Abstract
Where does Finnish science education come from? Where will it go? The following outside view reflects on relations, which Finns consider “normal” (and thus unrecognizable in introspection) in science education. But what is “normal” in Finnish culture cannot be considered “normal” for science education in other cultures, for example in Germany. The following article will trace the central ideas, which had a larger influence in the development of this difference. The question is, if and why the Finnish uniqueness in the philosophy of science education is empirically important. This puts Finnish science education into the perspective of a more general epistemological debate around Ernst Mach’s Erkenntnistheorie (a German term similar to the meaning of history and philosophy of science, though more general; literally translated “cognition/knowledge theory”). From this perspective, an outlook will be given on open questions within the epistemology of Finnish science education. Following such questions could lead to the adaptation of the “successful” ideas in Finnish science education (indicated by empirical studies, such as the OECD PISA study) as well as the further development of the central ideas of Finnish science education.
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Notes
The ideas of this article are the result of an intensive research and discussion process with a larger number of science educators from all levels (university, school, government) in Finland.
The article does not claim to have found all ideas which have contributed to this process or to offer the only possible description (i.e. explanation in the Machian sense) of the facts. But it aims to be up to now the most consistent and concise description, covering the broadest number of facts, many of which other interpretations of Finnish science education have not taken into account.
Epistemology is the philosophy of knowledge in a Machian sense.
In the following, the terms knowledge, epistemology, philosophy of science and world view will be used in this Machian sense, which actually is conceptually in-between the current mainstream usages of these concepts. In the cases, where these English approximations do not sufficiently “fit” the actual meaning (in terms of the conceptual gestalt), the German term “Erkenntnistheorie” (resp. its anglicized adjective “erkenntnis-theoretical”) will be used. This view will also guide the perspective on the ideas elaborated in this article. Thus, it will not be Mach the (perhaps more known) physicist, but only the erkenntnis-theoretical (natural philosophy) side of Mach’s ideas which are centrally considered. The German concept of Naturphilosophie (natural philosophy) developed via Wissenschaftstheorie (theory of science) to “philosophy of science” (see Feigl 1969, p. 633). The idea of monism was interpreted by the members of the Vienna Circle as the “unity of science”, which implied an “integration between the sciences and the humanities” (Frank 1951, p. 6), requiring in turn the “integration between science and philosophy”. “Philosophy of science” thus designates a mixture between science designating natural sciences and mathematics versus the humanities as well as science in general (including human topics of study, which are considered “scientific” in their approach). As both interpretations can be found in philosophy of science, “history” is often added to differentiate the two. Still, also “history and philosophy of science” puts the (implicit) focus on science and not on human knowledge in general. As in science education, knowledge is developed from general human knowledge to scientific knowledge, this focus might already abstract from some important learning processes. Naturphilosophie has been used as a description of monism in idealistic (e.g. nature is considered true), physicalistic (e.g. laws of nature are considered true) and neutral (e.g. the same laws as gestalts are as far as possible applied to all of nature) interpretations (see also Appendix 1). The importance is that no conceptual distinction is made between animated (living) and not animated nature. Unfortunately, none of these concepts describes Mach’s concept of erkenntnis-theory well enough, though natural philosophy in Kaila’s sense (see later) comes close. Erkenntnis-theory and natural philosophy are thus much broader concepts than “philosophy of science” as they do not only concern science, but human knowledge in general. Conant (1951) for instance proposes a broader concept of knowledge, including the thinking of the farmer or the thinking of businessmen and investors.
Here the double-dependency (or co-evolution, called by William James “reciprocity”) of the concept of knowledge becomes prominent: we—as humans—can enquire about knowledge because we have a concept of knowledge, but our enquiry about knowledge is also on the philosophical meta-level guided and limited by this very concept. The result is thus plastic: fundamental changes in both can lead to transformational results of knowledge (concerning form and content). Conceptual changes of fundamental concepts, such as knowledge are thereby difficult in a twofold way.
Mach’s conclusion is clear (see also Mach 1883): according to evolutionary theory (i.e. the only currently known theory consistently describing the geological, biological, etc. facts as developed by Lamarck, Spencer, Darwin and Wallace), biological evolution on earth is some thousands of million years old, while logico-rational thinking has culturally developed some thousands (maybe about 3,000 years ago). In erkenntnis-theoretical terms, genetic analysis (in its general sense) is therefore prior to (though not independent of) logical analysis, as this might transform the understanding of the fundamental concepts on which the logical analysis is based (such as the concept of what is empirical). One, alas, has to be methodologically very careful when doing so, as any form of genetic reconstruction also bears its metaphysical pitfalls. But for consistently integrating evolutionary theory into erkenntnis-theory, one has to adapt many fundamental scientific concepts used since Aristotle, to which of course many scientific and especially philosophical traditionalists object (at least intuitively). This article is to a larger part concerned with this question and the difficult process, which adapting the philosophy of science to evolutionary theory implies. As Mach notes, facts force themselves only slowly onto the concepts of scientists.
It also had a strong influence on natural science and mathematics education in general. For the purposes of this article, the initial focus will be on the relation between the physical and the mathematical world view, but the epistemological issues have general implications, independent of the specialization of perspectives in science education. For instance, the implications in biology education are rather obvious in the empirical meaning of the concept of evolution used here. Some implications can for instance be found in the biology school book by Pauli (1949). The implications in chemistry education have been elaborated for example by Wilhelm Ostwald and Henry Edward Armstrong.
Doppler had used the analogy of waves interchangeably for acoustic and optical phenomena. On the use of Analogies as scientific method by Mach, see Siemsen (2010d).
In quantum physics, this relation becomes more obvious. This was the origin of Wolfgang Pauli’s epistemological perspective as elaborated by Laurikainen (1989).
Kaarle Kurki-Suonio (KKS) commented (email 3/7/2009): “This has been one important emphasis of mine. My message to the teachers has been that all elements of science are present in the everyday experience and in the normal thinking of people—the teacher has just to identify them in order to be able to help developing them. Moreover, I am seeking these elements in the very primary process of sensual perception […].”
For an early similar methodological view in the US, see for instance G.K. Gilbert or T.C. Chamberlin and William James.
Our languages have gone through an evolution of several hundreds of thousands of years in order to make sure of this. Scientific languages can be more precise than this general language, but then the “users” need to be culturally trained in their specific usage. Thus for instance mathematics is a precise, but not a universal language. Erkenntnistheorie in the Machian sense is a search for the most general (widely applicable) scientific concepts regardless of specialization. It is therefore directed towards the most fundamental (in a genetic and sensual sense) concepts. For instance, there must be a general concept of science, otherwise its “division” into natural sciences, humanities, etc. would not make any sense. This fact at the same time epistemologically limits specialization, which can only be observed from the general “world view”. Several more examples of this erkenntnis-theoretical view will be provided in the article.
Thus for Mach a “reality” exists, but we cannot know about it except for the fact that it exists (otherwise we could think us the world as we would like it and empirical approaches would have no specific meaning). All other knowledge of “reality” is dependent on how our knowledge evolved in the first place and is therefore always relative to our (necessarily limited) knowledge about our knowledge. In this respect, for Mach everything we can know is epistemology (erkenntnis-theory). In this sense, Mach is a minimalistic realist.
KKS commented (email 3/7/2009): “Here I hear my own voice saying "perception of entities, phenomena and properties etc. is our strongest possible intuitive conviction about existence". You must have realized that this idea is the starting point of my idea about the physical reality.”
The historical-genetic approach follows the genesis (i.e. development) of central ideas from the status nascendi, including the unconscious aspects of this development as far as possible.
Thereby, Snellman and Tengstroem already voiced an important critique on Hegel, especially on his late works when he moved to Berlin and became regarded as the “Prussian” philosopher with a strong nationalistic streak. This was elaborated for instance by Karl Popper (1945/2002). The idea of “masses” of people entails the idea of the leadership personality embodying the absolute “Geist” (see below) of the people and the ensuing leadership cult.
The idea was gladly adopted by the German (Prussian) government, which in turn promoted Hegel into the rank of a state philosopher.
According to Haeckel (1905), Darwin’s central argument is actually the non-teleology of evolutionary processes, i.e. the independence of evolution of any postulated final “goal” or “cause”. Even under the same conditions, the process can have different outcomes, different conditions can lead to very similar outcomes and circumstances change because of external and internal conditions. Mach would add that the very notion of conditions depends on the empirical meanings we give our concepts. Any “final cause” would already be included in the basic assumptions seemingly “leading” to it.
“Der Absolute Geist ist der Persönliche Geist.“ (The absolute spirit/mind is the personal spirit.).
Cygnaeus’ influence can still be felt in current education in Finland. For instance the Finnish Board of Education has a room dedicated to Cygnaeus with an entrance door decorated with his writing.
