Abstract
There is nowadays consensus in the community of didactics of science (i.e. science education understood as an academic discipline) regarding the need to include the philosophy of science in didactical research, science teacher education, curriculum design, and the practice of science education in all educational levels. Some authors have identified an ever-increasing use of the concept of ‘theoretical model’, stemming from the so-called semantic view of scientific theories. However, it can be recognised that, in didactics of science, there are over-simplified transpositions of the idea of model (and of other meta-theoretical ideas). In this sense, contemporary philosophy of science is often blurred or distorted in the science education literature. In this paper, we address the discussion around some meta-theoretical concepts that are introduced into didactics of science due to their perceived educational value. We argue for the existence of a ‘semantic family’, and we characterise four different versions of semantic views existing within the family. In particular, we seek to contribute to establishing a model-based didactics of science mainly supported in this semantic family.
Notes
We use the expression ‘science education’ to refer to the practice of educating in science, whereas we call ‘didactics of science’ the academic discipline that reflects and investigates upon such practice (cf., Adúriz-Bravo and Izquierdo-Aymerich 2005). In accordance with this, we call ‘science educators’ the practitioners of science education; ‘didacticians of science’ would then be the academic researchers in our discipline. Equivalent expressions are standard in the main languages in continental Europe (e.g. French: didactique des sciences/didacticiens; German: Didaktik der Naturwissenschaften/Didaktiker; Spanish: didáctica de las ciencias/didactas).
In the last 35 years, there is an ever-increasing amount of philosophical work on scientific models. In this article, we centre our attention on the literature that considers models as an essential component of scientific theories, namely the already mentioned semantic view or family. We are of course aware that there exist very rich recent developments on models that analyse them without a reference to theories—as being ‘independent’ of theories, ‘autonomous’, or ‘mediators’ between reality and theories. For such views, which would demand a whole paper of their own, see e.g. Cartwright et al. (1995), Morgan and Morrison (1999), Morrison (1999) and Weisberg (2013).
However, it is only fair to make clear that just very few—if any—philosophical schools of science take as a case of study their influence on science teaching.
Other versions are: the partial structures approach of N. C. A. Da Costa, S. French, J. Ladyman and O. Bueno (Da Costa and French 1990, 2003; Bueno 1997; French and Ladyman 1999), the approach proposed by R. Torretti (1990), and many ‘European versions’ of the semantic view, such as those of M.L. Dalla Chiara and G. Toraldo di Francia (1973), M. Przełecki (1969) and R. Wójcicki (1976), G. Ludwig (1970, 1978), and E. Scheibe (1997, 1999, 2001).
The components of theories (i.e. constituting elements that give them their identity) are boldfaced in the ‘specified’ schemes of Sect. 4.
In addition, in some Anglo-Saxon circles the labels ‘German structuralism’ or ‘German structuralist school’ are also used.
The concept of theory-element may be seen as a precision and elaboration of a Kuhnian idea: “A theory consists, among other things, of verbal and symbolic generalizations together with examples of their function in use” (Kuhn 1969, p. 501, emphasis in the original).
It is worth noting that meta-theoretical structuralism per se is neutral with respect to the issue of scientific realism (see Sneed 1983; Stegmüller 1986)—understood either in terms of the ‘true description’ (or approximately true description) of the ‘real world’ given by a theory or of the ‘reality’ of the denotata of the T-theoretical terms of a theory—although there are supporters of this approach that have stated the problem within this framework and argued for, as well as against, scientific realism.
The concept of a theory-net may be seen, again, as a precision and elaboration of another Kuhnian idea, namely the ‘general principle plus specification relation’ idea: “[…] generalizations [like f = ma] are not so much generalizations as generalisation sketches, schematic forms whose detailed symbolic expression varies from one application to the next. For the problem of free fall, f = ma becomes mg = md2 s/dt 2. For the simple pendulum, it becomes mgsinθ = –md2 s/dt 2. For coupled harmonic oscillators it becomes two equations, the first of which may be written m 1d2 s 1/dt 2 + k 1 s 1 = k 2(d + s 2 − s 1). More interesting mechanical problems, for example the motion of a gyroscope, would display still greater disparity between f = ma and the actual symbolic generalization to which logic and mathematics are applied” (Kuhn 1969, p. 465).
