Abstract
In Conceptual Spaces (Gärdenfors 2000), dimensions and their relations provide a topological representation of a concept’s constituents and their mode of combination. When concepts are modeled as n-dimensional geometrical structures, conceptual change denotes the dynamic development of these structures. Following this basic assumption, we apply conceptual spaces to the dynamics of empirical theories. We show that the terms of the structuralist view of empirical theories can be largely recovered. Based on the logically possible change operations which a concept’s dimensions can undergo (singularly or in combination), we identify four types of (increasingly radical) change to an empirical theory. The incommensurability issue as well as the importance of measurement procedures for the identification of a radical theory change are briefly discussed.
Forthcoming in: Olsson, E.; S. Rahman, T., and Tulenheimo. Science in flux: Philosophy of science meets belief revision theory (Logic, Epistemology, and the Unity of Science Series). Berlin: Springer.
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Notes
- 1.
Forthcoming in: Olsson, E.; S. Rahman, T., and Tulenheimo. Science in flux: Philosophy of science meets belief revision theory (Logic, Epistemology, and the Unity of Science Series). Berlin: Springer.
- 2.
The construction and application of an empirical theory can naturally be seen as the paradigmatic example of rational human belief and its use. In this sense, structuralism also becomes a framework, albeit limited, for doxastic dynamics.
- 3.
- 4.
Balzer et al. (1987: 105) call these the constraints of equality and extensivity. Compare their ensuing discussion with respect to the simplifying assumption that gives rise to a third constraint: In any subsystem considered, e.g., moon and earth, masses are assumed to be impressed upon by the same forces, if these masses were related to the system as a whole, i.e., the cosmos. “Although this is not so if we look at things quite accurately, physical calculations work with such and similar assumptions” (1987: 106).
- 5.
NPM does, of course, presuppose its own theory of space-time, namely that of absolute (Euclidian) space and absolute simultaneity, see DiSalle (2006: 17–35, 98–130).
- 6.
This is not exactly Sneed’s definition, which may be found in his (1971: 171). Our above characterization of a core, however, captures what is essential about this concept.
- 7.
This is Sneed’s term, cf. Sneed (1979: 300); Stegmüller (1976: 107f.) uses fundamental laws. In addition, there are assumed characterizations of the single components of the model, so-called frame conditions. E.g., for NPM, that the set of particles is finite or that mass is a positive real function. These conditions “do not say anything about the world (or are not expected to do so) but just settle the formal properties of the scientific concepts we want to use” (Moulines 2002: p. 5).
- 8.
Hence, both basic laws and frame conditions are not open to refutation in the same sense that special laws are. Certainly, they can be revised, but not (without using stronger assumptions) falsified.
- 9.
The term “theory-element” denotes the set of the sets M, Mp, Mpp, L (links to theory elements specialized from different cores), C (constraints), I (intended applications) and blurs, B, used for approximation (see Balzer et al. 1987).
- 10.
- 11.
A fortiori for the so-called partial potential models, Mpp, i.e., \(Mpp(T_{n + 1} ) = Mpp(T_n )\).
- 12.
Strictly speaking, forces need not be represented as separate dimensions. After all, F = ma. Therefore, the dimensions mass, space and time are sufficient.
- 13.
For examples of different topological and metric assumptions within psychological domains, see Gärdenfors (2000).
- 14.
We use “isomorphic to” rather than “homomorphically embedded in”, as is the norm in standard accounts of measurement. Clearly, a very small difference, e.g., between in the lengths of two objects, will fall below the threshold of our cognitive capacity or our measurement apparatus, and is thus not measurable. Still, such differences are part of a conceptual space (see Batitsky 2000: 96).
- 15.
The “phenomenological” assumptions that Carnap (1971: 78f.) formulates are validated by the very structure of the space and need not be added as meta-linguistic constraints.
- 16.
However, it should be investigated whether the similarity naturally offered by distances in conceptual spaces can be exploited to give an account of the similarity of different applications.
- 17.
A data structure which can no longer be successfully completed to a full model may itself be hypothetically enriched, such as to include so far unobserved additional objects. E.g., postulation of the planet Vulcan is such a case. This, however, does not seem to be a relevant change, because the new hypothetical data structure – qua also obeying F = ma – had already been among the set of partial potential models. It had merely not been proposed as suitable for theoretical enrichment.
- 18.
This is the sense in which Sneed can explicate “having a theory” as “being committed to use a certain mathematical structure, together with certain constraints on theoretical functions to account for the behavior of a, not too precisely specified, range of phenomena” (1971: 157).
- 19.
See Diederich (1996: 80) for the claim that “the classical problems of incommensurability have [thereby] been circumvented”, rather than resolved. Also see Balzer et al. (1987, pp. 306–319) for attempts at tackling the incommensurability issue by relating two theories, T and T *, through their sets Mp and Mp *. For Kuhn’s largely negative reaction to the structuralist’s endeavor, see Kuhn (1976).
- 20.
Following Kuhn, incommensurability has been predominantly identified as a problem that occurs in relating the symbolic forms of two theories or frameworks. With our shift away from the symbolic and towards the conceptual level, we may end up not finding incommensurability at all. This sounds odd, but it is how it should be. After all, the practicing scientists that we know do not admit to any problems whatsoever in making a transition from one set of generalizations to the other.
- 21.
