“To know,” writes Bachelard at the beginning of his first book, “is to describe in order to retrieve.”1 A very great portion of his subsequent work elaborates this simple definition with its duality of description and recovery, of empirical observation and rational ordering. Like this opening sentence of his 1928 Essai sur la connaissance approchée, the entire monograph, which had been his major doctoral thesis, sets forth ideas and perceptions that are the seeds of much that is to follow in Bachelard’s philosophy of science. Together with his secondary thesis on the problem of heat transfer in solids,2 it sets the pattern for Bachelard’s early work on the philosophy of science in which he illustrates his explorations of specific epistemological questions with problems drawn from a particular science.
The four books discussed in this chapter—Essai sur la connaissance approchée, Étude sur l’évolution d’un probléme de physique: La Propagation thermique dans les solides, La Valeur inductive de la relativité, and Le Pluralisme cohérent de la chimie moderne—constitute a whole which, as Georges Canguilhem has pointed out, deals with the “distinctive traits of science at the beginning of the twentieth century—approximation, induction, coherence.”3 While Bachelard will eventually conclude that “man has a destiny of knowledge,”4 his epistemological interests at this early stage are more narrowly focused, more specifically concerned with determining how knowledge takes place in science rather than, as will be the case later, with exploring the broader philosophical and even pedagogical consequences of that epistemology.
Bachelard was less interested in developing a systematic theory of knowledge, as such, than in understanding and describing scientific thought.5 His conclusions concerning the process of knowing reflect the experimental activity of modern science, especially as it seeks to understand microphenomena. For when science, particularly physics and chemistry, explores the world of the atom, it deals with a different order of experience, one that is outside the realm of everyday observation. As Bachelard repeatedly indicates throughout his epistemological works, this microphenomenal world may require systems of thought that, in some ways, contradict the logic of everyday experience. The study of microphenomena demands new methods not only because certain macrophysical laws do not apply but because the more detailed the scientists’ measurements attempt to be, the more they discover the inherent indeterminism of the structure of things.
This would seem paradoxical to a Newtonian physicist, for whom what is measured exists and is known in proportion to the precision of the measurement. According to this positivistic outlook, all other means of knowing give way to measurement, and this in turn guarantees the permanence of being. For the positivist, therefore, reality is what is measurable. But even in the macrophenomenal world, where Newtonian laws can still apply, the reduction of reality to measurement is problematic enough. For there is, Bachelard reminds us, a discrepancy between the exactness of mathematics, which can be viewed as absolute, and the necessary imperfection of any attempt at exactness when dealing with concrete reality. Our knowledge of reality can be made relatively precise, but never absolutely exact.
The problem is vastly compounded when the positivistic approach is applied to microphenomena. Here the eye never penetrates for it is the instrument that guides scientists’ search for knowledge. Aware that their measurements, refined as they may be, are necessarily inexact, scientists attempt to limit errors since they cannot eliminate them completely. They recognize that they are dealing with a different order of magnitude, one that requires different approaches in order to yield knowledge successfully. They must adapt their methods either to the first order of magnitude of everyday visual reality or to the second order of magnitude of microphenomenal reality as an initial step in limiting errors. “The order of magnitude thus becomes a first knowledge by approximation. … It is, in physics, the first act of thought by approximation” (ECA, 78). To know by approximation is to recognize the reality with which we are dealing and the ultimate inexactness of our means of measurement. And, although Bachelard maintains that knowledge of the first order of magnitude is also necessarily approximate, the notion of an approximation to reality is particularly relevant to microphenomenal knowledge.
Contemporary science has taught Bachelard the need to go beyond the knowledge of first approximation, to recognize that the scientist must abandon methods that worked in the macrophysical world. “The enemies of the scientist in the realm of second approximation are the scientific habits acquired while studying the first” (ECA, 70). The scientist who explores the world of second approximation must reject the notion of an admitted reality, for in the realm of second approximation nothing can be accepted as merely “given.” Here the validity of what is known depends in large measure on mathematical precision. “If we want to know with maximum rigor, we must organize acts, totally substitute the constructed for the given” (ECA, 174, emphasis added). While Bachelard maintains that science eventually refers back to reality, it is his insistence on the new “constructive” role of mathematics that especially marks his epistemology.