Once again, the concept of a theory-evolution may be seen as a precision of some other Kuhnian idea, namely that of normal science.
Some authors have recognised the rich development of the structuralist programme. Nancy Cartwright suggests that, in comparison with other semantic approaches, “the German structuralists undoubtedly offer the most satisfactory, detailed and well-illustrated account of the structure of scientific theories on offer” (Cartwright 2008, p. 65). Sebastian Enqvist makes a similar point by claiming that “[t]he structuralist model of theories is impressive in two respects: first, it presents a very detailed analysis of what may be called the deep structure of an empirical theory. Second, it has been shown that a range of actual scientific theories can be reconstructed as theory nets” (Enqvist 2011, p. 107).
This approach can also be part of the meta-theoretical training of other professionals, for example in the formation of philosophers of science and general philosophers, or in other degrees that include contents of the philosophy of science in their curricula. It would then be necessary to adapt it to match the needs of each audience.
References
Abreu, C., Lorenzano, P., & Moulines, C. U. (Eds.). (2013). Bibliography of structuralism III (1995–2012 and Additions). Metatheoria, 3, 87–144.
Adams, E. W. (1955). Axiomatic foundations of rigid body mechanics. Doctoral thesis, Stanford University.
Adams, E. W. (1959). The foundations of rigid body mechanics and the derivation of its laws from those of particle mechanics. In L. Henkin, P. Suppes, & A. Tarski (Eds.), The axiomatic method (pp. 250–265). Amsterdam: North-Holland.
Adúriz-Bravo, A. (2001). Integración de la Epistemología en la Formación del Profesorado de Ciencias. Doctoral thesis, Bellaterra: Universitat Autònoma de Barcelona.
Adúriz-Bravo, A. (2005). Una Introducción a la Naturaleza de la Ciencia: La Epistemología en la Enseñanza de las Ciencias Naturales. Buenos Aires: Fondo de Cultura Económica.
Adúriz-Bravo, A. (2011). Epistemología para el Profesorado de Física: Operaciones Transpositivas y Creación de una Actividad Metacientífica Escolar. Revista de Enseñanza de la Física, 24(1), 7–20.
Adúriz-Bravo, A. (2013). A semantic view of scientific models for science education. Science & Education, 22(7), 1593–1611.
Adúriz-Bravo, A., & Izquierdo-Aymerich, M. (2005). Utilising the ‘3P-model’ to characterise the discipline of didactics of science. Science & Education, 14(1), 29–41.
Ariza, Y. (2015). Introducción de la metateoría estructuralista en la didáctica de las ciencias: Didáctica modeloteórica de las ciencias. Doctoral thesis, Buenos Aires: Universidad Nacional de Tres de Febrero.
Ariza, Y., Lorenzano, P., & Adúriz-Bravo, A. (2010). Dificultades en la introducción de la “familia semanticista” a la didáctica de las ciencias naturales. Revista Latinoamericana de Estudios Educativos, 6(1), 59–74.
Balzer, W. (1978). Empirische Geometrie und Raum-Zeit-Theorie in mengentheo-retischer Darstellung. Kronberg: Scriptor.
Balzer, W. (1982). Empirische theorien: Modelle, strukturen, beispiele. Braunschweig: Vieweg.
Balzer, W. (1985). Theorie und Messung. Berlin: Springer.
Balzer, W., & Moulines, C. U. (Eds.). (1996). Structuralist theory of science: Focal issues, new results. Berlin: de Gruyter.
Balzer, W., Moulines, C. U., & Sneed, J. D. (1987). An architectonic for science. The structuralist program. Dordrecht: Reidel.
Balzer, W., Moulines, C. U., & Sneed, J. D. (Eds.). (2000). Structuralist knowledge representation: Paradigmatic examples. Amsterdam: Rodopi.
Beth, E. W. (1948a). Natuurphilosophie. Gorinchem: Noorduijn.
Beth, E. W. (1948b). Analyse sémantique des théories physiques. Synthese, 7, 206–207.
Beth, E. W. (1949). Towards an up-to-date philosophy of the natural sciences. Methodos, 1, 178–185.
Beth, E. W. (1960). Semantics of physical theories. Synthese, 12, 172–175.
Birkhoff, G., & von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 37, 823–843.
