But in my opinion […] there are still deeper reasons why the scientist should give his attention to the history of science. I am thinking of those, which have been so splendidly illustrated by Ernst Mach in his Mechanics [In order to teach beginners,] nothing would be more useful from this point of view than to work out some textbooks in which science would be expounded in chronological order; this is indeed a very important task for which Ernst Mach has given us some admirable models.
George Sarton
Abstract
George Sarton had a strong influence on modern history of science. The method he pursued throughout his life was the method he had discovered in Ernst Mach’s Mechanics when he was a student in Ghent. Sarton was in fact throughout his life implementing a research program inspired by the epistemology of Mach. Sarton in turn inspired many others (James Conant, Thomas Kuhn, Gerald Holton, etc.). What were the origins of these ideas in Mach and what can this origin tell us about the history of science and science education nowadays? Which ideas proved to be successful and which ones need to be improved upon? The following article will elaborate the epistemological questions, which Darwin’s “Origin” raised concerning human knowledge and scientific knowledge and which led Mach to adapt the concept of what is “empirical” in contrast to metaphysical a priori assumptions a second time after Galileo. On this basis Sarton proposed “genesis and development” as the major goal of Isis. Mach had elaborated this epistemology in La Connaissance et l’Erreur (Knowledge and Error), which Sarton read in 1913 (Hiebert 1905/1976; de Mey 1984). Accordingly for Sarton, history becomes not only a subject of science, but a method of science education. Culture—and science as part of culture—is a result of a genetic process. History of science shapes and is shaped by science and science education in a reciprocal process. Its epistemology needs to be adapted to scientific facts and the philosophy of science. Sarton was well aware of the need to develop the history of science and the philosophy of science along the lines of this reciprocal process. It was a very fruitful basis, but a specific part of it, Sarton did not elaborate further, namely the psychology of science education. This proved to be a crucial missing element for all of science education in Sarton’s succession, especially in the US. Looking again at the origins of the central questions in the thinking of Mach, which provided the basis and gave rise to Sarton’s research program, will help in resolving current epistemic and methodological difficulties, contradictions and impasses in science education influenced by Sarton. The difficulties in science education will prevail as long as the omissions from their Machian origins are not systematically recovered and reintegrated.
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Notes
In a historical-genetic approach, the “birth” of an idea becomes very important. Only then, the idea can be studied in its raw condition and rough environment. Later “polished” versions of the idea often tend to hide the actual motives and conditions under which the idea was born. But it is often these hidden motives and conditions, which are necessary to understand the actual empirical meanings tacitly conveyed by the idea. Thus, Mach’s ideas played a larger role in many of Sarton’s initial ideas, while in the later adaptations and repetition of these ideas, Mach will rarely be mentioned, though his influence will still resonate in the concepts used. This genetic effect might lead to the assumption that Mach had little influence on Sarton, which is why a conceptual analysis (how and which concepts are used in context) is needed throughout.
The German title is: “Die Mechanik—historisch-kritisch dargestellt.” For a later English edition, Mach had asked the translator McCormack to change the English subtitle into “genetic” instead of “critical and historical” (see letters from Mach to McCormack at the Paul Carus Archive, Bloomingdale). For printing reasons, this idea had to be dropped eventually (this is at least the reason provided by McCormack in the letters).
Einstein kept this view (Einstein 1916) throughout his life. He later repeated it in a letter to his friend Besso (Einstein in 1948, see Speziali 1972, Doc. 153): “Now, as far as Mach’s influence on my development is concerned, it was certainly great […]. How far [Mach’s writings] influenced my own work is, to be honest, not clear to me. In so far as I can be aware, the immediate influence of D. Hume on me was greater […]. However, as I said, I am not in a position to analyze what is anchored in unconscious thought.”
Just as one tends not to remember sensual experiences from early childhood, such as sucking, early methodological concept formation (“erkenntnis-theoretical,” see next footnote) tends to become intuitive. It is thereby not accessible to the “usual conscious” process of reflecting thoughts (adaptation of the thoughts to each other). This accessibility or non-accessibility nevertheless has to be considered a methodological question of erkenntnis-psychology. Maybe one is just not sufficiently trained in reflecting these processes. It is for instance interesting to observe that Einstein (1916) in his obituary on Mach states four or five times that Mach had no “specific” contribution to science. If this would be so, why would Einstein feel the need to raise the question every few sentences? Erkenntnis-psychologically speaking, this might be considered a conceptual substitute for stating that one did not find a satisfying explicit answer to some intuitive knowledge.
The German Erkenntnistheorie literally translates as “theory of knowledge/cognition”. The meaning in the Machian sense is different from, but related to epistemology (which will be elaborated later). In order to gestalt-psychologically denote this difference, the usage of the German term “erkenntnis” will be kept. The term “erkenntnis-theoretical” will be used as an adverb. Mach used the terminology of erkenntnis-psychology in order to clarify—like Sarton with his concept of humanism (Sarton 1931/1962)—that he considered his view mainly derived from his experiences of natural sciences and not from classical philosophy.
Mach later also held the first university chair on “philosophy, especially history of inductive sciences.” Sarton in his 1922a, b article makes a detailed survey of university chairs “devoted to historical studies” in the world. He states that “the chair of the Collège de France [in the indirect succession of Comte] is to-day the only one in the world devoted to the history of science”. It was the year when Moritz Schlick took over Mach’s (previously vacant) chair in Vienna. It is striking that Sarton’s world view here seems to be centered on and his knowledge of facts somehow limited by the French and English speaking world.
Sarton (1918, p. 195) points out this bias: “The few serious courses that have been thus far devoted to [the organic development of science] have been, with the possible exception of Mach’s lectures, far too philosophical, I mean—far too prone to premature generalizations. In the case of France, this is due to the influence of Auguste Comte and more generally the French love of system. In the English speaking world, the influence of the positivist school has been working in the same direction.” So Sarton himself laments about this problem, but still sometimes intuitively becomes a victim of it.