Mathematics is not a science of objects but of abstract relations. As such it is nonempirical and what it constructs rationally can have a degree of arbitrariness with respect to empirical reality. Unlike the physics of first approximation that posits existence before knowledge, the constructive mathematics of second approximation prove the existence of a particular reality “only by comparison with other known elements or else by approximating them indefinitely” (ECA, 211). This indefinite approximation reflects the impossibility of ever applying absolutely exact measurement in a world where the “object” cannot otherwise be perceived. Scientists are literally at the mercy of their instruments and so must be extremely careful not to interject intuitions that belong to the more generally familiar macrophysical world. Indefinite approximation, for instance, does not presuppose, Bachelard reminds us, a fixed pole eventually to be reached by finer and finer approximations, one that would ultimately make approximation unnecessary. In the realm of second approximation, certainty is in the process, not in the never-to-be-attained goal.
Among the first-approximation notions that Bachelard feels compelled to transform in dealing with knowledge of second approximation is that of simplicity. It has long seemed axiomatic that the goal of science was to reduce or simplify reality in order to discover its hidden laws. In turn, such laws with their a priori simplicity were thought to guide the discovery of new details in a complex reality. Yet, if the value of a law lies in its simplicity but that law does not faithfully reflect microphysical reality, it does not meet the two tests of knowledge proposed by Bachelard: it does not adequately describe, and therefore it cannot serve as a reference point for subsequent retrieval. Either simplicity is to be valued at the expense of adequate description or description is to be sought at the expense of simplicity. Bachelard escapes between the horns of the dilemma by proposing that simplicity be defined as clarity rather than reduction. Pointing out that the criteria of simplicity are relative to the scientific means at one’s disposal, he suggests that “simplicity is not a state of things, but a veritable state of soul. We do not believe because it is simple, it is simple because we believe” (ECA, 101). Thus even ostensibly complex formulas are “simple” if they are believable, which, in this context, means if they are mathematically coherent, if they hold the “faith” of the rationalist.
The apparent paradox of defining rational complexity as simplicity is explained in Bachelard’s second book, Étude sur l’évolution d’un problème de physique: La Propagation thermique dans les solides (1928), where he stresses that each solution to a problem clarifies the state of our knowledge. With the help of such clarifications, new mysteries are explored and a new clarity is acquired at the end of a complicated process, although an unforeseen fact may obfuscate erstwhile clear theories. In short, there is no intrinsic order of simplicity in the evolution of science. Rather than a search for hidden simplicity, or even for an intrinsic evolution from the simple to the complex, science is a rational conquest of complexity.
Using the history of the problem of heat transfer in solids as his illustration, Bachelard demonstrates that the clarity of present-day concepts of thermodynamics, or even seemingly “natural” notions such as temperature, is acquired through mathematical physics in which differential analyses ultimately converge to yield their own integral hypotheses. The acquired simplicity of these hypotheses is so secure that physicists no longer need to accept a coherent group of inductive, but prematurely simple, generalizations merely because they have the practical advantage of providing immediate and accessible explanations. Thus “simplicity” for the physicist is what is mathematically clear, however complex it may be to the uninitiated. Simplicity has nothing to do with mere reduction.
Indeed, such reduction is a source of error that must be avoided by the scientist of second approximation. “We are less likely than before,” Bachelard points out, “to find in the simplicity of a law proof of its truth, but from a pragmatic point of view, we prefer the less complicated of the laws which explain a phenomenon just as well” (ECA, 93). Less complicated here means the use of easier, more accessible mathematics. Such “intrinsic simplicity” (ECA, 94) may serve the practical purpose of explaining a particular phenomenon, but it may also complicate the effort to incorporate the phenomenon within a more general account and thus to establish its validity as knowledge.
Here again, the history of thermodynamics illustrates how a reductive, pragmatic simplicity can impede scientific progress. Before it occurred to anyone to use a fluid, such as mercury, to indicate the effects of heat, it was long imagined, Bachelard recalls, that a real fluid, or “caloric,” helped determine the cause of heat. Epistemologically, the problem with such an explanation is that it was content to deal with a specific phenomenon rather than to seek relationships between this phenomenon and others. “It is in vain that we would want to concentrate scientific thought on a separate object, and even on a phenomenon of determined order. Even more than common thought, scientific thought lives by relationships and it can know a phenomenon only by incorporating it into a system, or at least by bending it to the principles of a method” (EEPP, 157). What is learned on the basis of a single phenomenon does not permit discovery about a different phenomenon.
