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Informative Models: Idealization and Abstraction

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Models and Idealizations in Science

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 50))

Abstract

Mauricio Suárez and Agnes Bolinska apply the tools of communication theory to scientific modeling in order to characterize the informational content of a scientific model. They argue that when represented as a communication channel, a model source conveys information about its target, and that such representations are therefore appropriate whenever modeling is employed for informational gain. They then extract two consequences. First, the introduction of idealizations is akin in informational terms to the introduction of noise in a signal; for in an idealization we introduce ‘extraneous’ elements into the model that have no correlate in the target. Second, abstraction in a model is informationally equivalent to equivocation in the signal; for in an abstraction we “neglect” in the model certain features that obtain in the target. They conclude that it becomes possible in principle to quantify idealization and abstraction in informative models, although precise absolute quantification will be difficult to achieve in practice.

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Notes

  1. 1.

    So is the concomitant terminology of ‘sources’ and ‘targets’ (Suárez 2004); yet, for reasons that will become apparent, it is best for the purposes of this article to refer to representational vehicles and targets, to aptly distinguish them from the terms employed in information theory.

  2. 2.

    See Bolinska (2015) for an application of these notions in the philosophy of science.

  3. 3.

    In fact, a 1–1 copy of the target—as in Borges’ (1954) beautiful parable—would be a 100% informative ‘channel’ and, yet, a perfectly useless model.

  4. 4.

    Indeed one of us (Bolinska 2016) has explicitly understood models as tools for conveying information, identifying the features responsible for their informativeness. See also the discussion of ‘objectivity’ in Suárez (2004, forthcoming).

  5. 5.

    Our use of the terms is inspired by the definitions in Thomson-Jones (2005) and Weisberg (2007); and is reflected most precisely in those used in Pero and Suárez (2016).

  6. 6.

    More recently, Pero and Suárez (2016), Suárez and Pero (2019) and Suárez (forthcoming) contain an extended historical discussion of this example that corrects some philosophical misconceptions.

  7. 7.

    It is actually worse than that: contrary to assumptions billiard balls are not perfectly elastic, but of course experience minor energy loss in the form of heat in collisions; but then again neither are gas molecules perfectly elastic, since they also experience loss of (kinetic) energy in collision. See the discussion in Pero and Suárez (2016, pp. 75–76).

  8. 8.

    Although, certainly, these assumptions can be contested. But nothing much hinges on the particular values. The only claim needed for the present proposal to go through is that there are some values for these probability distributions—whether they are within our reach to know is not essential. As Dretske points out (1981, p. 55) the probability distributions that go into communication theory, and in particular the conditional probabilities in the definition of equivocation, are objective, and may be very hard to get to know.

  9. 9.

    For instance, one could imagine a model where the colour of the elastic ‘billiard’ balls is taken to represent the initial velocity of each corresponding molecule in the gas, with purple representing the larger speeds and red representing the smaller speeds and all the other colours representing intermediate speed ranges in the prescribed order in the electromagnetic visible spectrum. Such model would not be very useful, but it is perfectly possible, for any given gas.

  10. 10.

    Determinism is also arguably an assumption for systems of billiard balls, if we assume an initial probability distribution over the dynamical variables of interest (as is done, e.g. in the tradition of the method of arbitrary functions). We shall ignore this complication and assume deterministic Newtonian dynamics.

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Acknowledgements

Mauricio Suárez would like to thank Tarja Knuuttila and the audience at the 2016 Valparaiso workshop on Models and Idealizations in Science for their comments and reactions, as well as financial support from the Spanish Ministry of Science and Innovation project PGC2018 099423. Agnes Bolinska would like to thank Anna Alexandrova and Joseph D. Martin for helpful feeback. 

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Suárez, M., Bolinska, A. (2021). Informative Models: Idealization and Abstraction. In: Cassini, A., Redmond, J. (eds) Models and Idealizations in Science. Logic, Epistemology, and the Unity of Science, vol 50. Springer, Cham. https://doi.org/10.1007/978-3-030-65802-1_3

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