In this article, quotations from Mach will be related to their English translations, although these translations might be adapted by the author according to the German original. Unfortunately, some of the translations of Mach into English, especially on psychological questions such as his Analysis of Sensations (1914), are conceptually lacking and therefore partly misleading.
It will become clear here that the concept of “action” is for Mach part of “sensation”, which Mach uses in a very broad sense (see Siemsen 2010d). The usage is similar in Finland, where it is called “perception” instead of “sensation” (this will be discussed later). The concept is different from its current mainstream usage in education in the USA, which has been mainly shaped by John Dewey. Dewey used the concept of “activity” in contrast to “passive” sensations and perception (see for instance Dewey 1910; 1997, p. 140). Also for Dewey as a trained logician, “proper” thinking is reduced to conscious thinking, while the type of intuitive “doing” advocated by Cygnaeus is seen as a “lower stage” (an anthropomorphic view from Dewey, which is similar to Piaget’s earlier—more known—view in this respect, see Siemsen 2010b). Dewey’s “activity” is a philosophical result of pragmatism, rather than a psychological necessity. William James in the change of his world view late in his life adopted Mach’s type of usage, which then led to controversies between him and Dewey (see Perry 1935, pp. 514).
The genesis as seen by Mach is dependent on the process and not dependent on age. If a concept is new for a 25 or 60 year old person, the basic sensual elements for construction, such as hapts or enacts, should be as intensive as for a baby, independent of the prejudice a teacher might have regarding the age of the learner. Mach found that abstraction (including categorization) can only start when the gestalts adapted from the earlier elements are well established. This principle can similarly be found in Kurki-Suonio’s concept of gestalt hierarchies (see Kurki-Suonio 2010, 2006).
The theoretical elaborations from Mach can therefore not be taken as a description of Cygnaeus’ intentions, but only as a description of his empirical results. Mach and Cygnaeus share common “doing” experiences in this matter, especially in woodworking as Mach had done a2-year apprenticeship as a carpenter.
These relations are still currently researched in detail.
Kaila was married to the granddaughter of Snellman.
The article “On Gestalt Qualities” by von Ehrenfels (1890) was regarded by Wertheimer and Köhler as the foundational article of gestalt psychology (von Ehrenfels was teacher of Wertheimer, see also Wertheimer 1924, Köhler 1920 and Ash 1995). In the beginning of this article, von Ehrenfels states that his ideas initiated from an intuition he had after reading Mach’s Analysis. “My starting point arose from several remarks and hints from E. Mach’s “Contributions to the Analysis of Sensations” (Jena 1886) practically by itself, which I owe a considerable strengthening of my opinions about the here described circumstances to, even though they seem to have originated in completely different circumstances. Mach sets up the, for some people certainly paradoxically sounding, hypothesis that we can immediately “sense” [empfinden] spatial patterns [Gestalten] and even “sound-patterns” or melodies. And indeed at least the second of these theses not only seemingly, but also from its contents should be undisputedly absurd, if it would not be immediately intelligible, that “sensation” here is used in a different than the usual sense. […] But if Mach, by using the term “spatial and tonal gestalts”, also wanted to stress its simplicity, it becomes clear that he […] viewed these “gestalts” not as mere combination of elements, but as something new (relative to the elements on which they base) and up to a certain degree independent. […] I hope to be able to show in the following that Mach [in his reflections] has shown us the way of resolving the problem mentioned.“(von Ehrenfels 1890, pp. 249-251) The problem von Ehrenfels mentions is what William James called “The knowing of things together” (1895). If one takes a “regular” concept of sensation, it is a question of descriptive psychology. For Mach, it becomes a question of genetic psychology. “Immediate” sensations are dependent on memorized gestalts (Mach does not ultimately distinguish between biological and psychic memory; memory is a general function of evolution). What is “simple” might therefore appear to be simple in its current sensational gestalt, though it actually is a result of a “complex” genetic process. Gestalts are not linear (additive), they are transformational (see Siemsen 2010d). Unfortunately, cognitivism has mostly lost this erkenntnis-psychological basis during the synthesis of its foundation (see Siemsen 2010d).
Ketonen (1992) quotes Kaila in his criticism of traditional philosophy. According to Kaila, the traditional method is to start with solving “the question of the relation between mind and matter. […] According to the new method, on the other hand, even before we can begin to speak about mind and matter we must find out the results of the relevant research, i.e. what the sciences of the mind, especially psychology, are teaching us about the mind, and what the natural sciences, especially physics, are teaching us about matter. Then the results must be submitted to a logical and critical epistemological analysis. The final conclusion must be based upon this analysis.” Here Kaila on the one hand follows Mach in his emphasis on the “psychic” part of the psychophysical relation (erkenntnis-psychology), which the Vienna Circle did not put much importance on. On the other hand, Kaila stresses the logical analysis, which is the main domain the Vienna Circle is known for.
The interesting question is why Kaila’s successors, such as von Wright, have near-exclusively worked on the second part of Kaila’s method (erkenntnis-logic) and not on the first (erkenntnis-psychology). Perhaps they were careful, as von Wright wrote on the discussion between Ch. Bühler and Kaila, and did “not feel competent” (Kaila 1979, p. xix) on issues outside of philosophy, namely natural philosophy and especially erkenntnis-psychology. This view might even apply internationally to the majority of the successors of the Vienna Circle including Karl Popper (see Hempel 1979 or ter Hark 2004). Here, I will instead adhere—in line with Mach and Kaila—to the view that the logical and the psychological are strongly genetically intertwined in concept formation (see Siemsen 2010d for a detailed elaboration, especially of the mathematical aspects). Thus, any erkenntnis-theory, especially one which includes pre-scientific concept formation, needs a (genetic) analysis in how far concepts are logically constructed and in how far they are genetically adapted (see also the footnote on Finnish concept of “rakentaa” later in this article). This view is all the more important in the learning of new concepts, i.e. in science education (see also Wittenberg 1957, p. 254). In the following, only Kaila’s natural philosophical erkenntnis-theory will be considered, as Kaila the philosopher-logician is already well researched (for instance Niiniluoto 1992).
Logical Positivism is now considered “one of the central strands in the fabric of twentieth-century thought” (Friedman 1999, p. xi).
Mach proposed a “neutral monism”, i.e. the idea that everything is ultimately “one”, but that neither the physical approach to this “one” (followed by materialists), nor the psychical approach (panpsychism) can by themselves sufficiently describe the “world” and our “selves”. “For most natural scientists and many philosophers, who do not admit it, the thought that all psychical could be deducible to the material in private is very congenial. Even if this materialism has a catch, it is not the worst possibility; it stands at least with one foot on secure ground. But if all psychical should be understandable physically, why not the other way round? […] Is the other [psychical] foot standing in the air? I would prefer […] to stand on both feet. There is no necessity to become dualist thereby for the one, who considers both feet as equal and both floor spaces under the soles to belong not to two different worlds” (Mach 1920, p. 434).
If one analyses the basic concepts, such as monism, natural philosophy, gestalt psychology and perception (sensual elements) of Kaila’s (and in the following Kurki-Suonio’s, see Kurki-Suonio 2010) ideas which he followed throughout his life, they are specific for a Machian approach (see Appendix 1). Also the meanings Kaila attaches to these concepts are similar to Mach. For instance, Kaila’s criticism of the monism of Ostwald and Haeckel (see von Wright in Kaila 1979) is nearly the same as Mach’s (see Hoffmann and Laitko 1991).
These differences can be found especially in his late works, when Kaila started developing his concept of “invariances” on which he wanted to found physics. Kaila (1941/1979, p. 150/151) used the term synthetically for “any kind of similarity, sameness, uniformity, lawfulness, constancy, analogy or structural identity (isomorphism)” (One might compare this erkenntnis-theoretically with KKS’s starting point in perception of entities, phenomena and properties etc.). In the concept of “invariance”, Kaila saw “essences” similar to Plato’s ideal ideas (1941/1979, p. 200). Kaila developed this concept explicitly in criticism to Mach, as enhancement of Mach’s concept of the “economy of thought” (Kaila 1941/1979, pp. 149). Kaila’s criticism of Mach’s interpretation of “economy” as a minimum (parsimony) principle was based on Mach’s early works on this topic. As Cohen (1968) already noted, Mach developed this in later works into an optimization principle, which Kaila was seemingly not aware of (the same problem and misinterpretation can also be found in Rolf Nevanlinna). Kaila was obviously not content with this solution, as he kept working on this concept until the end of his life (especially with his recalcitrant concept of “Terminalkausalität”). Again, Mach’s ideas were the yardstick, Kaila continuously measured and questioned his own ideas against. Mach might have objected to Kaila’s “invariances” that the way Kaila had defined them, the synthesis would include empirical meanings as well as logical categorizations. According to Mach (1905, p. 276), “singe elements are not invariable. If they appear to be invariable, like the colour at unaltered illumination, the weight at unchanged position relative to the earth, etc., it is only because of the coincidental constancy of other elements connected with them.” Therefore, the concept would partly be a metaphysical abstraction from the empirical conditions by observation in which the attention is concentrated on some elements. If the abstraction—once chosen—is empirically necessitated by the facts or not one cannot be aware of completely (see Bradley 1975; Siemsen and Siemsen 2009 and Siemsen 2010f). That Mach did not oppose such ideas a priori, one can see in his support of Vaihinger’s (1911) “As-If”, of which Kaila’s concepts could be seen as an example (see Thiele 1978).