Such practical description is too closely bound to the object and generalizes too quickly. It lacks the degree of abstraction necessary to relate concepts one to another and thereby to expand knowledge, and, as a hasty generalization, it “retards discovery by giving facile confirmations to immediate hypotheses” (EEPP, 160). Mathematical abstraction, on the other hand, because it can be arbitrary with respect to observed reality, can incorporate all the pertinent possibilities of the phenomenon as it reconstructs it within the interconceptual framework of other discoveries. “In the study of thermal phenomena, the first sign of positivity is the break with all research on the nature of heat” (EEPP, 57). It is then that science learns to forego the inadequate explanation of immediate empiricism in favor of the rigors of abstraction.
This emphasis on the importance of abstraction is in counterpoise to Bachelard’s insistence on physical reality as the ultimate test of knowledge. There is no contradiction here, for contemporary science has taught him that the old, a priori philosophical categories of empiricism and rationalism work dialectically in scientific practice. Dominique Lecourt, an informed critic of Bachelard’s epistemology, has pointed out that, for Bachelard, the meaning of science is to be found in its own activity rather than in a “philosophical ideology” or “ideological philosophy.”6 Bachelard is not interested in making science fit a philosophical model but in adapting philosophy to an active, open-ended science. In doing so, he repeatedly stresses the dialectic of matter and thought, or, to put it in terms of his original definition of knowledge, of description and retrieval. No other pattern is more constant in Bachelard’s entire epistemology.
In rejecting habits of first approximation, a priori simplicity, and immediate explanation, Bachelard emphasizes the preeminent role of epistemology. As he sees it, “truth seems … to refer solely to the procedures of knowledge. It cannot rise above the conditions of its verification” (ECA, 231). Any method, to be legitimate, “must be so, as a method, epistemologically. It has no call justifying itself by essentially ontological considerations” (ECA, 241). Contemporary science makes Bachelard highly skeptical of traditional ontology and its philosophical realism. Reality, for Bachelard, does not exist independently of the means of knowing. Thus traditional ontology must yield to a mathematically constructive rediscovery of reality. Such a “constructed realism” (ECA, 187) is perhaps best symbolized by the crystal, to which he returns in the conclusion of his Étude sur l’évolution d’un problème de physique.
The individual crystal repeats a pattern, with only slight variations, common to all crystals of the same substance, so that it may be seen both as a particular phenomenon and as a typical or generalized one. The patterns of the real crystal closely match those of an abstract, nonexistent crystal. “Between forms thus realized and ideal and abstract forms … , the correspondence is so narrow that we do not hesitate to see in them the trace of that intermediate realism that would doubtless be capable, if only we could extend it more, of bringing together mathematical and experimental laws” (EEPP, 173). The crystal symbolically unites not only the “descriptive,” or empirical side of knowledge, but also its “retrieval,” or rational side.
On the one hand is the phenomenon being studied; on the other is a constructive mathematics that goes beyond quantitative description and projects possibilities through an inductive process of synthesis. The success of such mathematics, not only as mathematics but also as physics, is assured both by its rational coherence and by an eventual accord with experimental reality. Such an accord is made possible by a “creative intuition [that] remains the choice intermediary between logic and experiment” (EEPP, 170). The source of this union is necessarily intuitive for Bachelard because the coherence of constructive mathematics is self-sufficient—there is no logical necessity for it to lead back to reality. Thus any ontological prejudices must be abandoned in favor of an intuitive, constructive method that “rediscovers” reality mathematically.
In 1919, Einstein’s theory of general relativity was experimentally validated when British astronomers were able to confirm certain predictions of his theory by measuring the gravitational deflection of starlight during a solar eclipse. While this event made Einstein “an almost god-like figure in the public eye,”7 as one biographer put it, his stature among his peers was already well established on the basis of his revolutionary theories. It would seem perfectly appropriate, therefore, that a philosopher of science such as Bachelard should not only include a discussion of Einstein’s special and general relativity in his epistemological studies but also devote an entire book to a consideration of theories that so fundamentally transformed contemporary science. In La Valeur inductive de la relativité (1929) Bachelard attempts to place the theory of relativity in the context of the history of science and to assess its revolutionary role both for physics and for mathematics. In so doing, he pursues his own preoccupation with a dialectically empirical and rational knowledge. Yet, in this case, he stresses the rational side of the equation to the virtual exclusion of the empirical aspect. He seems to have found in Einstein a congenial rationalist, or at least that is the aspect of Einstein’s thought that most appeals to Bachelard.