Bueno, O. (1997). Empirical adequacy: A partial structures approach. Studies in History and Philosophy of Science, 28, 585–610.
Cartwright, N. (2008). Reply to Ulrich Gahde. In S. Hartmann, C. Hoefer, & L. Bovens (Eds.), Nancy Cartwright’s philosophy of science (pp. 65–66). New York: Routledge.
Cartwright, N., Shomar, T., & Suárez, M. (1995). The tool box of science: Tools for building of models with a superconductivity example. In W. E. Herfel, et al. (Eds.), Theories and models in scientific processes (pp. 27–36). Amsterdam: Rodopi.
Chamizo, J. A. (2010). Una tipología de los modelos para la enseñanza de las ciencias. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 7(1), 26–41.
Chamizo, J. A. (2013). A new definition of models and modeling in chemistry’s teaching. Science & Education, 22(7), 1613–1632.
Clough, M. P. (2008). Teaching the nature of science to secondary and post-secondary students: Questions rather than tenets. The California Journal of Science Education, 8(2), 31–40.
Da Costa, N., & French, S. (1990). The model-theoretic approach in philosophy of science. Philosophy of Science, 57, 248–265.
Da Costa, N., & French, S. (2003). Science and partial truth. A unitary approach to models and scientific reasoning. Oxford: Oxford University Press.
Dalla Chiara, M. L., & Toraldo de Francia, G. (1973). A logical analysis of physical theories. Rivista di Nuovo Cimento, 3, 1–20.
Develaki, M. (2007). The model-based view of scientific theories and the structuring of school science programmes. Science & Education, 16(7), 725–749.
Diederich, W. (1996). Structuralism as developed within the model-theoretical approach in the philosophy of science. In W. Balzer & C. U. Moulines (Eds.), Structuralist theory of science: Focal issues, new results (pp. 15–22). Berlin: de Gruyter.
Diederich, W., Ibarra, A., & Mormann, T. (1989). Bibliography of structuralism I. Erkenntnis, 30, 387–407.
Diederich, W., Ibarra, A., & Mormann, T. (1994). Bibliography of structuralism II (1989–1994 and additions). Erkenntnis, 41, 403–418.
Enqvist, S. (2011). A structuralist framework for the logic of theory change. In E. J. Olsson & S. Enqvist (Eds.), Belief revision meets philosophy of science, logic, epistemology, and the unity of science (pp. 105–135). Dordrecht: Springer.
Erduran, S., & Duschl, R. (2004). Interdisciplinary characterizations of models and the nature of chemical knowledge in the classroom. Studies in Science Education, 40(1), 105–138.
Estany, A. (1993). Introducción a la filosofía de la ciencia. Barcelona: Crítica.
French, S., & Ladyman, J. (1999). Reinflating the semantic approach. International Studies in the Philosophy of Science, 13(2), 103–121.
Frigg, R. (2006). Scientific representation and the semantic view of theories. Theoria, 55, 37–53.
Giere, R.N. (1979). Understanding scientific reasoning. New York: Holt/Reinhart and Winston; 2nd ed., 1984; 3rd revised ed., 1991; 4th ed., 1997; 5th revised ed. 2006 (with J. Bickle & R.F. Mauldin).
Giere, R. N. (1983). Testing theoretical hypotheses. In J. Earman (Ed.), Testing scientific theories (pp. 269–298). Minneapolis: University of Minnesota Press.
Giere, R. N. (1985). Constructive realism. In P. M. Churchland & C. Hooker (Eds.), Images of science. Essays on realism and empiricism with a reply from Bas C. van Fraassen (pp. 75–98). Chicago: University of Chicago Press.
Giere, R. N. (1988). Explaining science: A cognitive approach. Chicago: The University of Chicago Press.
Giere, R. N. (1994). The cognitive structure of scientific theories. Philosophy of Science, 61, 276–296.
Gilbert, J. K., & Boulter, C. J. (Eds.). (2000). Developing models in science education. Dordrecht: Kluwer.
Izquierdo-Aymerich, M., & Adúriz-Bravo, A. (2003). Epistemological foundations of school science. Science & Education, 12(1), 27–43.
Khine, M. S., & Saleh, I. M. (2011). Models and modeling: Cognitive tools for scientific enquiry. Dordrecht: Springer.
