Abstract
The paper discusses the recent literature on abstraction/idealization in connection with the “paradox of infinite idealization.” We use the case of taking thermodynamics limit in dealing with the phenomena of phase transition and critical phenomena to broach the subject. We then argue that the method of infinite idealization is widely used in the practice of science, and not all uses of the method are the same (or evoke the same philosophical problems). We then confront the compatibility problem of infinite idealization with scientific realism. We propose and defend a contextualist position for (local) realism and argue that the cases for infinite idealization appear to be fully compatible with contextual realism.
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Notes
This point is for responding to a criticism we received that finds our using “idealization” to refer to the act or practice rather than the product as needing an argument to defend.
Here we assume a correspondence theory of truth since we are mostly dealing with issues relating to scientific realism.
There are numerous excellent standard texts of statistical mechanics in physics, but the work we rely on in this paper, a work in which an account of how the use of probability allows people such as Boltzmann and Gibbs to come up with an abstract study of thermo-systems, is Guttmann (1999). Our discussion of SM depends heavily on this work.
I thank a referee for pointing out that in (Morrison 2005) this traditional or textbook interpretation of the relationship between Boyle’s model and van der Waals’s model is challenged. Since the traditional interpretation is adopted here so that the case serves to make a distinction, I do not feel it is necessary to discuss the controversy. Granted, a better case whose interpretation is not subject to any controversies would have better served the purpose.
We thank a referee for raising the point that is dealt with in this paragraph.
Jones (2005) is a discussion of the distinction that predates (Godfrey-Smith 2009) but is of a more limited scope, dealing mostly with the distinction between idealization and abstraction in modeling practice. Woods and Rosales (2010) is a wonderful study of different sorts of distortion in model-building including abstraction without emphasizing the distinction.
To distinguish it from the former kind, Norton calls it“approximation.”
I thank a referee for pointing out that not all cases surveyed in Menon and Callender (2011) are in the KT approach camp. The conceptual point is that the KT approach encourages a study of the complex details of a finite system in order to recover the TD account of macroscopic phenomena.
If there is still any lingering doubt about how real the metaphysical implications are with the case of taking the TD limit to resolve the paradox of phase transition, the case concerning quantum measurement should supply more reason for serious concerns. It turns out that if one embraces the decoherence approach in general as a hopeful resolution to the quantum measurement problem, one has to inevitably face the use of thermodynamic limit on finite target systems in which quantum measurements take place. An infinite quantum system is the only type of systems in which unitarily inequivalent representations of algebraic quantum states appear that realize the measurement results. We shall reserve a discussion of the quantum measurement problem to another occasion, but see Ruetsche (2011) and Liu and Emch (2005).
Here, \({\mathcal {F}}_{\infty }(S)\) is the Gibbs free energy of the system in state S.
In our context, here it should be the “data model.”
As far as I know, there isn’t any known territory in philosophy that bears the name of Contextual Realism. The best known example of its mentioning is in Fine (1991) when referring to a position espoused by Miller (1987). Fine’s own name for the position is called “Piecemeal Realism.” It is a different position from the one we defend here; and we intend to reserve the discussion of its relationship with our position for another occasion.
I thank a referee of the journal for pointing out to us a recent work by Michael Shaffer, Counterfactuals and Scientific Realism (Palgrave 2012), which appears to have relevance to the position of contextual realism we defend here. It is a work that proposes and defends a contextual theory of idealization, which is in turn used to simplify the treatment of counterfactuals so as to relieve the pressure counterfactuals have on scientific realism. Upon viewing the work, we have come to the conclusion that it is not feasible to fully discuss in this paper the many ideas and arguments in Shaffer’s work; nor does it at all render the position of contextual realism we defend in our paper redundant or superfluous.
The analogy is actually evoked by Putnam (1981, p. 55).
There is a prima facie resemblance, in analogy, between the anchoring/grounding assumptions for contextual realism and what David Lewis calls ‘sotto-voce proviso’ for knowledge claims, see Lewis (1996). I thank a referee for suggesting this analogy. The similarity in analogy between the two items is quite striking. Both are needed in their separate domains to dispel possibilities that render the respective beliefs, the truth of a claim or the reality of an entity, suspect. Both are often given, say in textbooks, as passing remarks, as in the case of infinite population, complete randomness, etc.
I thank a referee of the journal for urging me to clarify the difference between epistemic contextualism and contextual realism.
I thank a referee of the journal for raising this objection in connection with Carnap’s work.
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First, let me thank Samuel Fletcher and Patricia Palacios, without whom this paper would not have been written. I also thank three anonymous referees for their constructive criticisms.
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Liu, C. Infinite idealization and contextual realism. Synthese 196, 1885–1918 (2019). https://doi.org/10.1007/s11229-018-1767-y
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DOI: https://doi.org/10.1007/s11229-018-1767-y