One important difference of Kaila to Snellman for instance is the abandonment of Hegel’s philosophical method of conscious introspection (introduced in his “Phenomenologie des Geistes”) in favour of gestalts and behavioural measurement of non-conscious psychological phenomena. This can be seen as a further step in abandoning any idea of absolute knowledge. The continuity to Snellman already becomes obvious in the title: Snellman and Kaila consider mainly the psychology regarding people in general and their psychological development, not primarily the extreme (abnormal) cases mainly dealt with in clinical psychology and psychiatry. This is a difference to the main focus of psychology nowadays in Finland and internationally (the problem of this methodological “bias” on psychological theory development was already under discussion among the empirical psychologists, such as Binet; see Siemsen 2010b). Nevertheless, for science education, a general perspective of psychology is of course much more applicable than one based on extreme cases.
Kaila (1956, p. 3) in the preface to his final unfinished work states that from a “modern purely analytic philosophy” perspective, the (Machian) Erkenntnistheorie he is using will not appear as part of philosophy. But it is also not natural science in the sense that it is restricted to any single science. He therefore introduces the term “natural philosophy” for approaching this erkenntnis-theoretical “problem of universal consequence”.
Kaila went to Vienna for researching with Charlotte Bühler in 1932 and 1934. He knew experimental psychology already from his dissertation in Finland (Kaila 1916), but the visits in Vienna were central for developing his syntheses of erkenntnis-theory, the Nevanlinna/Kaila synthesis as well as the synthesis of Snellman and gestalt psychology. This he published in his (in Scandinavia) widely read book on personality (“Persoonallisuus”) in 1934 and several subsequent books. Kaila’s psychological synthesis is very important for the subsequent implementation of the erkenntnis-theoretical ideas in science education (see Kurki-Suonio 2010).
Physicalism is the idea that physics (and its concepts) can be used as a (supposedly) empirically secure axiomatic basis for constructing all sciences.
Kaila used to be a dramaturge and theatre critique in his youth. Again, like with the intuitive “theory” of Cygnaeus, these theatrical elements find no direct theoretical reflection in Kaila’s writings. They had a reportedly strong influence on his contemporaries who visited his lectures, but nowadays are scientifically “lost” for the next generation. It would be interesting to recover this by interviewing the still living former attendants to Kaila’s lectures.
In how far Kaila was actually teaching haptically/enactively does not become clear from the retrospective descriptions up to now.
The verb “hahmottaa” corresponds to “perceive” in the meaning of “creating gestalts” and “hahmotus” is a noun for the perception process. Conceptually therefore it is not surprising that Kaila adapted Mach’s concept of “sense elements” into his concept of “perception”. For Mach, perceptions are the conscious result of the sensual elements (i.e. the psychological end of the psychophysical relation).
From a gestalt perspective, Kaila’s concepts of “invariances” and “Terminalkausalität” are thus a result of the gestalt learning process, not a precondition. The question of gestalt and teleology was also at the center of his discussion with Charlotte Bühler (see below). Because of the unfinished condition of his final work, the final meaning given by Kaila to this idea has to remain open for speculation. This has led to conceptual differences between Kaila’s successors, which have interpreted this for instance as “unus mundi” (Laurikainen), “unifying dualism” (Kurki-Suonio) or “truth” (U. Mäki).
Kaila’s development into this direction can be found in his discussion with Charlotte Bühler over his empirical findings (see Kaila 1934, 1935 and Ch. Bühler 1934, 1935). Kaila wanted to show experimentally that there is no “instinctive” imitation in the sense that imitations do not need instincts as a basis, but are purely social in nature. For this he asked caretakers at a suckling orphanage to approach the sucklings with their faces turned half-away so that only the side of their face would be visible to the suckling. The sucklings reacted with frowning, silence; they became seemingly “paralyzed”. Kaila’s initial interpretation was that the symmetrical eye area is “responsible” for facial recognition and the resulting salutatory reaction. For Bühler, Kaila’s arguments were based on arbitrary conventions (Willkür) of what is part and what is whole (gestalt). The sucklings’ reactions show some kind of recognition (in the description of Kaila they have a “strangeness reaction”, i.e. Fremdheitswirkung, which he interprets as non-recognition). This reaction for Bühler pre-requires some kind of formal recognition. For her it is a kind of hen-or-egg question.
In the usage of Ch. Bühler and Kaila at the time, instincts are assumed to be inherited. In current mainstream physiology, the concept of instincts and even reflexes have inherited and acquired properties (plasticity). In this respect, the Kaila-Bühler discussion anticipates modern developments.
It seems that the discussion with Kaila (with his background on Snellman) also had an important influence on Charlotte Bühler’s ideas, especially regarding the individuality of children’s development, which was the hallmark of her later research on humanistic psychology.
After his first research in 1932, Kaila in a second visit to the Bühler Institute in Vienna in 1934 tried to narrow the research question to what he thought to be the central difference between him and Ch. Bühler. “The following experimentum crucis will decide if Charlotte Bühler is right or me” (Kaila 1935). Kaila performed the experiment, but as Bühler’s (1935) reply shows, it did not resolve the discussion. Why? Because Kaila and Ch. Bühler were initially using a different conceptual (and epistemic) basis and this difference remained. Nevertheless—and here the scientific greatness of both of them show—they both learnt from the other and enculturated some of the other’s conceptual idea, not completely, but up to a certain degree (which required a substantial adaptation of their mutual concepts). Thereby, both were developing their own synthesis. These syntheses were different from the existing psychological paradigm and brought both (and their successors) to develop independent and fruitful ideas. From their discussion, it becomes nevertheless clear that both were at the time (and probably also later) not entirely conscious of this development.
Concerning “conventions”, the terminology of Mach and Poincaré is used here. Initially, these were implicit or explicit hypotheses, which became part of a cultural frame with time. One can also call this the “as-if”, as Vaihinger (1911; 1924) has done. This does not only concern basic concepts (i.e. basic in the sensual-genetic meaning), but also highly constructed scientific concepts. For instance, as Mach has shown, Newton’s assumption of absolute space is partly explicit, but also partly based on not-empirical unconscious intuitions (see Mach 1893; 1960, Einstein 1916 and Siemsen 2010d).
As this transmission is intuitive, we are by-and-large not aware of the “conventions” and even of the fact, which parts of our knowledge is in this sense conventional and which is empirical.
Enculturation is here used in the sense of cultural hybridity (as Jerome Bruner has developed, see Cole 2000), i.e. making a synthesis of ideas from different cultural origin.
Kurki-Suonio: “I know of no person, who proceeds logically.”
The general question to be asked here is what does one take as the “goal” of education (see also Wittenberg 1965): To make everybody an “ideal” logicist, or to lay the ground for a general method of thinking? Is logic a means or an end of education, i.e. is it a teleological (final) goal or only a local goal? Different philosophies have different answers to this question, but Kaila’s “natural philosophy” has a clear (Machian) evolutionary emphasis on avoiding logic as a general or total teleology. Kaila’s emphasis was followed mainly by his successors in Laurikainen and Kurki-Suonio. It thereby became a fundamental principle of Finnish science education. This article argues that it is specifically this emphasis, which makes this form of science education “successful”, relative to other views.
Only the first volume of what Kaila called “Terminalkausalität” was published. It deals with the physical part, while the next volume was supposed to deal with the biological questions and the final one with the philosophical and psychological questions of the psychophysical relation (see von Wright 1995).
Wittenberg (1968) provocatively asked in an article, if specialization was a “service or betrayal” of science. Conant (1951) asked a similar question in his General Education program: when is specialization helpful and when detrimental in science and especially in science education. Though the Vienna Circle member Phillip Frank (1951) held the opinion that specialism had “defeated itself”, the erkenntnis-theory of the General Education program seemingly did not yet provide a consistent answer to this question (see also Holton 2004 or Siemsen 2010f).
This synthesis lies in the answer to Mach’s (gestalt) question, why and when geometrically similar forms are also optically similar. From an evolutionary perspective, optical similarity is genetically earlier, while geometry—because of the practical requirements of for instance the craftsman building a house—introduces perspectivistic, numerical and logical elements to it (see Mach 1905, Clifford and Russell in Clifford 1885/1955). Geometry is the result of an adaptation of thoughts about different experiences to each other. Geometry is not a necessity of the empirical facts of these (for instance optical) experiences. It is in this sense metaphysical.
