencies, has only confirmed the inadequacy of positivism. Jaki has extended this perspective, examining the successive abortions that science experienced in ancient cultures and analysing the birth of modern science in the context of a Christian cultural matrix, which provided solid convictions about the rationality of the world, created by a God staff and infinitely intelligent, and about the cognitive capacity of man, created by God in his image and likeness. And he has shown that ontological and gnoseological realism, which is one of the presuppositions of natural science and was historically nurtured by Christianity, remains, also today, one of the basic conditions of any truly creative science (Jaki  and [1978a]).
This is the starting point for the second reflection, which refers to scientific realism. Science is a business that is framed within general human rationality. Therefore, the idea that one has about human cognitive capacities will necessarily influence the solution of the problem of realism. It is clear that Christianity as such does not guarantee that an adequate scientific perspective will be achieved. But it is also clear that Christianity implies an image of the world and of man which, while compatible with a wide variety of perspectives, has a clear realist accent.
In this context, it is understandable that the scientific research of nature, which would be meaningless without a minimum dose of realism, was stimulated by a Christian culture. And it is also understandable that epistemological realism shares a similar fate. Of course, it is not difficult to find examples of Christian phenomenists or agnostic realists, but in both cases, it is a question of approaches that in some way can be qualified as internally inconsistent.
Current epistemology offers clear examples of such inconsistencies. For example, Popperian epistemology rightly stresses the realist intention of the scientific research , but encounters serious difficulties when it tries to substantiate this realism. Its most coherent development is evolutionary epistemology, but this, in its most genuine expression, stresses the overlaps between animal and human knowledge , and sees science as an achievement of biological adaptation, precisely along the lines of Mach (Mach , 361). On that basis, a certain realism is often admitted which is evident from a phenomenological point of view, but which can hardly be formulated coherently in a perspective which, while affirming that the human knowledge has distinctive specific features, at the same time emphasises with emphasis the basic similarity of the processes of the knowledge from the amoeba to Einstein.
Other current epistemological perspectives are even more resistant to realism. But they are probably more coherent, if one starts from a naturalistic image of science, of epistemology and, at final, of man. It is not difficult to show that instrumentalism and relativism lead time and again to dead ends. But the construction of a realistic alternative, which is faithful to what science really is, requires deeper approaches. In this line, Duhem limited himself to pointing out some theoretical aspects and coherently living out their practical implications. But his indications are important when trying to reconcile the logical analysis of science with the realist assumptions and implications of the scientific knowledge .
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