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Infinite lies and explanatory ties: idealization in phase transitions

  • S.I.: Infinite Idealizations in Science
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Abstract

Infinite idealizations appear in our best scientific explanations of phase transitions. This is thought by some to be paradoxical. In this paper I connect the existing literature on the phase transition paradox to work on the concept of indispensability, which arises in discussions of realism and anti-realism within the philosophy of science and the philosophy of mathematics. I formulate a version of the phase transition paradox based on the idea that infinite idealizations are explanatorily indispensable to our best science, and so ought to attract a realist attitude. I go on to offer a solution to the paradox by drawing a distinction between two types of indispensability: constructive and substantive indispensability. I argue that infinite idealizations are constructively indispensable to explanations of phase transitions, but not substantively indispensable. This helps to resolve the paradox, I maintain, since realist commitment tracks substantive, and not constructive, indispensability.

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Notes

  1. There are a number of different types of idealization in science. See McMullin (1985), and Weisberg (2007) for more on types of idealization.

  2. See Bangu (2009), Batterman (2002a, b, 2005, 2009), Batterman and Rice (2014), de Donato Rodríguez and Santos (2012), Liu (2001, 2004), Pincock (2011, 2007), Strevens (2008), and Wayne (2011, 2012) for examples of infinite idealizations playing an explanatory role and for discussion of the nature of such explanations.

  3. This line has been pushed by Batterman (2002a, b, 2005, 2009), Batterman and Rice (2014), Strevens (2008), and Wayne (2011).

  4. See e.g., Callender (2001), Menon and Craig (2013).

  5. For discussion of the so-called paradox see Batterman (2002a, 2005), Butterfield (2011), Callender (2001), Liu (1999, 2001, 2004), Menon and Craig (2013), Prigogine (1997), and Shech (2013).

  6. For discussion see Baker (2005), Colyvan (2001) and Maddy (1992).

  7. Following Baron (2016), Woodward (2003) and Woodward and Hitchock (2003), I prefer to construe difference-making counterfactually: A makes a difference to B when if A had not occurred, B would not have occurred. Strevens explicitly resists this way of thinking about difference-making. For Strevens, difference-making is to be understood via causal entailment: A makes a difference to B when A is essential to a causal derivation of B, i.e., a derivation of B from A using a causal law.

  8. Similarly, consider the explanation for the bow-spacing of a rainbow. In our best explanations for the structure of rainbows, the wave-length of light is set to 0. By zeroing out the length of light-waves, it becomes possible to treat light as a ray. Once we’re in the arena of ray dynamics, the structure of a rainbow becomes explicable. On the picture that Strevens paints, the idealization here—treating the wavelength of light as 0—tells us that the wavelength of light makes no difference to the bow-spacing of a rainbow. For discussion of this case see Pincock (2011).

  9. Recall that these are our best scientific theories, and so realism is justified by the same broad realist attitude that gets us into the phase transition paradox in the first place. That being said, I relax this assumption in Sect. 5.1.

  10. To clarify the reasoning being used here:

    1. 1.

      If it is not possible to explain P in a manner that is consistent with background theories that we believe to be true, then either it is not possible to produce a complete and accurate scientific account of nature that is consistent, or it is not possible to produce a consistent and complete scientific account of nature that is accurate or it is not possible to produce a consistent and accurate scientific account of nature that is complete.

    2. 2.

      It is possible to produce a complete, accurate and scientific account of nature.

    3. 3.

      So, it is possible to explain P in manner that is consistent with background theories that we believe to be true.

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  1. University of Western Australia, Crawley, WA, Australia

    Sam Baron

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  1. Sam Baron
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Baron, S. Infinite lies and explanatory ties: idealization in phase transitions. Synthese 196, 1939–1961 (2019). https://doi.org/10.1007/s11229-018-1678-y

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