The Vienna Circle was a group of philosophers and logicians in Vienna known for their “Logical Positivism”. In their initial formation, the group had been heavily influenced by Mach’s ideas (for details, see for instance Stadler 1997). Kaila (1941, p. 154) describes “The positivist and phenomenalist tradition of Ernst Mach was still alive in many ways in [the ‘Vienna Circle’ (Wittgenstein, Carnap, Schlick, and others)], and it may have looked as though the novelty of the theory of science in question consisted merely in a shift of Mach’s psychologising positivism in a more ‘logicizing’ direction, brought about by complementing it with symbolic logic (Logistik), which meanwhile had matured, and with the anti-psychologistic attitude that derived from Frege.” It should be noted that Mach in his erkenntnis-theory was neither a positivist as his concept of empiry had shifted fundamentally (see Siemsen 2010f), nor a phenomenalist in the sense of Husserl after Husserl had also “converted” to Frege’s logicism (see Thiele 1978). Mach’s erkenntnis-theory could be much better described by Kaila’s gestaltist perceptionalism.
For details on the debate, see for instance DePauli-Schimanovich et al. (1995). Unfortunately, the idea of intuitionism is mostly reduced to the interpretation of L. E. J. Brouwer, which differs substantially from the interpretations from Paris (Poincaré, Hadamard) or from Zurich (Weyl, Bernays, Polya, Wittenberg). As Wittenberg (1957) observes, Brouwer does not really have an erkenntnis-theoretical foundation of his theory (he initially had an erkenntnis-theoretical first chapter of his dissertation for which he read Mach’s Knowledge and Error, but this was scrapped by his supervisor). Nevanlinna in his synthesis was more influenced by the views from Paris and Zurich through his visits there. As a result, the concept of “intuition” becomes more a question of (Machian) historical-genetic concept formation in mathematics in Nevanlinna’s (and Kaila’s) later works.
Through the Vienna Circle and his students, Carnap’s position at that time (see Stadler 1997 and Friedman 1999) became foundational for the philosophical thinking in the US, especially the constructivist view. The whole of the Vienna Circle came to be equated with this view. Carnap’s own shift back to Machian foundational concepts described in the following has been largely overlooked, also by recent philosophy of science scholars (see Friedman 1999).
Feigl (1969, p. 635) gives a slightly more detailed view. “Carnap sketched in considerable detail how the concepts of empirical knowledge could be defined on the basis of concepts pertaining to immediate experience. This seemed indeed the fulfilment of the original intentions of Mach’s positivism, as well as a brilliant application of the tools of modern logic to some of the perennial issues of epistemology. […] In this regard, we favored the different attitude already adumbrated by Leibniz and developed much more fully by Frege and Russell. The truths of pure mathematics (i.e., not including physical geometry or other branches of the factual sciences) are a priori […] precisely because they are analytic, i.e. because they are validated on the basis of the very meaning of the concepts involved in the propositions of mathematics. Empirical certification of mathematical truths is neither required, nor indeed possible. […] Our concern was not with the psychological origins or the social conditions of the cognitive enterprise. Our distinction was based on differences in the method of validation. […] We always admitted that all sorts of intuitive processes […], may well be extremely instrumental (heuristically) in the genesis of hypotheses and theories. […] Bridgman […] is very close to one aspect of Carnap’s and Wittgenstein’s views. "Don’t ask me for the ‘meaning’ of a concept, ask me about the rules according to which the concept is used. "” But as Nevanlinna argues (see later), meanings are important for the rules of usage. If foundational empirical meanings change (such as the meaning of what is empirical) all rules might change as a result.
Mach had already noted 1890 that this question becomes especially important in science education. The step from phenomena to axioms looks seemingly small for a scientist, but opens a yawning chasm for many students. The article is published in the first journal for physics and chemistry education, which Mach had helped founding. In it, Mach (1890, p. 4) observes, ““[…] This view seems to be shared little in the circles of teachers, and even those, who agree with them theoretically, in practice abdicate from them again and again, which manifests itself in the overestimation of the logical and a disregard of the psychological moment in education. [In education,] criticism cannot begin where empirical meanings [konkrete Vorstellungen] are still lacking.”
The question was part of the critique of Feyerabend and Quine on Logical Positivism, but it is for instance not at all mentioned in recent re-evaluations of positivism, such as Michael Friedman’s (1999) book. As an example of the permanence of Carnap’s Fregeian idea assuming for mathematics an “independence from the contingencies of the real world” (Carnap 1961 in the second edition of his Aufbau, quoted in Friedman 1999, p. 9), Friedman uses the term of “undigested immediate sensory data” for describing the difference between the view of Mach and the logical positivists. Interestingly, from a Machian perspective, “undigested immediate sensory data” is a contradiction within itself and therefore cannot describe anything. Kaila’s research with Charlotte Bühler showed this quite clearly from an empirical perspective. In Kurki-Suonio’s description of learning, perceptions and interpretations are “intricately linked”. If there has been so much “digestion” going on during childhood, adapting thoughts to logical concepts, how can a logician assume to sense anything immediate, which is undigested?
The initial version of this article was held as a presentation at the Summer University of the Science Teaching Group at Helsinki University 2008. In the same session, lectures were held by Kurki-Suonio and Matthews with an ensuing panel discussion between the three of us. Several aspects of this discussion are central to understanding the specific ideas of science education in Finland. The views of Matthews on constructivism in education have been well published in Science & Education.
Weyl (1928, p. 44) gives an interesting interpretation of this problem regarding the intuitionist critique from Brouwer on formalism. “And with pain the mathematician sees the larger part of his tower, formed of stabile ashlar as he thought, dissolve into mist.” According to Weyl’s comment, mathematics based on ideal entities, construction, etc. has the same relation to the erkenntnis-theoretical questions elaborated in this article as Newtonian physics has to quantum physics and relativity theory: it seems to work as long as the approximations are used for questions far away from the more anthropomorphic “everyday experience”, i.e. the “very small” in the case of quantum mechanics and the “very large” in the case of relativity theory, do not seem to have a larger impact on this standard experience. But the theory also limits experience to what was once historically defined as standard everyday experience. In the case of science education and mathematics education, this impact—through much stronger genetic effects relative to teleological logic—certainly has to be considered much stronger than for the standard experience of a trained mathematician as a result of Darwin’s findings.
For the long-term influence of this idea on science education, see for instance Warren (1980) exemplarily on physics education in the UK.
It is interesting to note here that the Finnish words for building/constructing “rakentaa”, building”rakennus” and structure “rakenne” do not exactly correspond to the English meaning implied in “constructing”. It does not require an “architect” of construction. It can also be “structured” without. For instance it can signify developmental processes in nature, i.e. the structure and growth of plants. The empirical meaning of “rakentaa” is therefore closer to a genetic understanding of the scientific knowledge process. The criticism of Michael Matthews on constructivism in education (Matthews 1994, 1995) may thus not culturally fit the Finnish concept of “rakentaa”. The question, if the construction analogy is an adequate concept to describe the learning process of children shall be left to future research and not be further considered here.
For the mathematical description of the concept of manifolds, see next part on Nevanlinna.
This happens for instance, if one does not accept the assumption of the “excluded third” in mathematics, or if as described by Wertheimer (1912/1925), one assumes a genetic definition of the concept of numbers instead of a logicistic one. Because of exponential effects of genesis, such changes are important for science, but for science education the implications can be dramatic (most students not understanding versus most students understanding).
The problem here is introduced by Carnap’s initial “framing” of colour as “data”. Colours are processes and products of gestalts, which are partly cultural (see for instance Segall et al. 1966). They are classificatory conventions. “Red can therefore be regarded as the terminal link of a chain of interrelated circumstances. The appearance of red presupposes as a rule, but not always nor necessarily, the existence of the whole chain” (Mach 1916/1926, p. 1). The classification of red as physical and physiological also depends according to Mach only on “convenience and uniformity”. The question, which “part” is cultural and which part is not can only be analyzed genetically. But then, as cultural anthropology has long found out (see Boas 1911/1938 or Stocking 1968/1982), such reductionist approaches might not make much sense for cultural gestalts (the cultural gestalts of the observer can “cut” through the cultural gestalts of the observed culture, making them unintelligible). Carnap here unknowingly follows in Kaila’s empirical footsteps (the discussion with Ch. Bühler).