Taking as his point of departure the newness of relativity theory, its “dialectical” break with Newtonian doctrines, he begins by showing that, despite some attempts to see in Einstein’s theory a continuation of Newton’s system through quantitative rediscovery, “the two systems, Newtonian and Einsteinian, appear to have no resemblance, no link, no inductive kinship.”8 The break between the two methods is “irrevocable,” their systems of thought are “entirely heterogeneous” (VIR, 44), Bachelard insists. “Relativity does not continue former doctrines, it rectifies them” (VIR, 184). And while he recognizes that Newtonian physics continues to have a practical application, Bachelard warns of the danger for epistemology of accepting what is now only a pragmatic solution as a general and valid method of knowing reality.
In dealing with the newness of Einsteinian theories, Bachelard’s central preoccupation is with the revolutionary role of mathematics, which he had previously identified as the hallmark of contemporary science. He points out that in Einsteinian physics the mathematics of discovery does not proceed deductively from certain quantified laws based on prior observation and experiment. Rather, the calculus of relativity initially generalizes in order to account for all variables. It is synthetic, or inductive, rather than analytic, or deductive, in its initial approach. Mathematics is not used merely to describe reality in quantitative terms; through its constructive processes, it has become a means of discovering reality. “We are thus led to oppose to the simplifying role of mathematical information, the constructive role of mathematical induction” (VIR, 84–85). It is not merely a question of physics having become more mathematical, “it is to the very center of physics that mathematics has just gained access and it is now the mathematical impulse that gives to the progress of physical science its force and its direction” (VIR, 83–84). Inductive mathematics has become the tool of discovery for the new physics.
From a philosophical perspective, the striking value of an inductive mathematics that sets out to account for all the variables is that it incorporates possibility into a rational system: “In the doctrines of relativity more than in any other, the affirmation of a possibility appears as an antecedent to the affirmation of a reality; the possible is then the a priori framework of the real. And it is calculus that places the real in its true perspective, at the heart of a coordinated possibility. The mind then accepts a reality that has become a piece of its own game” (VIR, 81). The inductive mathematics of relativity aims at establishing, through differential calculus, “the map of the possible” (VIR, 140). It is guided, not by what is realizable within existing experimental constraints, but by what can be conceived within much broader rational constraints, “what it is possible to imagine and coordinate with other possible experiments” (VIR, 143–44). Here imagination and intuition no longer merely bridge the gap between a rational system and reality. Because inductive mathematics incorporates possibility, the imagination has an important collateral role to play within the rational system itself.
Indeed, in relativity, where “one sees only because one foresees” (VIR, 52), the epistemological relationship of reason and reality has been reversed, so that instead of being followed by retrieval, description is now preceded by prediction. The delicate balance between empiricism and rationalism is preserved in Bachelard’s epistemology, but, following the lessons of relativity, the initial emphasis is given to the rationalistic side of the equation. For it is the formal, mathematical aspect of relativity that, for Bachelard, revolutionizes physics. Here, after all, is a theory in which the speed of light is formalized into a postulate, so that “it is the sign c rather than the number 3 × 1010 centimeters [per second] that counts” (VIR, 148). In Bachelard’s view, the empirical value of the speed of light is secondary in relativity; it has become a fundamental speed that serves as a reference for other relations.
Here, then, is a theory that initially stands on its own internal coherence rather than on its reference to empirical evidence. In fact, experimentation has followed this mathematically inductive theory with some delay. Bachelard sees in these delays “one of the most decisive proofs of the formal character of relativist construction” (VIR, 154). It is a synthetic method that constructs before it describes, one for which mathematical invention precedes reality. Thus it is not surprising that at least one commentator suspects that Bachelard, despite his frequent protestations to the contrary, latently adheres to an a priori rationalistic tradition.9 Such a view is surely extreme when the entire body of Bachelard’s epistemology is taken into account, although it is somewhat more understandable when one considers his treatment of relativity in particular.