It would be interesting to know alternatively, what would have happened to science education, if Sarton, instead of learning Arabic in his late years, would have learnt German. Then he could have read Mach’s Knowledge and Error in its full (but still difficult to understand) German version instead of the faulty abridged French version. He might also then have discovered Mach’s school books, which describe the use of history of science as an integral tool of teaching science to young children, something which Sarton thought is impossible.
Maybe Sarton’s lapses are due to a central conceptual error which Sarton makes, regarding his concept of genesis: Mach’s approach is post-Darwinian genetic and not “organic”. The antique concept of genesis as the ancient Greeks, especially Empedocles, saw it was a god’s puzzle game with organs (Freeman 1947/1971, p. 58/59). Aristotle adopts this part of Empedocles’ speculations. Mach instead, following Darwin’s traces, sees genesis as adaptive and transformative (Mach 1883/1888).
Sarton might have felt that one has to choose between Scylla and Carybdis, between a “ratiocinating tendency” and “handcraft”. The question is, if it might be preferable to sail in different conceptual waters altogether. Mach’s more general and coherent concept of psychophysics and sensualism is not reducible to either of these concepts, though it often has been misunderstood in such ways or ignored.
“Decidedly” here for Mach implies an intentional (and psychologically difficult) process to do so, not a fait accompli.
Ernst Mach Archive, German Museum, Munich, NL 174/2869.
According to Marc de Mey, this influence is supported by letters in the Sarton archive, which still needs to be researched in detail.
The concept of empiry is used here in the German sense of Empirie, i.e. the noun to “empirical”. As the concept is very central for the following part of the article, its unusual usage also denotes a shift in meaning relative to its mainstream usage. From this point of view (which William James called “radical empiricism”), the question regarding which metaphysical theory is “economical” and which is not is not over, but has barely begun. For Mach (1905a, b, p. 153), empiry is the “adaptation of the thoughts to the facts” and metaphysics the “adaptation of the thoughts to each other”. As nevertheless, our memory strongly plays into this process, additional genetic inquiry is needed to entangle metaphysics and empiry, for instance in understanding what is factual. A fact is dependent on the circumstances under which it appears and by focusing on some of these and abstracting from others, the fact necessarily acquires a metaphysical dimension, which needs to be identified.
This was Mach’s first teaching course at the university. He kept teaching it at different positions throughout his life. It is probably the experience from this course he sometimes relates to as his “early teaching experiences” (Mach 1905a, b). The course is also special as it was one of the first courses of its kind. Mach therefore published the course material as a book out of necessity for a teaching aid. The relatively newly founded Allgemeine Krankenhaus (general hospital) in Vienna had enabled the empirical observation of a much larger number of cases in medicine, which previously with smaller hospitals was unprecedented (Swoboda 1973). Mach’s teaching activity brought him to the center of medicine, physics and physiology, a combination which became very fruitful for his later research and genetically central to his ideas.
See “Appendix I” and part II of the article.
It might take many generations of scholars to do so. It is of course necessary for effectively criticizing the ideas. In terms of the overall scientific process, such a method has to be considered quite inefficient.
From the first physics course for school children to the Mechanics for graduate university students, Mach intended a repetition of subjects about four times, each genetic “loop” successively transforming the conceptual gestalts of the students from basic everyday (common sense) phenomena towards scientific concepts. Mach’s strategy for education is fundamentally genetic, although the reason for this approach might not have been clear to everyone. For Mach, this way of proceeding is necessitated from a historical-genetic approach. “Even such important persons such as Galilei, Huygens and Newton could not see this fact at once, but grasp it only bit by bit […]” (Mach 1883/1976, p. 244).
For the concept of “gestalt” as an idea from Mach, see von Ehrenfels (1890).
Although Mach did not elaborate much on his usage of genetic “loops” for his school books, he uses this method before Dewey did (who generally counts as their inventor). Methodological “loops” were subsequently used in many areas, for instance by systems theory or POPBL. The principle seems to have older roots than it is generally assumed.
Mach (1905/2002, p. 131) criticizes concepts based on “premature abstraction” in teaching like concepts based on hearsay of insufficiently and superficially known facts as “containing potentially only badly described and shadowy individual images, which can especially easily misled towards errors”. They are “like building made from brittle materials”. Depending on how deep these concepts are hidden within the walls and how well the walls are decorated, their brittleness might nevertheless come to light only in the process of the next fundamental renovation unless they take the whole building down beforehand.
According to Hayman (1982, p. 422), Hilbert commented after one of the lectures of the Finnish mathematician Rolf Nevanlinna (who as a friend of Eino Kaila in his mathematics and erkenntnis-theory was Machian, see Siemsen 2011a): “You have opened a hole in the wall of mathematics; soon other researchers will come and close it.” What if this “hole” was not—as alleged—in the “wall,” but in the empirical “fundaments” of mathematics? How should one then “close” it? In Finland, the discovery of the “hole” did not lead to the “patching-up” as suggested by Hilbert, but rather on a fundamental revision of how mathematics and science is taught (see Kurki-Suonio 2011; Siemsen 2011a). In USA (and as a result in many other places strongly oriented towards ideas from there), this revision was initiated in mathematics (by Alexander Israel Wittenberg, see Ahlfors 1962; Wittenberg 1965, 1968), but became stuck in the conceptual confusions of the so called “math wars” (see Siemsen 2010d; 2011a).
In these institutional “wars,” specific “perspectives,” such as the social perspective or the formalist perspective and the phenomena one can observe from this specific perspective are generalized from each side. Regarding for example the question of “premature abstraction,” one could argue that in the extreme, the “social” perspective considers premature abstraction as individual experience not compared in analogy to the experience of others. Or, any teaching of the teacher is considered as enforcing “premature abstraction” (e.g. in extreme forms of discovery learning). Similarly, the formalist “perspective” implicitly assumes that one has experienced many details in order to be able to abstract to their general form. It abstracts from many details of the concrete experience, but in order do so the concrete experiences have to provide the general basis (Hadamard 1945). A more general concept of what “premature abstraction” is (see also “Appendix I”) based on synthesizing different experiential frames (including the social and formal perspectives) would probably make the actual motivations explicit and help in clarifying the conceptual confusions involved. A more generalized concept of what actually is empirical would help to clarify the limitations of the experiential domains from which the (implicit) foundational examples are taken. Then one could specifically look at phenomena, which lead to experiential facts in-between and beyond (i.e. important for science education but not covered by these domains).
