Abstract
In the present paper, I argue that at least some models are abstract entities and hence that at least some of the content of scientific theories is abstract. I further argue that abstraction, which is ubiquitous in science, is the vehicle for the discovery and representation of abstract objects. Finally, I argue against taking models to be fictions. In Sect. 9.2, I present in some detail the case of the Carnot Engine as a typical case of a model in science and defend the view that it is best seen as a real but abstract entity. In Sect. 9.3, I distinguish and discuss three modes of abstraction in science, which I call Aristotelian, Newtonian and Duhemian. In Sect. 9.4, I offer reasons to resist fictionalism about models. I discuss Kendall Walton’s pretence theory of representation and I argue against extending it to the case of scientific models. I show that the current neo-fictionalist account of models fails and that considering models as real but abstract entities is a better account of models than neo-fictionalism.
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- 1.
“Two classes have the same number when, and only when, there is a one-one relation whose domain includes the one class, and which is such that the class of correlates of the terms of the one class is identical with the other class” (1903, 113).
- 2.
In Grundlagen, he showed the power of abstraction principles by introducing the concept of direction over the equivalence relation ‘being a parallel line to’ (1884, 74–78; §63–67).
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(D=) The direction of the line a is the same as the direction of the line b if, and only if a is parallel to b.
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or,
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(D=) D(a) = D(b) iff a//b.
For Frege, lines are given in (spatial) intuition and yet directions (introduced as above) are abstract entities not given in intuition. The concept of direction is discovered by a process of intellectual activity which takes its start from intuition. For Frege abstraction principles explain our capacity to refer to abstract objects. ‘The direction of the line a’ is a singular term; it refers to an object. (D=) enables us to identify this object as the same again (criterion of identity) under a different description, e.g., ‘The direction of the line b’. We thereby have a criterion of identity: the criterion of identity of the new entities S (e.g., directions) is given in terms of a relation R (which is an equivalence relation) on things of some other kind G (e.g., parallel lines).
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- 3.
For a succinct but informative account of abstraction principles see Horsten and Leitgeb (2009).
- 4.
For more discussion of the transfictional statements, see Peter Godfrey-Smith (2009).
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Acknowledgement
An earlier version of this paper was presented at the workshop “Scientific Contents: Fictions or Abstract Objects?”, organized by the EPISTEME Research Group, at the University of Santiago de Compostela, in January 2017. Many thanks to Xavier de Donato and José L. Falguera for their kind invitation and to the participants for useful comments and questions. Thanks are due to an anonymous reader and the editors of this volume for their patience and support.
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Psillos, S. (2020). The Scope and Power of Abstraction in Science. In: Falguera, J.L., Martínez-Vidal, C. (eds) Abstract Objects. Synthese Library, vol 422. Springer, Cham. https://doi.org/10.1007/978-3-030-38242-1_9
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