Aside from the decidedly preeminent role of reason, the philosophical conclusions to be drawn from Bachelard’s consideration of relativity are not appreciably different from those of his two earlier studies. Here, as before, traditional ontological perspectives have no philosophical bearing. The attributes of a phenomenon are not related to its “substance” but are a function of mathematical relation. “The attribute without relation,” quips Bachelard, “is a check with insufficient funds” (VIR, 209). For any talk of “being” to still have meaning in such circumstances, it must be recognized that mathematical relation is fundamental: “By pushing relativity to what we believe to be its metaphysical consequences, in this way, we have the impression that the mathematical conditions that serve as its point of departure are multiplied and extended in an ontology that is all the more coherent for being of mathematical essence” (VIR, 211). As was the case in his two earlier studies, such an “ontology” cannot be confused with the traditional ontology of philosophical realism with its emphasis on substance rather than relation. We see, once again, that the real does not exist independently of our method of knowing for Bachelard. Indeed, in the case of relativity, he even takes a further step in the direction of a preeminent rationalism. When he points out that relativity “organizes entities before posing … the essentially secondary problem of their reality” (VIR, 213), he seems to be saying that the real does not preexist our method of knowing it.
In suggesting a conclusion that is so extreme and paradoxical (at least from the standpoint of realism), Bachelard is well aware that he is going beyond Einstein’s own position. “Einstein seems to adopt the traditionally realist point of view in that he supposes that matter is in a sense anterior to space” (VIR, 219). Bachelard’s view on the philosophical consequences of Einstein’s theory, particularly that of general relativity, is inspired instead by those of Sir Arthur Stanley Eddington, one of the British astronomers who confirmed that theory during the solar eclipse of 1919. While it would be beyond the scope of this book to explore at length Eddington’s epistemology, it is illuminating nonetheless to take into account certain striking similarities with Bachelard’s position.
Eddington, like Bachelard, stresses the dichotomy between common sense, three-dimensional realism from which science began and the four-dimensional world of relativity that replaces it: “the real three-dimensional world is obsolete and must be replaced by four-dimensional space-time with non-Euclidian properties.”10 But, again like Bachelard, and unlike Einstein, Eddington is not prepared to assume the antecedence of matter. He is struck, instead, by the formal character of relativity, by its structural properties: “The theory of relativity … is knowledge of structural form, and not knowledge of content. All through the physical world runs that unknown content, which must surely be the stuff of our consciousness. … Where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature.”11 For Eddington, the rational patterns of the mind determine what we know of reality.
Bachelard’s view of reality as secondary to its organization is consistent with Eddington’s supposition that “the investigation of the external world is a quest for structure rather than substance.”12 In taking note of Eddington’s particular emphasis on the structural aspect of scientific knowledge, the reader of Bachelard can appreciate a similar point of view in the latter’s epistemology. While Bachelard does not insist, as does Eddington, on the term “structural” or “structure,” the proximity of both philosophers’ views and Bachelard’s frequent insistence on the “constructive” or “reconstructive” role of mathematics make it apparent that he too was thoroughly familiar with the structural aspect of modern science.
Having explored the rationalistic dimension of knowledge in the congenial realm of relativity theory, Bachelard then undertakes, in Le Pluralisme cohérent de la chimie moderne (1932), the challenge of demonstrating the fundamental rationalism of that seemingly less kindred domain, the “supremely experimental and positive science”13 of chemistry. His stated goal is to examine the dialectic oscillation in chemistry between the diversity of heterogeneous elements, or “pluralism, on the one hand, and the reduction of plurality, on the other” (PCCM, 5). Since much of this fluctuation takes place over time, his approach is necessarily partly historical, although he disclaims any intent to write a history of chemistry, as such.14 As was the case previously, knowledge is conceived in terms of a binary opposition—in this case, of pluralism and coherence—although it would be a distortion, as Bachelard shows, ultimately to assume a facile association of empiricism and rationalism with either pluralism or coherence. Such an association may well be justified historically, but he is able to demonstrate the eventual interplay of both pairs of oppositions in modern chemistry.