One can “generalize” this claim for more general concepts: A more general view and more general foundational concepts on science and science teaching might thus help in finally clarifying the unfruitful decades-old debate. According to the OECD (2006, 2007) PISA results, the debate has not provided any broader-based empirical results in terms of mathematics education, at least in comparison with most OECD countries. The empirical “successes” used were probably thus based on self-comparisons.
An example of this shall be given by an observation of a daughter of the author at the age of two. After for the first time playing in the snow and building snowmen for the whole day, she was sitting at the dinner table and playing with mandarins which were put there for desert. She took three of them of different sizes and stacked them on top of each other with the biggest at the bottom and the smallest on top. Then she laughed at her accomplishment and shouted to the puzzled adults “snowman”. Thus, the concept of a “snowman” became the abstracted gestalt of three flat balls stacked on top of each other. Shortly after, she easily repeated the conceptual gestalt on a computer “snowman game” by herself (she had never used a computer, screen or mouse before).
Sarton is not the only scholar with such an attitude. As the Finnish science educator Kurki-Suonio pointed out in a private statement, Feynman’s famed lectures are excellent—if one already knows physics. This can be taken as criterion between Mach’s Darwinian genetic and non-Machian ancient-genetic science education. The second takes its knowledge base (and systemic frame) as already given a priori.
Sarton here intuitively includes the idea of teaching in genetic “loops” (ever-increasing quantities), although he does not seem to grasp the value of this intuition. The passage seems to be quite directly inspired from Mach’s Mechanics (for instance by the introduction, Mach 1883/1976, p. 1).
At Conant’s time (in 1945, p. 7), 90–95% of an age group completed grade six, 45% grade twelve, 15% the second year of college and 7% the fourth year of college.
For instance Binet, Schwarzwald or also the much lower influence of the parent’s educational background in Finland coupled with a much higher outcome of sophisticated students there (see Siemsen 2011a).
It might of course be argued that other science educators, such as for instance Piaget have already done so. As the experiments from Binet (1911) and from Bruner et al. (1966/1967) show, Piaget’s method suffers from the same problem as Sarton’s. He only makes it partly more sensualistic and up to the point he does, students from well-off Geneva families (about the upper 20%) benefit from it enough to produce beneficial statistical effects. The method does not reach the same level in other cultural (less Western-“civilized”) backgrounds (see Bruner et al. 1966). Also what Piaget actually made to work in his lab might not comply very highly with what he describes as working in his writings (see Ratcliff 2006). In his first book, because “realism is thus anthropocentric illusion”, Piaget (1926/1929, p. 34/35) starts from the “boundary the child draws between the self and the external world […]. The work of Mach and Baldwin has long since made [this method of starting] familiar to psychology […]. Mach’s hypothesis is not based on a true genetic psychology and “the genetic logic” of Baldwin is constructive rather than experimental.” Piaget then supposes that the views of Mach and Baldwin are the same, which they are not. For Mach as well as the non-teleological adaptation process supposed by Darwin, “genesis” is based empirically and never logically. Thus, biological adaptations do not happen because of logical reasons, but logic is an adaptation of human thought to questions of consistency of thoughts to each other.
As far as Piaget is concerned he tries to implement a “logical genesis.” Piaget’s method has to be considered as not Machian (not post-Darwinian) genetic. It is rather logic-linguistic, i.e. starting with the high-level “initiation” of the use of language instead of starting with Machian sensualistic elements (Piaget did some of his first research on child language; Mach did his first research on sensualism). This in principle became the criticism of Piaget’s approach by many, such as Bruner, Freudenthal and the successors of Boas (see Siemsen 2010b). Piaget’s “genetic psychology” is actually not genetic, at least in a post-Darwinian sense.
It was called so initially for the Prague edition, which was only generally approbated in Austria after several German states had adopted the book. According to Hohenester, this influence in Germany was at least partly due to Mach’s presentation “On Instruction in the Classics and the Mathematico-Physical Sciences” in 1986 at the Congress of Delegates of the German Realschulmännerverein (Mach 1893, p. 338). For Germany, the title of the book was changed into Grundriß der Physik. As the German states have legal authority on educational issues, different books and editions had different co-authors. The “Grundriß der Naturlehre” is an example of consequent abstinence of paraphernalia. See Appendix II in part II of the article for a part-translation from one of the books.
The “Real”-Schools are the more technically-oriented schools, while the classical Gymnasien are oriented on Greek/Latin education. Different and sometimes contradictory terminologies are used in the German and the Austrian systems at different times.
“Again” tends to be one of the first words used by the child as it provides command of repetition by the caretaker.
This is the difference to Piaget’s “stages” model in which all students are categorized into “age-groups” and become laggards if they do not manage some topic within a certain time-frame and order of development. As already the initial inventor of the “stages” model Alfred Binet later recognized, many people develop their thoughts quite apart from such an ideal logician’s path. Should they therefore all be considered to be imbeciles and unfit for learning scientific concepts later or in a different way (see Siemsen 2010b)?
This material has remained partly unpublished, so even in Austria and Germany, these sources have not been properly evaluated yet.