James took his method from Mach (see Siemsen 2010d; Mach’s view is therefore also very close to pragmatism as the members of the Vienna Circle intuitively noticed when they emigrated to the USA). Mach (1905, pp. 281/282) states on the question of the inherent a priori “however, it became clear that the physiological space and the physiological time without the help of physiological experience can neither found a scientific geometry, nor a scientific mathematics. The question “How is pure mathematics (a priori) possible?” certainly engrained one of the most important seeds for research. It would though have been even more important, if it would not have contained the presupposition that the knowledge of mathematics is gained a priori. Because not philosophical decrees, but only the positive psycho-physiological research can find out, what is inherited. [… The philosopher Beneke states] "The [internally given] does indeed contain, as it were, knowledge of what is given within us prior to all experience. Yet attempts at defining this relation more closely have hitherto failed in that they presuppose the forms prominent in the fully educated soul as already prior to experience, or more specifically, as given for the development of the soul. This is wrong: The forms, which are at first given for knowledge, result from the development of the soul. They are only prior determined before by inherited dispositions and relations, which carry completely different forms in themselves."“Unfortunately, Beneke’s view was despised in Prussian Germany. Hegel had driven away the more liberally thinking Kantian philosopher Beneke from Berlin to teach in Goettingen.
Mach describes this as “adapting the thoughts to each other” in contrast to “adapting the thoughts to the (sensual) facts”. See also Kurki-Suonio (2010).
For instance, the question of the role of phenomena and what they are epistemologically is strongly related to how this synthesis is formed (see for instance Krafft 1965). The centrality of this question for science education was highlighted already by Wagenschein (1983) when he asked to “save the phenomena” in science education. What does it mean when the phenomena are in such a “bad state” in science education that they need “saving”, while at the same time they are so central and basic as for Kurki-Suonio or Wagenschein? Mach (1905, p. 172) gives an example in the form of a problem (no. 49) in the “Thaumaturgus mathematicus” (Coloniae 1651). A bridge is built around the earth from which then all pillars are removed simultaneously. What happens? Depending on people’s training in natural science, the answers provided can be quite different. The question for science education is: how would one grade a student according to this question? In how far do exam questions contain this type of problem?
Space and Geometry was the title under which Mach’s late articles on the origin of mathematics (see below) were published in one volume in 1906. In it Mach (1905, p. 340) for instance mentions that the tactile space of the skin is not Euclidean, but a two-dimensional Riemannian space, which gains its third dimension through a conceptual enlargement by the haptic/enactive space of the hand and limbs.
This can already be seen from the Doppler-Petzval debate described in the beginning.
Mach fundamentally changed his world view again (for at least the second time, see Appendix 2), when late in his life he came back to his forty year old question. As a result, he published several articles in The Monist around 1900 (which were republished as the last chapters of his Knowledge and Error, 1905). The articles seem to have been partly a response to an article from Poincaré in The Monist in 1898 on the same question. This shift in his world view led Mach to successively adapt many passages in new editions of his books (he first adapted the basic concepts and later the resulting changes in higher-level concepts, which in turn led to some adaptations in the basic concepts). This is a mostly unknown fact that unfortunately led to confusions in many later interpretations of his ideas, for instance by Kaila, who was seemingly not aware of these changes which one can see in his criticism of Mach’s concept of the “economy of thought” (repeated nearly exactly by Nevanlinna). On the general level, Mach himself was aware of this genetic problem of continuing conceptual change for the development of his own thoughts, though he has not been very explicit and consciously aware about the specific changes in his texts (see for instance Mach in Appendix 2). The latter poses a larger problem in Machian research, especially when combined with the limitations of the perspective (i.e. physics, philosophy, etc.) most researchers tend to have.
It is interesting to note here that Kaila in his 1928 articles does not develop his arguments from the psychological perspective, but from a mathematical, respective an erkenntnis-theoretical one. His synthesis with his psychological views seems to have been added slightly later for his criticism of Carnap.
For instance, every 4 years the International Congress of Mathematicians awards a Rolf Nevanlinna Prize for outstanding contributions in mathematical aspects of information sciences.
Nevanlinna’s father was also a cousin of Lindelöf.
Landau was successor of Hermann Minkowski (who had supplied the mathematics, which Einstein used for his Relativity Theory). Among Landau’s doctoral students were Max Born, who brought Pauli to Göttingen as his assistant for a year in 1922, Harald Bohr, the mathematician and brother of Nils Bohr, as well as Paul Bernays, who was assistant of Hilbert and later moved to Zurich.
The similarity of the views from Hadamard to Nevanlinna and his successors can be seen in Hadamard (1945) or Kurki-Suonio’s views on Hadamard in this edition.
This was the time of Kaila’s epistemological shift from logicism to erkenntnis-psychology, especially regarding the foundations of mathematics.
Pauli was the godchild of Mach and thereby—like Kaila—had been influenced by Mach’s ideas early in his life (see Laurikainen 1989, p. 4 and 14 or Smutny 1990). He became famous when he—at the age of 19—wrote a 237 pages introduction to Einstein’s ideas, which still is regarded as a standard reference on the subject. He worked with Born, Bohr and Heisenberg on quantum physics, developing such important concepts like “spin” or the “neutrino”. His focus was the epistemic implications of the “new physics” (quantum mechanics and relativity theory). The new physics was derived from Mach’s question about the generality concerning the intuitive assumptions of the Descartian/Newtonian world view. Now the new physics in turn required a new world view for its consistency. The implications of Mach’s question had to be rethought anew.
Weyl seemingly admired Nevanlinna’s mathematics, but criticized his political closeness to German National Socialism (see for instance http://www.history.mcs.st-andrews.ac.uk/Biographies/Nevanlinna.html or Hayman 1982). Nevanlinna was for instance the chairman of the Committee for the Finnish Volunteer Battalion of the Waffen-SS.
In two presentations by Nevanlinna held 1932 in the context of a German-Finnish exchange of researchers in Marburg, he already elaborates the main elements of his intuitionism-formalism synthesis mentioned above. As an example he uses the first sentences of Hilbert’s introduction to his new geometry and shows that this formal view does not actually abstract from the perceptional meanings of basic concepts. It only conceptionally generalizes them. The same example is then used for the same purpose by Hadamard (1945).
According to Hayman (1982, p. 422), Hilbert commented after one of Nevanlinna’s lectures: “You have opened a hole in the wall of mathematics; soon other researchers will come and close it.” Regarding the epistemology of mathematics, what Hilbert perceived as a hole is actually a glimpse on the fundament. Therefore, it cannot possibly be “closed”, only hidden and gilded. What Gödel showed for the “roof” of the mathematical construction, Nevanlinna showed for its foundations; only that much fewer people noticed as he would not write this in mathematical language, which he exactly did not want to presuppose. Nevanlinna just did what the formalists had done themselves, albeit in a more limited area: acquire a more general point of view which granted consistency and a higher freedom for thought. The formalists had done this within mathematics, while Nevanlinna combined a mathematical and a physical view into a single world view without compromising the strengths of each.
Nevanlinna’s view in consensus with Kaila’s view on concepts in mathematics and in physics is the same (monistic) and very similar to Mach’s on the relation between images and concepts. Mach (1900) writes: “The concept is enigmatic for the reason that on the one hand it appears in a logical aspect as the most definite of psychical constructs; while on the other hand, in a psychological aspect, when we seek for its real visualisable contents, we discover a very hazy picture only. Now the latter, whatever its composition, must necessarily be an individual picture. The concept, however, is not a finished image, but a body of directions for testing some actually existing image with respect to certain properties, or of constructing some image from given properties. The definition of the concept, or the name of the concept, disengages a definite activity, a definite reaction which has a definite result. […] Just as a technical operation may serve for testing a given object […], or for constructing a new object […], so also a concept may be used in a testing or constructive sense. The concepts in mathematics are mostly of this character, whereas the concepts of physics which cannot create its objects, but finds them already present in nature, are ordinarily of the first-mentioned kind. But even in mathematics, figures arise independently of the inquirer, furnishing material for subsequent investigation; and in physics also concepts are constructed for economical reasons. But the fact that mathematics operates in the main with constructions of its own creation, containing only that which it itself has put into them, whilst physics must wait before it finds out how far the objects of nature answer to its concepts—this fact is the foundation of the logical superiority of mathematics.”
Basically the same criticism can be found in Mach (1905).
For education, this tends to be doubly detrimental: by early abstraction as well as early specialization. Through the schools, such an approach is leading to the rejection of science and mathematics in a majority of people (outside of Finland).
As Wittenberg was student and research assistant in mathematics in Zurich at the time when Nevanlinna was teaching there, it is rather likely that Wittenberg knew the ideas of Nevanlinna, although he does not give a reference to him. Wittenberg instead quotes especially Polya, Pauli, Weyl and Hopf (all of whom are known to have had a close relation to Nevanlinna), as well as his doctoral advisors Bernays and Ferdinand Gonseth. Gonseth has a close affiliation to Piaget’s thoughts, which is interesting to note as the direct links between Kaila/Nevanlinna and Piaget seem to be strangely scarce for the fact that their research interests are closely linked. The similarity between Wittenberg’s and Nevanlinna’s ideas regarding the Erkenntnistheorie of mathematics and mathematics education, especially regarding fundamental concept formation shall not be further elaborated here. The details can be found in his dissertation “On Thinking in Concepts” (1957), especially regarding his use and criticism of Hilbert’s view, his view on the fundamental erkenntnis-theoretical and psychological duality of concepts as well as the closeness of several of his examples to Machian examples. No one of the other prominent mathematicians and physicists in Zurich at the times has stated a similar erkenntnis-theoretical view. The main difference seems to be the psychology. Wittenberg at the time states that he did not have the scope in his dissertation to work on this question, though he devoted several sections of his thesis to stating the importance of psychology (and of the genetic approach). But he certainly worked on this question later (Wittenberg 1963, 1965).