Of course, such changes are traceable and, therefore, not without repercussions in the theory. Thus, if T n is the respective theory element, its set of applications I(T n ) will simply be zero.
- 22.
A science-historical account of the process leading to a current concept of temperature as mean kinetic energy is provided in Chang (2004).
- 23.
If L0 is the length of an object in a rest frame, and L1 the length measured by an observer, then the contraction is given by \({\textrm{L}}_1 = {\textrm{L}}_0 /\gamma\), where γ is defined as \(\gamma = \surd (1 - u^2 /c^2 )^{ - 1}\) (with u for relative velocity between observer and object, and with c for the speed of light).
- 24.
In 1901, the Bureau International des Poids et Mesures conventionally defined as much “to put an end to the ambiguity which in current practice still exists on the meaning of the word weight, used sometimes for mass, sometimes for mechanical force” (BIPM 1901: 70).
References
Balzer, W., D.A. Pearce, and H.-J. Schmidt. 1984. Reduction in science. Structure, examples, philosophical problems (Synthese Library Vol. 175). Dordrecht: Reidel.
Balzer, W., C.U. Moulines, and J.D. Sneed. 1987. An architectonic for science. The structuralist program. (Synthese Library Vol. 186). Dordrecht: Reidel.
Balzer, W., C.U. Moulines, and J.D. Sneed. (eds.). 2000. Structuralist knowledge representation. Paradigmatic examples. Amsterdam: Rodopi.
Batitsky, V. 2000. Measurement in Carnap’s late philosophy of science. Dialectica 54:87–108.
BIPM. 1901. Comptes Rendus de la 3e Conférence Générale des Poids et Mesures, Paris 1901. http://www1.bipm.org/en/CGPM/db/3/2/
Carnap, R. 1971. A basic system of inductive logic, part 1. In Studies in inductive logics and probability, vol. 1, eds. R. Carnap, and R.C. Jeffrey, 35–165. Berkeley, CA: UCP.
Chang, H. 2004. Inventing temperature. Measurement and scientific progress. Oxford: OUP.
Chen, X. 2003. Why did John Herschel fail to understand polarization? The differences between object and event concepts. Studies in the History and Philosophy of Science 34:491–513.
Diederich, W. 1996. Pragmatic and diachronic aspects of structuralism. In Structuralist theory of science. Focal issues, new results, eds. W. Balzer, and C.U. Moulines, 75–82. New York, NY: De Gruyter.
DiSalle, R. 2006. Understanding space time. The philosophical development from Newton to Einstein. Cambridge: CUP.
Ellis, B. 1968. Basic concepts of measurement. Cambridge: CUP.
Gähde, U. 1997. Anomalies and the revision of theory-elements: Notes on the advance of Mercury’s perihelion. In Structures and norms in science. vol. 2 (Synthese Library Vol. 260), eds. M. L. Dalla Chiara. et al., 89–104. Dordrecht: Kluwer.
Gähde, U. 2002. Holism, underdetermination, and the dynamics of empirical theories. Synthese 130:69–90.
Gärdenfors, P. 1988. Knowledge in flux: Modeling the dynamics of epistemic states. Cambridge, MA: MIT Press.
Gärdenfors, P. 2000. Conceptual spaces. Cambridge, MA: MIT Press.
Garner, W.R. 1970. The processing of information and structure. Potomac: Wiley, New York, NY: Erlbaum.
Kuhn, T. 1962/1970. The structure of scientific revolution. Chicago: CUP.
Kuhn, T. 1976. Theory change as structure change. Comments on the sneed formalism. Erkenntnis 10:179–199.
Kuhn, T. 1987. What are scientific revolutions? In The Probabilistic revolution. vol. 1, eds. L. Krüger, et al., 7–22. Cambridge: MIT Press.
Maddox, W.T. 1992. Perceptual and decisional separability. In Multidimensional models of perception and cognition, ed. G. F. Ashby, 147–180. Hillsdale, NJ: Lawrence Erlbaum.
Melara, R.D. 1992. The concept of perceptual similarity: From psychophysics to cognitive psychology. In Psychophysical approaches to cognition, ed. D. Algom, 303–388. Amsterdam: Elsevier.
Moulines, C.U. 2002. Introduction: Structuralism as a program for modeling theoretical science (special issue on structuralism). Synthese 130:1–11.
Roseveare, N.T. 1982. Mercury’s perihelion from LeVerrier to Einstein. Oxford: Clarendon.
Sneed, J.D. 1971. The logical structure of mathematical physics. Dordrecht: Reidel.
Stegmüller, W. 1976. The structuralist view of theories. Berlin: Springer.
Stevens, S.S. 1946. On the theory of scales of measurement. Science 103:677–680.
Suppes, P. 1957. Introduction to logic. New York, NY: Van Nostrand.
Acknowledgements
We would like to thank the organizer and the audience of the Science in Flux workshop at Lund University and, especially with respect to our exposition of structuralism, J. D. Sneed and C. U. Moulines for helpful comments and criticism. Frank Zenker acknowledges funding from the Swedish Institute (SI) and Peter Gärdenfors from the Swedish Research Council.
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Gärdenfors, P., Zenker, F. (2010). Using Conceptual Spaces to Model the Dynamics of Empirical Theories. In: Olsson, E., Enqvist, S. (eds) Belief Revision meets Philosophy of Science. Logic, Epistemology, and the Unity of Science, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9609-8_6
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