This was Mach’s most epistemological book, subtitled: “Sketches to the Psychology of Research.” The translations of this book are problematic. The French translation leaves out important parts, while the English translation appeared late in 1976. Both contain many translational “simplifications” to be easily misleading. For instance, Mach used erkenntnis-psychology (Erkenntnispsychologie) in the German subtitle instead of the simple “psychology”. For Mach (see "Appendix I"), this conveys a very different meaning. His initial intention of using the term carefully repeated many times in the first chapters of Knowledge & Error was to show that he did not mean to develop a “philosophy” in the sense of classical philosophy. Here Sarton shortly after coming to the USA had the same experience as Mach. Sarton then took great pains to clarify his meaning of history and philosophy of science as fundamentally and methodologically different from a propedeutic course in philosophy. This was the standard of how it was taught at many US universities at the times (Sarton 1918). “The few serious courses that have been thus far devoted to [the history/development of science], here and abroad, have been, with the possible exception of Mach’s lectures, far too philosophical, I mean—far too prone to premature generalizations. In the case of France, this is due to the influence of Auguste Comte and more generally to the French love of system. In the English speaking world, the influence of the positivist school [exemplified by John Theodore Merz] has been working in the same direction” (Sarton 1918, p. 195).
As seen before, Sarton’s understanding of the concept of “genesis” is different from Mach’s, but he is not aware of it.
Conant called his program “General Education”. In order to explain the idea, he described the avoidance of scholasticism and “bad poetry and wrong philosophy” which for him led the Germans to Nazism as the central question of the US after WWII (Conant 1944).
For Sarton, these concepts seem to have different empirical (factual) meanings than for Mach. Though Sarton mentions the concepts of evolution and of transformation as central, he partly continues to use the antique understanding through the concept of fixed, eternal forms rather than transformations. This aspect will be more fully explored in part II of the article.
Italics added by the author.
From a sensualist perspective, thoughts necessarily have to be individual. It is only by analogy one can compare these to the ideas and experiences of others. Both processes then in turn are mimicked by others, first by individuals with similar previous experiences (e.g. fellow villagers, scientists, etc.) and then maybe by other individuals as well. The scientific community and other cultures certainly share ideas among the members of their social group, but many scientific communities, even close ones would probably not find it very accurate to be described as “collective”. Sarton’s moralistic utopian concepts used here will probably not be shared by many as ideal. They do not seem to constitute an empirically generalizable basis, neither for psychology, nor for sociology. Sarton’s suggestion that a generalizable basis of psychology and sociology is needed for teaching the history of science, of course remains a fruitful one. It opens the possibility to integrate psychological and sociological facts into a consistent frame.
Deviations during enculturation are individual psychological processes. Psychology might apply “cold” statistics analyzing what leads thoughts into a wrong direction, into error. Because it helps people to learn, the term “cold” is deceptive. It is a tool which can be used to analyze what is going wrong during learning. Its usage is nevertheless often not accepted by educationalists, for example Wagenschein. Their argument is that it diverts energy away from teaching.
The recent research in “mirror neurons” (see for instance Rizzolatti and Sinigaglia 2006/2008), i.e. neurons specialized on mirroring the behavior of other, similar beings is a research in this direction. It would be especially interesting to find out more about the plasticity of the construction of the “self” and the “other” related to experience over time.
It seems impossible to look into individual errors by sociology or to have an imagination how to cope with these errors in relation to the community. To analyze these errors, repairing them or avoiding them with statistical methods in psychology leads to dramatic changes in the social statistic. A greater number of the former laggards suddenly are within top field of learners (see Siemsen 2011a, Appendix II). In Finland, “no student is lost for education.” The normal distribution of the grades of students changes to an upwards shifted distribution with many more students at the top then by educating a pre-selected elite (see footnote 16 p. 9).
The anthropologists from Franz Boas’ school of thought have elaborated much on this topic (see Siemsen 2010b). A current interpretation of this is for instance the concept of “cultural manifolds” (Lloyd and Sivin 2002). For instance an early alternative psychology has been developed (or rather recorded) by Buddhists (Rhys Davids 1900). Regarding genetic questions it can—from a post-Darwinian perspective—be regarded as more sophisticated than Aristotle’s De Anima.
For an interesting alternative, see Solaris by Stanislav Lem, which through Bogdanov’s Machian erkenntnis-theoretical science fiction novel “Red Star” seems to have some Machian inspired background (see Siemsen 2010a).
The generalized understanding of institutions as formal or informal carriers of ideas in societies as used here is taken from historical institutionalists, such as Weber, but especially economic institutionalists, such as Veblen, Coase, Williamson or Hayek.
This is here to be understood in a Machian erkenntnis-psychological, not in a Freudian way (see Siemsen 2010a).
The physics educationalist Pohl became famous for using the shadow image of instruments projected on white walls (see Wittje 2011).
What is meant here with “basic sensualism” is that some senses (doing, hapts, some feelings) developed genetically earlier (in biological evolution as well as in child ontogenesis) than for instance the sense of sight and especially (culturally constructed) space perception. Teaching focused on this additional genetic perspective in sensualism might thus have access to more intuitive learning throughout the senses (see also Thiele and Reinert 1977). This is a hypothesis from K. H. Siemsen (1981), which has roots in some ideas of Mach and Spencer. Mach did not elaborate on this further than sensualism. It would be interesting to know, in how far Mach used pantomimic elements for his lectures, but this would be purely speculative (though James described Mach’s lessons as “artistic”, see Thiele 1978, p. 169). Nevertheless, it is probably not by chance that some of Mach’s successors in sensualistic teaching (for instance Eino Kaila) were famous for their “performances” in their lectures. Unfortunately, these have not been filmed. Also Sarton is supposed to have given impressive lectures. Maybe his success could be found more in his intuitive “doing” than in his conscious reflection on it. Few people who have seen his lectures are still alive to remember these details.
Not understanding Mach’s idea of sensualism led Sarton into a wrong direction of high cost paraphernalia. The consequence was to make a premature and arbitrary distinction between teaching science and teaching history. Mach’s school books are a lucent example of how to avoid a high cost paraphernalia situation without reducing educational effectiveness.
Probably the quality of the teaching does not depend on the lecture hall, but Sarton’s implicit personal motive is to have a lecture hall of his own.
One can compare Mach’s definition of “scientific precision” in "Appendix I" as an economy and simplicity, which is quite independent of the scientist and of the lecture hall used. The question is which definition fits more to the facts of science.