Kuhn, T.S. (1962.1970). The structure of scientific revolutions (2nd edn.). Chicago: Chicago University Press.
Kuhn, T. S. (1969). Second thoughts on paradigms. In F. Suppe (Ed.), The structure of scientific theories (2nd ed., pp. 459–482). Urbana, IL: University of Illinois Press.
Lakatos, I. (1971). History of science and its rational reconstruction. In R. C. Buck & R. S. Cohen (Eds.), PSA 1970, Boston studies in the philosophy of science (Vol. 8, pp. 174–182). Dordrecht: Reidel.
Lakatos, I. (1978). The methodology of scientific research programmes (Vol. 1). Cambridge: Cambridge University Press.
Lorenzano, P. (2013). The semantic conception and the structuralist view of theories: A critique of Suppe’s criticisms. Studies in History and Philosophy of Science, 44, 600–607.
Ludwig, G. (1970). Deutung des Begriffs ‘Physikalische Theorie’ und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens. Lecture Notes in Physics, Bd. 4. Berlin: Springer.
Ludwig, G. (1978). Die Grundstrukturen einer physikalischen Theorie. Berlin: Springer.
Matthews, M. R. (1994). Science teaching: The role of history and philosophy of science. Nueva York: Routledge.
McComas, W. F., Clough, M. P., & Almazroa, H. (1998). The role and character of the nature of science in science education. In W. F. McComas (Ed.), The nature of science in science education: Rationales and strategies (pp. 3–39). Dordrecht: Kluwer.
McKinsey, J. C. C., Sugar, A., & Suppes, P. (1953). Axiomatic foundations of classical particle mechanics. Journal of Rational Mechanics and Analysis, 2, 253–272.
Morgan, M., & Morrison, M. (Eds.). (1999). Models as mediators. Cambridge: Cambridge University Press.
Morrison, M. (1999). Models and autonomous agents. In M. Morgan & M. Morrison (Eds.), Models as mediators (pp. 38–65). Cambridge: Cambridge University Press.
Moulines, C. U. (1975). A logical reconstruction of simple equilibrium thermodynamics. Erkenntnis, 9(1), 101–130.
Moulines, C. U. (1982). Exploraciones metacientíficas. Madrid: Alianza.
Moulines, C. U. (2002). Introduction: Structuralism as a program for modelling theoretical science. Synthese, 130, 1–11.
Moulines, C. U. (2008). Die Entwicklung der modernen Wissenschaftstheorie (1890–2000): Eine historische Einführung. Münster: LIT-Verlag.
Oh, P. S., & Oh, S. J. (2011). What teachers of science need to know about models: An overview. International Journal of Science Education, 33(8), 1109–1130.
Passmore, C., Gouvea, J. S., & Giere, R. N. (2014). Models in science and in learning science: Focusing scientific practice on sense-making. In M. Matthews (Ed.), International handbook of research in history, philosophy and science teaching (pp. 1171–1202). Dordrecht: Springer.
Przełecki, M. (1969). The logic of empirical theories. London: Routledge & Kegan Paul.
Scheibe, E. (1997). Die Reduktion physikalischer Theorien, Teil I, Grundlagen und elementare Theorie. Berlin: Springer.
Scheibe, E. (1999). Die Reduktion physikalischer Theorien, Teil II, Inkommensurabilität und Grenzfallreduktion. Berlin: Springer.
Scheibe, E. (2001). Between rationalism and empiricism. In B. Falkenburg (Ed.), Selected papers in the philosophy of physics. Berlin: Springer.
Sneed, J. D. (1971). The logical structure of mathematical physics. Dordrecht: Reidel.
Sneed, J. D. (1983). Structuralism and scientific realism. Erkenntnis, 19, 345–370.
Stegmüller, W. (1973). Theorienstrukturen und Theoriendynamik. Berlin: Springer.
Stegmüller, W. (1979). The structuralist view of theories. New York: Springer.
Stegmüller, W. (1986). Die Entwicklung des neuen Strukturalismus seit 1973. Berlin: Springer.
Suppe, F. (1967). The meaning and use of models in mathematics and the exact sciences. Doctoral Thesis, Michigan: University of Michigan.
Suppe, F. (1972). What’s wrong with the received view on the structure of scientific theories? Philosophy of Science, 39, 1–19.