While Bachelard emphasizes that any unifying thought in science must facilitate a new diversity, he claims that, in the abstract, it does not really matter if knowledge begins with the perception of diversity or the constitution of identity since knowledge stops neither in diversity nor in identity. Yet, because the prescientific era and even the early scientific age15 assumed not only a naive realism but a universal natural order or “naive barmony” that was impatient with “the delays and precautions of empiricism” (PCCM, 225), modern chemistry had to begin not with unity but with diversity. Thus chemistry originally multiplied the number of substances. In doing so, it reinforced naive realism while it abandoned an assumed unconstructed harmony.
In a series of chapters, Bachelard shows that the chemist began by looking for individual qualities of substances but ended by finding general laws as the initial, surface realism of experimental chemistry opened the way to the rationalism of mathematical chemistry. Contemporary chemistry, Bachelard points out, is suspicious of immediate sensation. It goes beyond the immediate quality to a hidden one that is relative because it appears as the result of a relationship of bodies. Accessible bodies in a chemical phenomenon are primarily of interest as pieces of a construction. “It is therefore on a deep plane that chemical analysis must find its root” (PCCM, 39). In contemporary chemistry, depth of rational construction replaces surface description.
Recounting the efforts, principally of Mendeleev, to fix the order of elements according to atomic weight, Bachelard gives particular emphasis to the subsequent shift from atomic weight to atomic number as a classificatory principle. Unlike the atomic weight, the atomic number did not initially correspond to empirical observation; it was merely the ordinal number of a particular element in Mendeleev’s chart. Yet this apparently artificial variable, which originally had no experimental meaning, gradually took on increasing value as an experimental tool and point of reference. For Bachelard, this was “one of the greatest theoretical conquests of the century” (PCCM, 134). It meant that a particular substance could be known by its place on the periodic chart even before it was empirically “discovered” or “produced.” It is hardly surprising that Bachelard should underscore this particular aspect of chemistry, for it is difficult to imagine a more immediate and vivid example of the rationalism of discovery.
Bachelard’s examination of the chemistry of second approximation, that of the chemical atom, or what he calls “electrical chemistry,” further reinforces his thesis that in chemistry, too, the balance needs to be struck in the direction of rationalism. “Beneath the interplay of multiple and mixed qualities which constitute our immediate phenomenon and which the phenomenon of ordinary chemistry still reaches, a profound quality is disclosed in the experiments of electrical chemistry. This quality turns out to be totally uniform, it is suitable for constituting an essentially instrumental and schematic phenomenon that is eminently accessible to reason” (PCCM, 167). As chemistry becomes more theoretical and mathematical, as it moves away from a first approximation study of substance, the variety of the elements is gradually replaced by the uniformity of electrons. As it becomes increasingly rational and ordered, chemistry turns away from the naive realism of its beginnings. Having relinquished an assumed harmony in favor of realism, chemistry now has made a paradoxical reconversion to harmony. Yet the paradox is only apparent, for the real transformation is not from harmony to realism and back again, but from a naive view of harmony and reality to a rationally constructed view of each. For, despite its rational aspect, chemistry does not really abandon reality; it ultimately deals with chemical elements, even if the qualities of such elements are now considered secondary to the uniform qualities of the chemical atom.
In becoming more rational, chemistry demonstrates “how diversity can be born of identical components” (PCCM, 169) by constructing well-ordered variations from the uniform qualities of the chemical atom. In chemistry, what is systematically possible can be, and often is, brought into being. It becomes an empirically inventive, constructive science that actively combines the pluralism of diversity with the coherence of ordered harmony. “Chemical substances, included in a coherent and harmonic pluralism, suggest possibilities of construction” (PCCM, 228). The dialectical oscillation between pluralism and coherence that took place sequentially in the history of chemistry has been transformed through rationalism into the very means of knowing in modern chemistry. An equally dialectical but synchronic “coherent pluralism” has replaced diachronic oscillation as modern chemistry has grown more rational.
While Bachelard never abandons the empirical or “descriptive” side of the knowledge equation, it is quite evident that the “retrieval” or, increasingly, the “constructive” side is given significant attention. Contemporary science is always experimental, of course, but in Bachelard’s early epistemology and beyond, it is its rational aspect that makes it distinctive. In Bachelard’s view, contemporary science teaches us the need not so much to see better, but to think more accurately.