Sarton’s self-professed ignorance seems strange though, if one considers his profound thoroughness in historical research, asking for instance from any historian of science no less than learning all necessary languages personally. Sarton at this central point surprisingly does not apply his own method to himself, i.e. to his central idea, and also does not notice this omission later on. Mach’s ideas concerning this issue were at least partly published in The Monist, the very same journal Sarton published the previously quoted passage in. Also, Mach had published an article regarding these questions in the French journal from Alfred Binet l’Annee Psychologique (see also Siemsen 2010d). Furthermore, Sarton seems to be totally unaware of the influence of Mach’s “method of teaching” in the US, for instance on the late William James (see Siemsen 2010a) or on the “Pearson Circle” from the anthropologists at Columbia University discussing Mach’s books (Sarton himself taught for a semester at Columbia), such as Lowie or Boas. They were responsible for awarding the honorary membership of the New York Academy of Science to Mach in 1911 (under Boas’ presidency). The successors of the Pearson Circle later became instrumental in the empirical development of Jerome Bruner’s critique against Piaget (for a more detailed account, see Siemsen 2010d).
What is here called experimentalism is actually part of a wider phenomenon, which can be observed for several natural scientists, who tried to implement a Machian Erkenntnistheorie in science education, such as Henry Edward Armstrong in England or Čeněk Strouhal in what is now the Czech Republic (details can be found in Siemsen 2010a, b respectively). The phenomenon has long-term historical roots as shall be elaborated later.
See article part II for a more detailed analysis.
Mach’s concept of thought experiment is much broader than commonly used. For Mach, every comparison with previously experienced facts is a thought experiment (Mach 1905a, b, pp. 183). See "Appendix I" for a detailed view from Mach.
Some of the greatest experiments are actually those, where from one gestalt perspective the result seems obvious, but from another it is doubtful. The problem is then to find a third perspective, like in the case of Galileo.
A more detailed account can be found in Siemsen (2010a).
This does not exclude, that there are other areas of jurisdiction, but then the claims cannot be regarded as scientific claims.
Mach published his initial ideas already in 1863, 4 years after the publication of Darwin’s “Origin” and much before Haeckel and Darwin himself tried to elaborate the implications of Darwin’s theory for human (and scientific) knowledge.
Mach (1890) stated that he had actually developed this view because of his research in psychophysics so that he would not constantly have to change his world view. Therefore he had been looking for a “neutral” view consistent with the physical, physiological and psychical facts. He also stated that fundamentally, one can only have one world view (as a fundamental gestalt). Seemingly different world views are therefore the result of inconsistent conceptual hierarchies.
Aristotle himself was actually very careful about the biological aspect of teleology. The main problem seems to have been the dominant scholastic interpretation of teleology as god’s thoughts and the resulting inflexibility in reinterpreting the concept. It was seemingly Huxley’s crucial influence to have popularized this shift in concepts against an implicit alliance of philosophers and theologians believing in an initiatory concept of knowledge instead of an adaptive one (see also Mayr 1972). As one can see in the current debates on intelligent design, the conceptual problem has not been resolved in general. Even in modern philosophy of science, there has been much confusion about this. Therefore, this specific aspect will be elaborated in more detail in further research. Mach’s shift in his concept of causality from a natural law to a working concept resulting from human biology has led him early to a synthesis in erkenntnis-theory fundamentally consistent with Darwin’s ideas (see Mach 1883/1888). The shift in his concept of empiry is a result of evolution. Unfortunately, as it is a secondary shift, not all his comments on empiry and metaphysics are consistent with the new view. This has led to many confusions among Mach’s intellectual successors, especially concerning their critique of metaphysics, which often implies elements of naive empiricism (see Siemsen 2010a).
The epistemologically more elaborate version of this idea is monism, i.e. the idea that on a fundamental level “all” should be considered as “one”. In Mach’s interpretation, this is a requirement of an economy of thought, as one idea is far more economical for replicating thought than two ideas if one considers that all other ideas are derived from these. Thus, in the case of dualism, all successive ideas, concepts, etc. in principle need to be duplicated.
Concepts (also in science) become increasingly intuitive and thus less accessible to our conscious reflection with their use. Fundamental concepts are indirectly involved when thinking about higher-level concepts. Therefore the intuitivizing effect is exponential for very basic concepts, for instance concerning our world view. This is not necessarily corrected by empirical observations. As James (1905/1967, p. 206) had observed, “I speak also of ideas which we might verify if we would take the trouble, but which we hold for true although unterminated perceptually, because nothing says ‘no’ to us, and there is no contradicting truth in sight. To continue thinking unchallenged is, ninety-nine times out of a hundred, our practical substitute for knowing in the completed sense. As each experience runs by cognitive transition into the next one, and we nowhere feel a collision with what we elsewhere count as truth or fact, we commit ourselves to the current as if the port were sure.” So 99% of the times we just do not experience anything contradictory and this is normally interpreted as empirical agreement, though it might just be a sign of metaphysical “metastasising”.
The problem of this misunderstanding is probably manifold and has similarly occurred to many others close to Mach’s thought. It is partly related to the editions of Mach’s most philosophical work “Knowledge and Error” (1905a, b): First, Sarton had read only the French translation of Mach’s “Knowledge and Error” from 1908, which unfortunately is regarded as a very bad and fragmentary translation for instance omitting most of the footnotes. The footnotes in Mach’s works often contain the most important information. They have an erkenntnis-psychological function.
Secondly, Mach’s publisher Paul Carus died before he could publish the book in English. The English translation appeared late, in 1976. Regarding Sarton’s influence on later scholars, Hiebert in his introduction to the English translation Knowledge and Error reprinted the title page of Sarton’s French version which he found at Harvard. Both, this English translation and the translation of Mach’s previous “Analysis of Sensations” (and its predecessor the “Contributions to the Analysis of Sensations”) cannot compare with the ingenious translation of Mach’s “Mechanics” by Thomas J. McCormack. The problem translating Mach is that he changed his world view more than once with many interdependent conceptual gestalts shifting their meanings as well (like previously described for Erkenntnistheorie). As a result, even in German language, Mach changes concepts and their meanings from edition to edition of his books. He continuously adapts old higher-level concepts to their new (internally consistent) meanings. This psychological process takes—as he noted—time and mental effort, a process which he never finished.