Suppe, F. (1974). The search for philosophical understanding of scientific theories. In F. Suppe (Ed.), The structure of scientific theories (pp. 3–241). Urbana, IL: The University of Illinois Press.
Suppe, F. (1977). Afterword. In F. Suppe (Ed.), The structure of scientific theories (2nd ed., pp. 617–730). Urbana: University of Illinois Press.
Suppe, F. (1989). The semantic conception of theories and scientific realism. Urbana, IL: University of Illinois Press.
Suppe, F. (1998). Theories, scientific. In E. Craig (Ed.), Routledge encyclopedia of philosophy (Vol. 9, pp. 344–355). London: Routledge.
Suppes, P. (1957). Introduction to logic. New York: Van Nostrand.
Suppes, P. (1962). Models of data. In E. Nagel, P. Suppes, & A. Tarski (Eds.), Logic, methodology and philosophy of science: Proceedings of the 1960 international congress (pp. 252–261). Stanford: Stanford University Press.
Suppes, P. (1969). Studies in the methodology and foundations of science: Selected papers from 1951 to 1969. Dordrecht: Reidel.
Suppes, P. (1970). Set-theoretical structures in science. Stanford: Stanford University.
Suppes, P. (2002). Representation and invariance of scientific structures. Stanford: Center for the Study of Language and Information (CSLI).
Torretti, R. (1990). Creative understanding: Philosophical reflections on physics. Chicago: The University of Chicago Press.
Toulmin, S. (1972). Human understanding: The collective use and development of concepts (Vol. 1). Oxford: Clarendon Press.
van Fraassen, B. (1970). On the extension of Beth’s semantics of physical theories. Philosophy of Science, 37(3), 325–339.
van Fraassen, B. (1972). A formal approach to the philosophy of science. In R. Colodny (Ed.), Paradigms and paradoxes (pp. 303–366). Pittsburgh: University of Pittsburgh Press.
van Fraassen, B. (1974). The formal representation of physical quantities. In R. S. Cohen & M. W. Wartofsky (Eds.), Logical and epistemological studies in contemporary physics (pp. 196–209). Dordrecht: Reidel.
van Fraassen, B. (1976). To save the phenomena. The Journal of Philosophy, 73(18), 623–632.
van Fraassen, B. (1980). The scientific image. Oxford: Clarendon Press.
van Fraassen, B. (1987). The semantic approach to scientific theories. In N. Nersessian (Ed.), The process of science (pp. 105–124). Dordrecht: Nijhoff.
van Fraassen, B. (1989). Laws and symmetry. Oxford: Clarendon Press/Oxford University Press.
van Fraassen, B. (1997). Structure and perspective: Philosophical perplexity and paradox. In M. L. Dalla Chiara, et al. (Eds.), Logic and scientific methods (pp. 511–530). Dordrecht: Kluwer.
van Fraassen, B. (2008). Scientific representation: Paradoxes of perspectives. Oxford: Oxford University Press.
von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.
Weisberg, M. (2013). Simulation and similarity: Using models to understand the world. Oxford: Oxford University Press.
Weyl, H. (1927). Quantenmechanik und Gruppentheorie. Zeitschrift für Physik, 46, 1–46.
Weyl, H. (1928). Gruppentheorie und Quantenmechanik. Leipzig: Hirzel; 2. Auflage, 1931.
Wójcicki, R. (1976). Some Problems of formal methodology of science. In M. Przełecki, K. Szaniawski, & R. Wójcicki (Eds.), Formal methods in the methodology of empirical sciences (pp. 9–18). Dordrecht: Reidel.
Acknowledgments
Research reported in this article was supported by Research Grants FFI2012-37354/CONSOLIDER INGENIO CSD2009-0056 (Spain), FFI2013-41415-P (Spain), PICT-2014-1741 and PICT-2013-0503 (ANPCyT, Argentina), and PIP 112-201101-01135 (CONICET, Argentina).
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Ariza, Y., Lorenzano, P. & Adúriz-Bravo, A. Meta-Theoretical Contributions to the Constitution of a Model-Based Didactics of Science. Sci & Educ 25, 747–773 (2016). https://doi.org/10.1007/s11191-016-9845-3
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DOI: https://doi.org/10.1007/s11191-016-9845-3