According to von Wright, natural philosophy or “Naturphilosophie” became very prominent in Kaila’s late view of his own work, exemplified in the subtitle “Eine naturphilosophische Untersuchung” (for his final unfinished work on the “Terminalkausalität”).
Both use the concept of gestalt in their writings and are cofounders of the Society of Natural Philosophy in Finland.
His last book “Science has its Limits” from 1997, Laurikainen dedicates “To my great guides in natural philosophy: Eino Kaila, Rolf Nevanlinna and Wolfgang Pauli”.
KVL also initially heard lectures of Lindelöf and Myrberg.
According to Kurki-Suonio, Laurikainen also referred to Kaila in his lectures and seminars. In his book “The Message of the Atom”, Laurikainen quotes three references from Kaila: “Über den physikalischen Realitätsbegriff”, Kaila’s criticism on Carnap’s physicalism, “Zur Metatheorie der Quantenmechanik” (1950), one of Kailas late works on quantum mechanics and “Syvähenkinen elämä” (1943, The Depths of Spiritual Life. Discussions on the Ultimate Questions), a late religious essay from Kaila.
This was also an important issue for Pauli: when he postulated the Neutrino, he thought that he had betrayed Mach’s ideas because it was—at the time—a particle for which no experimental evidence was possible. But Mach actually held a much more differentiated view on these questions than many have interpreted from him (see also Wilczek 2002 and 2004). He mainly urged to be very careful with such postulations as they might entail unintended properties showing only much later when it would be very difficult to change the intuitions shaped by the initially introduced concept.
Laurikainen’s account of his initiatory experience is rather short (see also Appendix 2). “In the summer of 1938 I experienced at once very strongly the miracle of the intuitive vision. The figures of mathematics began to live and to link up in new way” (Laurikainen 1982, p. 11). Since then he began a closer relation with Rolf Nevanlinna—who was greatly respected by KVL during his life. KVL chose Nevanlinna’s special field, topology of surfaces and began with him to develop mathematical physics as a research topic in Finland.
See Laurikainen et al. (1994). The concept of the unconscious in science and in learning is a central question as I will briefly describe at the end of the article.
William James in his late works questioned his own idea of a “stream of consciousness” and concluded that according to psychological facts, consciousness does not exist and should be “universally discarded” as a concept in psychology (James 1904). This area is still neglected in current cognitive psychology (see Hassin et al. 2005 and Siemsen 2010d for a detailed account of this question).
According to KKS, this focus was probably also due to the personal health condition at a specific moment in KVL’s life.
According to KKS (stated in several interviews), KVL might have been unconsciously looking for such a solution because of a religious “initiation” after severe health problems. KVL in later discussions with KKS did not acknowledge this “turn from agnosticism”.
Laurikainen even wanted to found a chair on natural philosophy, a goal which was prevented by the strong opposition of an alliance between physicists and the philosophers. There are probably more late influences of the Nevanlinna and Kaila synthesis to be found in this society. For instance, the dissertation of the current chairman Viljo K. Martikainen, on “Science in Technology”, also centrally follows the question of “Concepts and Mind”, a topic which has obvious relations to the question of the physikos and the mathematikos and the Mach/Nevanlinna/Kaila solution.
Kurki-Suonio was later told that Rolf Nevanlinna helped in 1960 to convince KVL to accept KKS’ application for a scholarship at NORDITA, the Nordic Institute of Theoretical Atomic Physics, which had just been founded in close connection with the Nils Bohr Institute. Kurki-Suonio is not anymore aware of a closer personal relationship between himself and Rolf Nevanlinna (who was at the time mostly in Zurich), except maybe through his brother Fritjof and several lectures, especially at the annual congresses of the mathematics and physics teachers. He nevertheless acknowledges a strong impression and a certain closeness of their ideas (detailed in his article in this issue).
Kurki-Suonio had already been Laurikainen’s assistant for a course of mathematical methods of physics in the late 1950s.
Laurikainen also uses the concept of gestalt in his works (for instance Laurikainen 1997, p. 23) and in his lectures.
This has been partly done by Heimo Saarikko, who has been teaching the historical part of KKS’ courses based on the book from Simonyi (1995). It would be interesting to consistently add a philosophy and psychology of science (respective psychological anthropology) perspective to it. In this respect it is perhaps unfortunate that Kaila had never developed his ideas on the history in greater detail in the tradition of a historical-genetic approach. But this again would mean to be prepared “to go deep into the details sparing no pains” (Kaila quoted by Ketonen 1992, p. 68).
From this erkenntnis-theoretical perspective, the “logos” in “psychology” seems can be intuitively misleading if translated as “logic”. The initial Greek term of “logos” had different meanings, for instance “word, thought, grounds for belief or action” from which logic is a rather specific derivative.
This is one of the favourite passages by Kurki-Suonio from Mach. The “force” can be seen as a metaphor for empiry.
Huxley in his American addresses (1877, p. 3) argues like Mach for a pragmatic and as a result probabilistic concept of knowledge (concerning causality, laws, etc.) “We must recollect that any human belief, however, broad its basis, however, defensible it may seem, is, after all, only a probable belief, and that our wildest and safest generalizations are simply statements of the highest degree of probability.” This applies all the more to statistical results. Statistical results might be less “biased” in the sense of the use of heuristic “shortcuts” (Gigerenzer 2007), i.e. the “common sense” heuristics even statisticians tend to use in daily life. But statistics lacks the “common sense” human lifetime experience (in the sense of Clifford 1885/1955, where what is common sense depends on the area of application). Statistics can only show correlations relative to the initial categorization (Pearson 1911). Thus, what is “A” and “B” in a statistical relation is not given, but ideally abstracted. Similarly, what are considered “dependent” and “independent” variables depends on the relation between the observer and the “system” (i.e. the “common sense” experience of the observer). In this sense, connecting Finnish science education with the PISA study is a consequence of the “force of empiry” (which one can also choose to ignore because one finds other facts more compulsory or regard as due to “mistakes” within the design of the study), not a logical consequence.
Helsinki University tends to exert a strong influence on other universities in Finland, as it has for a long time been the only university, while the others tend to be relatively newly founded. Also, Kurki-Suonio was for a long time the only professor of didactical physics in Finland. If one wanted to implement ideas on the didactics of physics in Finland, his was basically the only local reference. According to members of the Finnish board of education, the influences of his ideas can now be found in all science curricula in Finland.
The experiments were different though as they were conducted at a German university in mathematics education with haptic Machian teaching.
The idea is not new in principle, but is also the erkenntnis-theoretical basis for the idea of history and philosophy of science. The consistent experimental implementation has up to now unfortunately been rare though and often not measured adequately. Inconsistent (part) implementations cannot be considered to have the same type of effect.
Freudenthal’s epistemology is phenomenological (for instance based on daily experiences), while Mach’s is genetic (for instance considering the effect of the evolution of different senses over time on concept formation). The phenomenological PISA scale therefore is still not consistently evolutionary and does not capture all of the genetic effects. A genetic scale would for instance include more transformative questions.
Kurki-Suonio recognizes the unique similarity of the genetic-adaptive approach from KH Siemsen with his perceptional approach, though at the time there was certainly no contact between them (see Kurki-Suonio 2010).
In both cases, the actual effect from the laboratory experiment is probably more pronounced as could be expected.
As further empirical evidence still to be historically evaluated, there had been schools founded—at least partly—on teaching in a Machian way, for instance Laemmel (1910) in Zurich or Schwarzwald (2005) in Vienna. Both schools had a focus on science education, the integration of arts and sciences, personality education and a reformed history education focussing on cultural and science history (similar to Sarton’s idea implemented in the USA by Conant’s General Education program, see Siemsen 2010f). One subject area in the Schwarzwald school was for example “free hand drawing and geometrical perception” instead of the usual subject categorization of hand drawing as part of arts education and geometry as part of mathematics education. The schools were initially focussed on female secondary education at the times when the universities were being opened for female students. Regarding empirical results, Laemmel for instance claimed that all his students passed the university entry exams (indicating a “right shift” of the average) while the Schwarzwald school acquired a reputation for bringing worker’s girls to university education (indicating a reduced influence of parents’ background). The success of these schools regarding female tertiary education can certainly be regarded empirical as well. University exams as well as primary education at the times can certainly be considered to have been biased against women if possible (see also Siemsen and Siemsen 2009).