In this view, Aristotelian and medieval ideas are “common sense”, because they had time for their popularization and dissemination process. This at the time had an effect only for the intellectual elite, but with the introduction of compulsory education the ideas became “common sense” to the general public (in Western cultures). This “common sense” is not necessarily the same for children and adults from other (non-Western) cultures.
It is interesting to note here that experimentalism has an inherent problem with naïve “empiricism” as well as naïve “theorism” in principle because the relation between theory and empiry is not sufficiently clarified initially.
In Britain, the idea of experimentalism has similar roots as in the US in the pre-Darwinian erkenntnis-theory and the concept of natural science as experimental science. It was especially conveyed by Huxley and Spencer. Though they stressed the need for more science education, they did not detail how science should be taught, except for the fact that it should involve experiments. This was implemented mainly by their successor H.E. Armstrong. For a detailed account of the development of ideas from Armstrong to Nuffield, see Jenkins (1979). Armstrong did introduce a “heuristic” (genetic) way of teaching (based on the ideas of Mach’s close friend Wilhelm Ostwald), but largely left the emphasis on experiments uncriticized. Only in his last years, Armstrong noted the empirical problem (see Armstrong 1934 and Siemsen 2010a).
Reflecting Bradley’s critique and maybe independent or as an implicit result of it, Nuffield employed Eric M. Rogers as a consultant to reform its approach in physics education (see for instance Lewis 1994). Rogers certainly also had an experimentalist bias (see for instance Rogers 1960/1977, p. 8 on Galileo: “He cleared away cobwebs of muddled thinking and built his scheme on real experiment […]”; interestingly the next part is on the importance of Galileo’s ingenious use of—obviously not so “real”—thought experiments), but like Galileo, he has strong empirical instincts leading him into a genetic direction (where this originates from in the early development of his ideas still needs further research). As a result, Rogers’ new approach clearly identifies the lack of general scientific concepts at the basis of the course as the main direction of reform.
Unfortunately, he does not make an analysis on how these concepts should be introduced genetically, but instead uses an intuitive mind-map (Lewis 1994, p. 158). The main problems of naïve empiricism and naïve theorism are thereby touched, but not resolved. For instance, in Rogers’ “web of knowledge,” “measurement” is introduced on the same basic level as “observation,” which in an empirical and genetic sense is very problematic (see for instance Kurki-Suonio 2011 for a detailed elaboration of this conceptual relation). As can be seen from Bradley’s comments, even Bradley himself noted the necessity of this idea, i.e. rethinking scientific categorizations regarding their empirical and educational necessity, only late in his life. Interestingly, similar late empirical insights are known from Armstrong, Piaget, Binet and others (see Siemsen 2010a). Unfortunately, late insights are rarely adopted or even noticed by intellectual successors, especially from early students.
The middle and higher schools for girls were introduced later partly due to the insistence by Mach (see Hohenester 1988).
The meaning of “formal” for Mach is here the erkenntnis-theoretical and especially erkenntnis-psychological method, i.e. a genetic concept of the method of learning and transformative knowledge process, not a logicistic concept of knowledge as ideal form to be achieved. For Mach, the “form” is a result of partial abstraction as an element of scientific analysis. One nevertheless should not mistake the results of the method of analysis with synthesis: if one leaves too many parts out, the form becomes empty. For instance, if the genesis process is abstracted from, the “form” looses its ability as a gestalt to become transformed and becomes simply non-Darwinian “holistic”.
Mach later changed his view regarding how mathematics is taught as he realized that what he was criticizing in physics had its origin in the application of Euclidean methodology in physics (a specific application of some of Pythagoreian and Socratian method). Also in mathematics, this approach tends to be detrimental to the understanding of the empirical meanings of fundamental mathematical (and pre-mathematical) concepts. Even one of the founding fathers of modern logic and mathematics, Bertrand Russell in his introduction to Clifford’s “the common sense of the exact sciences” criticizes Euclid as a bad teacher. Russell struggled for 3 years to understand Euclid’s theory of proportion. “As Euclid treats it, it is a puzzling subject, not only because it is inherently complicated, but because Euclid never mentions his perfectly adequate reasons for not adopting the much simpler arithmetical procedure, of which the fallacies are not obvious until they are pointed out. Clifford, by telling just what is necessary and no more, makes the matter as clear as noonday. In this and in other matters [Clifford’s] book is invaluable to the schoolboy who, though interested by mathematics, is bewildered, as any intelligent boy must be if he is badly taught.” (Russell 1946, p. v) Mach (1905 p. 401/402) describes the historical-genetic process, which led to this Euclidean presentation of geometry and the subsequent problem of understanding it, starting from the manifolds of Riemann and Kronecker. “Thus were reached the highest and most universal notions regarding space and its relations to analogous manifolds which resulted from the conviction of Gauss concerning the empirical foundations of geometry. But the genesis of this conviction has a preliminary history of two thousand years, the chief phenomena of which we can perhaps better survey from the height which we have gained. The naïve humans who, role in hand, acquired our first geometric knowledge, held to the simplest objects or figures: the straight line, the plane, the circle, etc. and investigated, by means of forms which could be conceived as combinations of these simple figures, the connection of their measurements […]. The first geometry was of course not based on purely metric notions, but made many considerable concessions to the physiological factors of sense. […] The straight line was conceived as a rigid mobile body (measuring-rod), and the angle as the rotation of the straight line with respect to another (measured by the arc so described) […]. An idea is best made the possession of the learner by the method by which it has been found. This sound and naïve conception of things vanished and the treatment of geometry underwent essential modifications when it became the subject of professional and scholarly contemplation. The object now was to systematize the knowledge of this province for purposes of individual survey, to separate what was directly cognizable from what was deducible and deduced, and to throw into distinct relief the thread of the deduction. For the purpose of instruction the simplest principles, those most easily gained and apparently free from doubt and contradiction, are placed at the beginning, and the remainder based upon them. Efforts were made to reduce these initial principles to the utmost, as may be observed in the system of Euclid. Through this endeavor to support every notion by another, and to leave to direct knowledge the least possible scope, geometry was gradually detached from the empirical soil from which it had sprung. People accustomed themselves to regard the derived truths more highly than the directly perceived truths, and ultimately came to demand proofs for propositions, which no one ever seriously doubted. Thus arose—as tradition would have it, to check the onslaughts of the Sophists—the system of Euclid with its logical perfection and finish. Yet not only were the ways of research concealed by this artificial method of stringing propositions on an arbitrarily chosen thread of deduction, but the varied organic connection between the principles of geometry was quite lost sight of. This system was more fitted to produce narrow-minded and sterile pedants than fruitful, productive investigators. And these conditions were not improved when scholasticism, with its preference for slavish comment on the intellectual product of others, cultivated in thinkers scarcely any sensitiveness for the rationality of their fundamental assumptions and by way of compensation fostered in them an exaggerated respect for the logical form of deductions. The entire period from Euclid to Gauss suffered more or less from this affection of mind.” “Euclid’s system fascinated thinkers by its logical excellences and its drawbacks were overlooked amid this admiration. Great inquirers even in recent times, have been misled into following Euclid’s example in the presentation of the results of their inquiries and so into actually concealing their methods of investigation to the great detriment of science. But science is not a feat of legal casuistry. Scientific presentation aims so to expound all the grounds of an idea that it can at any time be thoroughly examined as to its tenability and power. The learner is not to be led half blindfolded.” (Mach 1905a, b, p. 402 footnote).
