Abstract
Our aim in this article is to show how the theory of conceptual spaces can be useful in describing diachronic changes to conceptual frameworks, and thus useful in understanding conceptual change in the empirical sciences. We also compare the conceptual space approach to Moulines’s typology of intertheoretical relations in the structuralist tradition. Unlike structuralist reconstructions, those based on conceptual spaces yield a natural way of modeling the changes of a conceptual framework, including noncumulative changes, by tracing the changes to the dimensions that reconstitute a conceptual framework. As a consequence, the incommensurability of empirical theories need not be viewed as a matter of conceptual representation.
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Notes
Mormann (1996) shows that category theory may be used to reconstitute the set-theoretic apparatus of structuralism.
This is an advantage when engaging working scientists in debates that are currently held almost exclusively between philosophers of science. Moreover, the conceptual spaces approach recommends itself for didactic purposes.
The quality dimensions of the conceptual space underlying the original Newtonian mechanics are ordinary space s (isomorphic to R3), time t (isomorphic to R), mass m (isomorphic to R+), and force F (isomorphic to R3). All spaces are Euclidean. See Gärdenfors and Zenker (2013, 1048f.).
The organization of dimensions into domains thus depends on the definition of separability, which may be based either on theoretical motivations (e.g., transformation classes) or practical ones (e.g., measurement procedures). A practical criterion for identifying domains can then be connected to the measurement procedures for the domains (for instance, in experimental research). But domains may also be identified in purely mathematical fashion, if only to find out in a later step whether such “pure” distinctions can be supplied with feasible measurement methods.
For Sneed, a T-theoretical dimension is one for which the value of an object cannot be determined without applying the theory T itself. For example, mass and force become T-theoretical dimensions in Newtonian mechanics (Sneed 1971). With respect to measurement procedures, see Suppes (2002, 114): “[W]e may define a scale as a class of measurement procedures having the same transformation properties.” In this sense, ‘measurement procedure’ denotes the pragmatic aspect of mathematical invariance.
Insofar as some domains are presumed to govern a problem, the law will more or less “fall out,” depending on how the domains constrain the form of the special law. In principle, the selection of domains may determine the form of the law. As Lord Rayleigh observed, “it happens not infrequently that results in the form of ‘laws’ are put forward as novelties on the basis of elaborate experiments, which might have been predicted a priori after a few minutes’ consideration” (Rayleigh 1915; cited after Roche 1998, 211).
We lend ourselves of expressions commonly used in dimensional analysis. For instance, one may refer to the mass dimension as [M], use [L] for a length, and [L3] for volume or space, comprising three length dimensions. Thus, [ML−3] expresses density, i.e., mass per volume. Entities so designated are representational objects; they need not be understood as real world things or relations.
The standard way of unifying microscopic particle dynamics with macroscopic fluid dynamics is by demonstrating that, for the limiting case of infinitely many particles, the microscopic theory collapses into the macroscopic one. Therefore, density is, strictly speaking, not always assumed to be unimportant; rather, under certain macroscopic assumptions, its complexity is disregarded.
Moulines furthermore employs the stability of a scientific community as a criterion, which is disregarded here.
Since, historically, Lagrangian mechanics (LM) arose for the explicit purpose of matching all applications of Newtonian mechanics (NM), it can hardly surprise that LM yields predictions that are equivalent to those of NM. However, given suitable assumptions, LM may be extended to structures not provided by NM. Therefore, one may argue, NM and LM differ not only with respect to the T-theoretical terms employed, but also with respect to their empirical content.
Stegmüller (1976, esp. 122ff.) has used this case as an example of “[the task of] the explication of an adequate concept of the equivalence of two theories … [which] becomes really interesting … since the desired concept should … enable us to speak of the equivalence of different theories built on the basis of an entirely different conceptual apparatus” (124; his italics). With our approach, the phrase “entirely different” is an overstatement, insofar as the conceptual framework has not undergone a radical change.
It seems that noninterpretability promised to make communication breakdown understandable to some extent, and the communication breakdown to make noninterpretability significant. Although Kuhn toned it down ever since his postscript to Structure (Kuhn 1970), this claim remains virulent.
One might perhaps cite cognitive or motivational factors, in the sense of people remaining, or becoming, unable to adopt (and switch between) different conceptual frameworks. Other factors might be strong quasi religious biases leading individuals to disregard that claims to an ultimate ontology (“final description of the world”) may be dogmatic. Finally, group-level sociological or institutional factors may leave actors rationally uncompelled to consider alternative frameworks while investing in, or after having profited from, a particular research program.
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Acknowledgments
We thank two anonymous reviewers for this journal, the participants of Perspectives on Structuralism, Feb 16–18, 2012, at the Center for Advanced Studies, LMU Munich, and Graciana Petersen for comments that improved our manuscript, as well as Heather Ogston for language editing. Both authors acknowledge funding from the Swedish Research Council (VR).
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Zenker, F., Gärdenfors, P. Modeling Diachronic Changes in Structuralism and in Conceptual Spaces. Erkenn 79 (Suppl 8), 1547–1561 (2014). https://doi.org/10.1007/s10670-013-9582-9
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DOI: https://doi.org/10.1007/s10670-013-9582-9