According to OECD data (2006, p. 30), the Finnish educational expenditure is average (rank 12 of 30 OECD countries at purchasing power parity basis), while the country with the highest educational expenditure per student, Denmark, scores only average in the PISA study. The ranks in educational expenditure per student (rank 12, OECD 2006, p. 30), the expenditure on educational institutions (rank 14; p. 32) or teacher salaries (rank 14; p. 56) are even lower and sometimes even below OECD average in absolute terms. Similarly misleading interpretations focus on the low Finnish score in student motivation in the latest PISA study (OECD 2009). This is a question of Finnish culture. Given a questionnaire with motivational scales, no modestly thinking Finn would rank him- or herself too high (like for instance Chinese, they try to avoid voicing extreme opinions in public). Interestingly, the countries with the highest motivational scores, for instance Azerbaijan or Mexico, were all very low-scoring for mathematics and natural sciences in PISA. Bruner (2004) suggested from his experiments with rats that the relation between motivation and intellectual performance has a bell-curved shape according to the Yerkes-Dodson law and might mainly be dependent of framing (how one is motivated). The cultural plasticity tested was obviously much higher than any actual motivational differences. Unfortunately, in quite some of the ensuing discussion, this seems to be distracting from the fundamental issued involved rather than clarifying them.
One can of course by design fabricate a selection of dozens of formal factors, which together improve statistical correlation, but this seems a rather arbitrary set approach based on probabilistic variations of white noise. As one can see from this article, a historical-genetic approach can provide a much simpler and economical explanation, from which several secondary factors, such as the relative independence of the student’s performance from the parent’s level of education in Finland, result (6% in Finland relative to 11% OECD average or 14% in Germany, see OECD 2008, p. 243). The Finnish school seems to teach science (at least the “foundations” of the initial empirical meanings) more effectively and better than in other countries, where this is left to the parents. Again, what is considered simple and what is complex depends on the explanatory gestalts found.
This application has already been done for several other countries, the results of which have partly been published (see Siemsen 2010b, e). If one would make for science teaching an epistemological scale between “pure logicism” on the one hand and the historical-genetic method on the other (with phenomenalism in-between, but closer to the genetic-adaptive side), the result approximates roughly the distribution from the PISA scale. At the lower end of the scale, enculturation effects of the general cultural distance to logicism become more important, similarly to the effect observable on immigrant groups. The memorandum on mathematics education in the US and the people involved is only one of many such influences—in this case even from Finland itself.
Many explanations are factually excluded by the similarity of these factors within the Nordic countries and difference of the Nordic countries in PISA results. As the example of Denmark shows, some factors such as spending on education can even surprisingly be negatively correlated. Such factors as centralization, equal opportunities or an increased reading of students because of long winter nights are thus not consistent with the broader facts. The latter hypothesis for instance additionally implicitly predicts a south-north improvement of reading literacy in general also within countries, a logical result which does not comply with the statistical facts as well. If the usual half-a-dozen factors used in most PISA “explanations” are reduced in such a way, the factors left over tend to look not very convincing. The effect of convincing seems to be mostly achieved by adding these factors together without showing in any way that they are actually statistically additive, i.e. that their joint correlation with the PISA results increases substantially relative to the low individual correlations.
Also if one asks the Finns about the person, who has most shaped their current philosophical ideas, the result will be Eino Kaila and his successor von Wright.
I will here provide just two examples of this: First, at the end of a 2-h interview with a renowned Finnish economics professor, which revolved mostly on his biography and ideas of Mach and Kaila, I asked him at the end, if he thinks he has had any influences by Kaila on his own thinking. He looked a bit surprised as he said that nobody had asked him this question before, but yes, his father—also an economist—was a great admirer of Kaila and had visited Kaila’s lectures. And he remembers that from this his father developed ideas on epistemological issues in economics, which he discussed with his young son. This fact is not mentioned in any of the published biographies or interviews with this professor, although it seems to be quite straightforward. The second example concerns a German science teacher observing a Finnish science class. He afterwards stated that he did not see anything special, different from other countries. He even found the class relatively boring. On closer questioning though he admitted that he did not pay attention to the way the Finns would use fundamental scientific concepts or how the teacher would respond to “errors” of students. Why, he asked, should he have done so?
If for instance as the Chinese have reportedly done, a Finnish school is “copied”, i.e. mainly its formal system, it will probably not achieve anything. Similarly, the idea that the factors leading to Finnish science education are too complex to reproduce them in another country will lead to nothing. As the other examples showed, similar effects have been produced by different persons in several countries at different times, sharing mainly the origin of their central ideas (probably a similar effect can be shown in India, but this still needs to be researched in detail). One might even postulate a correlation between the similarity of such ideas in science education and the PISA results in each country (this seems to apply at least for the countries researched in detail up to now).
For example McKinsey in their report on “How the world’s best performing school systems come out on top” (2007) identifies three factors: getting the right people to become teachers, developing these people into effective instructors and ensuring that every child is able to benefit from this instruction. In the erkenntnis-theoretical perspective, the three factors are actually one. Teachers teaching similar to the “perceptional approach”, as for instance described by Kurki-Suonio (2010), thereby become the “right people” to teach, because of the plasticity of learning processes. They are then able to teach children in a way nearly all the children can understand.
The previous PISA studies have in a sense been implicitly searching for explanatory factors. As none of the factors successively introduced in each subsequent study had seemingly any strong correlation with the results measured, each of these previous attempts has been discontinued. Probably in the next study, the little illuminating results specialized splitting between physics, chemistry and earth sciences as well as the misleading motivational factors will be dropped again in favour of new ideas for explanatory factors (according to Siemsen 1981, all types of self-evaluations of the learners tends to be consistently misleading in the genetic-adaptive method as it is not accessible to consciousness; see also Siemsen 2010d). It will be interesting to see, if maybe in 30 years (as long as it took from Wittenberg’s criticism of the OECD to the PISA study), the history and philosophy of science or even the erkenntnis-theoretical background of the science teaching in each country will be additionally evaluated by the PISA study, for instance by looking at the closeness of teaching to the suggested scale regarding logicist, phenomenological or genetic ideas (ranging “from early to late Carnap” so to speak). According to the countries already researched in detail, such a factor might finally yield surprisingly strong correlations, but only if the question is asked specifically enough.
Most statistical tools are designed to evaluate linear and direct (i.e. Bayesian) influences, not exponential and transformative developments (e.g. genetic into phenomenological or logical conceptual frames; see for instance Pearson 1911).
As noted before, this development has not been limited to Finland. How important the gestalt concept is for generalizing the psychology of teaching has been for instance also been found by Vygotsky and Luria (1992) in their book synthesizing Köhler’s chimpanzee experiments, the anthropological findings of Wertheimer, Lévi-Bruhl, etc. and their own child development theory. It seems that if one has been working intensively on these ideas, the “necessary” conclusions tend to present themselves, although unfortunately often only at the end of the researcher’s careers, as can be seen from the examples of Ch. Bühler and Carnap. Similar “conversions” or at least a growing empirical uneasiness regarding their initial logicist assumptions can interestingly also be found for many other eminent educationalists, such as Binet, Piaget, Armstrong, etc. (see Siemsen 2010d). Unfortunately, intellectual successors tend to ignore such late conversions.
For research in this direction, one could for instance make gestalt psychological investigations along the lines suggested by Lipmann and Bogen in their Naive Physik (“Naïve Physics”, 1923).
It would for example be interesting in the next PISA evaluation to statistically compare the PISA results of Finnish teachers with a “perceptional approach” with those without.
In a discussion about Mach’s concept of sense elements, Kurki-Suonio (email 27/04/2010) mentions “This sounds like my understanding of "perception" extending from the elementary sensory perception to formation of highly structural gestalts.”
Pearson in his introduction to Clifford (1885/1955, p. lxv), after confirming the closeness of these views to Mach, quotes the mathematician Clifford stating that “no mathematician can give any meaning to the language about matter, force, inertia used in current text books of mechanics. […] Force is not a fact at all, but an idea embodying what is approximately the fact.”
In this combination, the use of these concepts might be unique in the world, especially in science education.
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Acknowledgments
I would like to thank our many Finnish discussion partners, especially Kaarle Kurki-Suonio, Ismo Koponen, Agnes Airola, Juha Manninen, Jaakko Hintikka, Uskali Mäki, Maija Rukarjärvi-Saarela, Jari Koivisto, Juhani Ihanus, Eero Saksman, Olli Lehto, Viljo Martikainen, Marja Montonen, Ari Hämäläinen, Jari Lavonen, Heimo Saarikko, Antti Laherto, Suvi Tala, Pirkko Kärnäh, Timo Karkkainen, Raimo Lammi, Päivi Ojala, Temu Kansakangas, Taina Makkonen, Marjaana Lindeman, Erkki Pehkonen, Juha Oikkonen, Raimo Koponen, Veli-Matti Vesterinen, Ansu Saarela and many more for the lively exchange of ideas and their instructive introduction to Finnish culture and science teaching culture. Special thanks also to Henf Visser for his valuable literature suggestions and his view on Dutch science education in comparison as well as Karl Hayo Siemsen for his tireless proofreading.