Mach’s analysis of the historical genesis of the Euclidean system highlights the strengths and weaknesses of the axiomatic approach. Axiomatization also happened in science education. Warren (1980) for instance describes the long-term shift from a historical approach to axiomatization in science education in the UK over the last century. Interestingly, both approaches have something from a Machian education, but also from this perspective, both are equally lacking in some important aspects as well, such as the focus on the “status nascendi” (see Siemsen K. H. 1981). That this (non-genetic) view of axiomatization is contradictory to a historical perspective is not a necessary property of axiomatization itself (nor of history) as might be seen from Mach’s different usage of central concepts, such as “proof,” “precision,” etc.
Mach here uses a different concept of “proof” than used in mathematics. It is a thought-economical proof which he thinks of.
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Acknowledgments
I would like to thank especially Marc de Mey, Gerald Holton, Richard Kremer, Michal Kokowski and Edgar Jenkins for the information they provided on many specific historical details discussed in this article. Also the College Archives & Corporate Records Unit at Imperial College London, especially Anne Barrett and Catherine Harpham, as well as the British Library, especially Jeremy Nagle, have been very supportive in aiding my research and accessing some of the rarer items. An additional thanks goes to the Philosophical Archive at the University of Konstanz for permitting the translation of Mach’s teacher instruction. Michael Matthews helped with many suggestions, which added to the initial version and shifted the general focus of the article. I would also like to thank Kaarle Kurki-Suonio and my father, Karl Hayo Siemsen for their invaluable help in proofreading.
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An article on the same topic, but with a focus on the psychological dimension is upcoming as ‘Ernst Mach and George Sarton: History of Science as Metapsychical Method,’ In: Pléh, C., Gurova, L. and Ropolyi L. (Eds.), New Perspectives on the History of Cognitive Science. Budapest: Akadémiai Kiadó.
Because of its length, this article is published in two parts. This part I focuses on Sarton’s teaching ideas and how he was influenced and not influenced by Mach. Part II will look into Sarton’s influences on successors in science education, i.e. which ideas of Sarton were continued and how this process further dilutes Mach’s educational epistemology, namely the concepts of genesis and empiry, which have undergone a substantial shift with Mach. These concepts then in turn change the empirical meanings of important questions for science education, such as what is an experiment. Some issues might only be fully understandable when reading both parts.
Appendix I: Exzerpts from Ernst Mach’s Teacher’s Instruction (Entwurf einer Lehrinstruktion für den physikalischen Unterricht an Mittelschulen) (Mach 1876)
Quoted with permission of the Philosophical Archive of the University of Konstanz. All rights reserved.
Appendix I: Exzerpts from Ernst Mach’s Teacher’s Instruction (Entwurf einer Lehrinstruktion für den physikalischen Unterricht an Mittelschulen) (Mach 1876)
Italics are by the translator, underlinings are in original. It should again be remembered, that for Mach, everybody is a student in a domain previously unexperienced. The less the experience and the broader the domain, the more one is a student in the sense of Mach.
“The teaching at a Mittelschule can either give the education of a young manFootnote 64 a degree by itself, or it can be a preparation for higher education. In both cases, one should see that the fruit of the teaching is not only in acquiring a sum of certain kind of knowledge, but that it also achieves formal education,Footnote 65 i.e. that the ability to judge and observe is trained through the subject matter. In both cases, the formal education is a seed, which by itself will develop fruitfully. This process is not to be underestimated relative to the positive skills, when the student immediately transfers to the practical life, because then he can easily acquire what is missing by himself. On the other hand, an unnecessarily stuffed head cannot help to lead him in times of need out of the critical situation. Formal education is on the other hand the main goal if the teaching is continued in higher education. Then all elements have to be transformed anyway and have to be taken as material and foundation of the new. It is therefore practical to limit the subject matter as far as possible, but work on it in a many-sided way. Only by dealing differently with the same issue, one understands the basis of the method and achieves ability in its usage. Also the broader educative parts of physics (like the mechanics) will be favored relative to others” (p. 1/2).
“One can certainly provide the student with a broader knowledge by starting from ready-made definitions and concepts, placing ready-made doctrines in front of him and proving them. This method is not even so bad in mathematics, because there the step from the experience [blosse Anschauung] to the definition and to the theorem might be very short and can therefore be complemented by each able student.Footnote 66 The physical knowledge which is acquired in this way nevertheless always appears as externally imposed. Especially for the student who reflects, sudden gaps of clarity will appear which he will not be able to resolve, if he does not know, how one has arrived at the concepts put at the top” (p. 2/3).