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Initial Remark This article was written for two purposes: for teachers, who are interested in the influence of ideas from the philosophy of science on Finnish science education and secondly for researchers, who would like to elaborate on the historical and philosophical relations of these ideas more in detail. In order to satisfy both, I have tried to focus the text on the central ideas, while the details are found in the footnotes.
Appendices
Appendix 1
Mach | Kaila | Kurki-Suonio | |
|---|---|---|---|
Monism/dualism | Neutral monism; sensualistic empiricism; natural erkenntnis-theory | (Non-materialistic) monism; perceptional empiricism; natural philosophy | Unifying dualism; perceptional empiricism; natural philosophy |
Nature/empiry | Nature is “no trickster” | “Nature answer me” | Problem of posing the right question and forcing nature to answer |
Basic unit of psycho-physical relation | Sense elements | Perceptions | Perceptional approach |
Psychology | Father of gestalt psychology | Gestalt psychologist | Gestalt as central psychological concept |
The table above provides examples of similarities between central concepts from Mach, Kaila and Kurki-Suonio. Kaila for instance explicitly developed his concept of perceptions based on Mach’s sensual elements. Kurki-Suonio then centrally uses the concept of the “perceptional approach” (see Kurki-Suonio 2010).Footnote 129 He states for instance that “There is certainly no perceived Gestalt behind, if you take F = ma as the starting point.”Footnote 130 Regarding monism, Kurki-Suonio mentions: “Elementary particles have no individual, only species identity, it is a great misconception. They are the expression of ‘one’.” “Gestalt psychology”, a “perceptional approach”, as well as “natural philosophy” can otherwise not be generally found in Finnish academic literature (except of course by a few direct students of Kaila and Kurki-Suonio).Footnote 131
Furthermore, in a discussion on Laurikainen (KVL), Kurki-Suonio (KKS) made an interesting observation on conscious and unconscious memory and ideas. In an email (10/11/2007) KKS recalls details of his relation with KVL. The recollection is based on a meeting he had before with Agnes Airola, a close friend of both:
I don’t think KVL can be considered a link between Kaila and myself. At the time of my early talks and writings on world view questions I did not know about Kaila, nor about the related thoughts of KVL, who started his public activity around these themes somewhat later, while mine slowed down. […]
At this point I went back to the file of my own “history” to realize that we have had more interaction than I could find in my conscious memory. Throughout that time we have been acting now and then as invited speakers in the same occasions. And it was earlier than I thought that KVL started to arrange regular seminars and meetings where I also attended […] participating actively in the discussions with my own comments, trying to project his thoughts onto mine, or vice versa. Thus, in spite of my strong feeling of independence, KVL has probably given some impulses, at least, encouragement in the development of ideas. And I dare to think that this acted to some extent also the other way. KVL also asked me to give talks in his seminars and sometimes even chair them in the case of his absence. These seminars then led to foundation of the Society of Natural Philosophy (17.11.1988) […].
It might be interesting to note that in certain aspects, the Finnish Society of Natural Philosophy thereby resembles other discussion groups in which aspects of Mach’s question were discussed, such as the Vienna Circle in Austria, or in the US the Pearson Circle (see Lowie 1947). The result of these discussion groups has always been a variety of specific individual views on the epistemology of science. But these personal views became more developed through the joint discussion.
Appendix 2: Initiatory Experiences
According to von Wright (1992, p. 71), “Kaila describes an episode, which he calls his “philosophic awakening”. […] The episode is located to a beautiful summer day when he was 16 years of age and lay floating in a rowboat on a Finnish lake watching the clouds drifting in the sky. Then it seemed to him suddenly—these are his words—“that everything which there is in some very deep sense a unified whole, so to say an ‘all-unity’, a self-structuring totality”.”
Interestingly, Mach (1885; 1914, p. 30) describes a similar initiatory experience: “I have always felt it as a stroke of special good fortune, that early in life, at about the age of fifteen, I lighted, in the library of my father, on a copy of Kant’s Prolegomena to any Future Metaphysics. The book made at the time a powerful and ineffaceable impression upon me, the like of which I never afterwards experienced in any of my philosophical reading. Some 2 or 3 years later the superfluity of the role played by “the thing in itself” abruptly dawned upon me. On a bright summer day in the open air, the world with my ego suddenly appeared to me as one coherent mass of sensations, only more strongly coherent in the ego. Although the actual working out of this thought did not occur until a later period, yet this moment was decisive for my whole view. I had still to struggle long and hard before I was able to retain the new conception in my special subject. With the valuable part of physical theories we necessarily absorb a good dose of false metaphysics, which it is very difficult to sift out from what deserves to be preserved, especially when those theories have become very familiar to us. […] I only seek to adopt in physics a point of view that need not be changed the moment our glance is carried over into the domain of another science; for, ultimately, all must form one whole.”
Laurikainen tells of his initiatory experience in a book “Fyysikon tie” (“The Physicist’s way”, 1982, p. 11): “In the summer of 1938 [in the year after he had started to listen to lectures from Kaila] I experienced at once very strongly the miracle of the intuitive vision. The figures of mathematics began to live and link up in a new way. […] I started first to make closer acquaintance with the topology of surfaces, where I believed I could realize the intuitive vision which I had got in summer 1938 inspired by the lectures by Nevanlinna and Kaila.”
This is similar to what Kurki-Suonio tells (in his lecture on “Empirical and Mathematical Meanings of Concepts”, 2003) “For me, with just the short mathematics syllabus of secondary school as background, the differential and integral calculus caused great difficulties in the beginning. I still remember the great experience in the middle of my first spring semester, when, quite suddenly, the enormous freedom offered by mathematics for representation of most different kinds of empirical meanings was opened to me. It is notable that the idea was born specifically in the context of mathematics [and as KKS later added in a letter, especially that of differential geometry: “it was the way to empirical meanings of maths” from which “I started to do some of my own on the physics lectures and was happy to realize that I could in that way understand many of the results taught”]. This experience carried me through all my studies and through the whole of my academic career both as a researcher and as a teacher. Later on, it was crystallised into the philosophical starting point of my teaching: “Meanings are first”, which many of you know as my motto characterising learning of physics and as the carrying principle of the perceptional approach of teaching. According to it, the main thread through the teaching should be an observation-based and systematically proceeding creation and conceptualization of empirical meanings.
The keyword is “meaning”. The purpose of the introduction was to emphasize that meanings are intuitive. They are born through perception. This means that they arise from a cooperative action of observation and mind, where the empirical and theoretical elements are completely inseparable. Perception is at the same time observing based on and making use of mental images and forming and constructing and developing mental images on the basis of observations. In perception both theory-ladenness of observations and observation-ladenness of theory is realised simultaneously.”
Appendix 3: Distribution Patterns of the Perceptional Approach and Genetic Adaptive Teaching
Figures 1 and 2 show the typical “shift” of the distribution of grades observable in Machian teaching compared with a normal distribution. The similarity should only be seen as an interesting “gestalt” of this shift. The actual figures are only partly comparable, as the type of measurements, methods, scales, etc. are quite different. The similarity of the curves is interesting especially because the approaches have been quite different.
Distribution of “grades” in PISA (grade “6” is best, i.e. more than 708 out of 1,000 points total). Source: OECD (2008)
Typical distribution of grades in the Siemsen (1981, p. 199) experiment; averages and standard deviations of control group (left K) the experimental group (right E) for easy, average and difficult exercises. The OECD average distribution in Fig. 1 corresponds to the normally distributed medium-level exercise of the control group (left middle)
The lower variance in the Finnish distribution in Fig. 1 might be due to two effects. Siemsen (1981) noted that scale effects can be observed at the extremes of the distribution, which would require a different scale (more Machian-type questions) in order to be reduced. Secondly, as the Finns themselves continuously emphasize, their society is very homogenous as they have had relatively little immigration and the formerly ruling Swedish “upper class” was driven out of power during the Finnish struggle for independence at the end of the nineteenth century. Anyway, other countries and regions with homogenous population or an immigration history with no equivalent “upper class” do not equally share the same empirical “success” in PISA. On the contrary, some countries with high immigrant population such as Canada have relatively high PISA scores, while others, such as the USA, score low. The Siemsen experiment indicates that homogeneity of the population does not matter in the plasticity of the genetic teaching effect.
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Siemsen, H. Ernst Mach and the Epistemological Ideas Specific for Finnish Science Education. Sci & Educ 20, 245–291 (2011). https://doi.org/10.1007/s11191-010-9303-6
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DOI: https://doi.org/10.1007/s11191-010-9303-6