It is for instance a mistake, if one deduces the concept of “free fall” the following way: Heaviness is a constant force, “which gives the body in each equal following time-particle the same increase in velocity, therefore v = gt, therefore, s = gt/2*t, etc.” (p. 3).
“One knows heaviness by the pressure on a support and through the falling motion. Nobody, who has tried or observed can know that pressure is turned into motion and even less how it turns into motion. Nobody can therefore a priori know that by removing the support, pressure transforms into acceleration” (p. 3/4). Here Mach suggests to either use Galileo’s third dialogue (which was seemingly opposed by the ministry partly because of the printing costs involved) or alternatively to let the teacher read the dialogue and tell the narrative to the students. Even though Mach shows here the possibilities of historical-genetic teaching, he stresses the importance of taking the most naïve exposition of the transformation of a concept (status nascendi). As far as this is historical, it should be preferred as the historical exposition additionally teaches how concepts are adapted and to which facts.
“It is therefore a fact, that the body freely exposed to the earth gains an acceleration (inertia) against the centre of the earth. To this one can, after the relation of mass and weight is explained, connect the definition of force. Similarly, it should be shown in all analogous cases, how the concepts have originated historically, which observations have urged towards them. The most naïve historical exposition is always the best. The discoverer of a truth in natural science and the able student both stand before a new theorem without presuppositions. For both the same way is therefore most natural” (p. 6). Mach further suggests reading Huyghen’s “horologium” and “de percussione” as well as the introduction to Newton’s “Principia.” He stresses the initial elementary description “understandable for the most modest mental capacity which still in form and content contain treasures for teaching” (p. 7). “Apart from the culture-historical and ethical value, which the description of the difficulties overcome and the sudden expansion of the view has (Toricelli, Guericke, etc.), for the new concepts only such an exposition provesFootnote 67 their right to exist […]. The teacher using historical material […] will not run into the danger of expecting from the student to understand in one attempt, what could develop in the most important heads but slowly and gradually” (p. 6/7). “The historical exposition will lead to the comparison of different chapters and thereby separate the fundamental from the accidental and conventional” (p. 8). “The historical [genetic] exposition will apart from clarity have the advantage that the teaching stops to be dogmatic. Science appears as something evolving, not finished, still to be shapable in the future. Mental educability instead of simple education should be the result of such a teaching” (p. 9).
“One will have to be careful not to turn the physics lesson into a mathematical lesson. The goal of studying physics is the knowledge of the relations of the appearances in inorganic nature. The student should be guided to observation and deriving rules from the observations. For this, mathematics is only an aid. There is very much remaining to be understood in physics, even if all of mathematics would be left aside. Where mathematics is used, the meaning of this usage should always be made clear together with the student” (p. 9/10). Formula can be seen, for instance, as a thought-economical “compendious replacement of a whole row of tables, which, because their numerical content proceeds by simple rules, become tedious to produce and can be disposed of by a rule of production (formula) […]. One will choose the shortest, simplest and most vivid demonstration. A deduction does not become clearer or stricter by making it more laborious and long-winded. Discouraging examples with pretended strictness are amply provided in the modern teaching books. One might remember for instance the deductions regarding the pendulum movement, the lenses, etc. One could instead for instance in the first case put the assumption of sufficiently small excursions, at which sinus and directed edge might be confounded, at the top. Then the accelerations are proportional to the elongations […]” (p. 10/11).
“Such considerations are completely strict under the given assumption, but at the same time very vivid. Each step provides a new mathematical or geometrical perspective, as can be found amply with the old physicists, who did not have a method and therefore had to rely on the power of their imagination. Such considerations will always be more fruitful than hourly milling long calculations on the blackboard. The advice given here to take care of everything by very brief consideration of details, this does not misconceive the educational value of general methods. The value of such general methods lies in the economization of thinking about the single case, in the easy templating of it. This cannot be understood, unless initially a whole host of single cases has been sufficiently dealt with through the consideration of very different details. More general methods in science are a result of much detail work and have to be that also in teaching. Without this, method is an un-comprehended gift. In the method lies the insight that one can think a thought one-and-for-all and does not have to think it again in each case […]. ‘What you have inherited from your forefathers, gain it in order to own it.’” (p. 13) Something gained without effort has no value. “Mathematics has no other task in physics than showing that with certain properties of a phenomenon certain others are already included in the thought as well (co-determined)” (p. 17). Mathematics saves effort, but also expands the narrowness of our conceptions in perceiving too much simultaneously.
Based on a specific case, one should sometimes comment on general topics, such as the nature of theory and explanation: “A true and complete explanation always shows how a complicated phenomenon is a combination of simpler, known phenomena. Where one postulates a still unknown phenomenon for explaining, it is always a makeshift assumption and the assumption has to be of such kind which improves the overview and involves the possibility to be tested” (p. 17/18). Such assumptions are a necessary part of science, but making them explicit and questioning them is so as well. This becomes especially important and difficult if such assumptions remain intact for thousands of years and thus become very intuitive like the Platonian/Aristotelian assumption of reason as godly thought implying that “no bodily activity has any connexion with the activity of reason” (Aristotle 1930, p. 2068).
One should let students guess the “success” of an experiment before it is conducted. “Not only thereby the attention is increased, but youths will from the errors which occur in this also draw the lesson that natural laws cannot be philosophized-forth [lassen sich nicht herausphilosophieren]. A body does not, as most will guess, in double the time also fall double the way. The pendulum of fourfold length does not also show the fourfold duration of oscillation. One here does not have to construct a priory, but to observe” (p. 20/21).
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Siemsen, H. Ernst Mach, George Sarton and the Empiry of Teaching Science Part I. Sci & Educ 21, 447–484 (2012). https://doi.org/10.1007/s11191-011-9389-5
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DOI: https://doi.org/10.1007/s11191-011-9389-5