Abstract
How do philosophers of science make use of historical case studies? Are their accounts of historical cases purpose-built and lacking in evidential strength as a result of putting forth and discussing philosophical positions? We will study these questions through the examination of three different philosophical case studies. All of them focus on modeling and on Vito Volterra, contrasting his work to that of other theoreticians. We argue that the worries concerning the evidential role of historical case studies in philosophy are partially unfounded, and the evidential and hermeneutical roles of case studies need not be played against each other. In philosophy of science, case studies are often tied to conceptual and theoretical analysis and development, rendering their evidential and theoretic/hermeneutic roles intertwined. Moreover, the problems of resituating or generalizing local knowledge are not specific to philosophy of science but commonplace in many scientific practices—which show similarities to the actual use of historical case studies by philosophers of science.
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Notes
- 1.
Kinzel gives also Chang (2012) as an example of a proponent of a hermeneutic approach.
- 2.
Some vestiges of the confrontation model seem to be at play here, even in the rejection of it.
- 3.
In recent discussion on modeling, the idea of models as fictions has been entertained by several authors, e.g. Suárez (2008).
- 4.
Godfrey-Smith (2006) likewise distinguishes between indirect representation and abstract direct representation—and invokes examples in trying to account for the difference between the two strategies of theorizing. Godfrey-Smith studies two influential books on evolutionary theory: Leo Buss’s The Evolution of Individuality (1987) and Maynard Smith and Szathmáry’s The Major Transitions in Evolution (1995). Buss examines the “actual relations between cellular reproduction and whole-organism reproduction in known organisms” (Godfrey-Smith 2006, p. 731), while Maynard Smith and Szathmáry put forth “idealized, schematic causal mechanisms.”
- 5.
- 6.
We are here largely following the discussion by Scholl and Räz (2013).
- 7.
Our case studies are based on our earlier work (Knuuttila and Loettgers 2016).
- 8.
Volterra had started his scientific career as a mathematician and had made important contributions to the theory of calculus. This work is summarized in Volterra’s book Theory of Functionals and of Integral and Integro-Differential Equations (Volterra 1930).
- 9.
- 10.
For this so-called Volterra principle, see Weisberg and Reisman (2008).
- 11.
Lankester suggested that to protect edible prey-fish their enemies should be destroyed in the same proportion as the adult prey fish were “removed” (Lancaster 1884, p. 416).
- 12.
On Volterra’s Darwinism, see Scudo (1992).
- 13.
Volterra made use of the method of encounters also in his study of the demographic evolution of a single species: There he applied the method of encounters to mating.
- 14.
Today Volterra is mostly known for the Lotka-Volterra equation. For a discussion on how Volterra’s various models anticipated several theoretical advances in theoretical ecology, see Scudo (1971).
- 15.
A partial English translation of this paper can be found in Scudo and Ziegler (1978).
- 16.
- 17.
The biologists with whom Volterra corresponded included Georgii F. Gause, R.N. Chapman, Jean Régnier, Raymond Pearl, Karl Pearson, D’Arcy W. Thompson, William R. Thompson, Alfred J. Lotka, and Vladimir A. Kostitzin. The correspondence of Vito Volterra on mathematical biology also provides interesting material as regards modeling methods. Among other things, it provides material on the choices between deterministic and probabilistic approaches; between continuous and discrete models; between closed-form solutions and numerical solutions, and between qualitative and quantitative models.
- 18.
Lotka dealt with the rhythmic effects of chemical reactions already in his earlier writings, see e.g. Lotka (1910).
- 19.
Our reading of Scholl and Räz (2013) differs somewhat from their later reading of their own article (this volume). In their original article, they do not clearly offer causal inference as a contrast to modeling (that would provide an alternative for Weisberg’s contrast between modeling and abstract direct representation). According to them “much of our discussion will focus on models of causal structures” (Scholl and Räz 2013, p. 117, emphasis added). Their earlier focus was on causal inference in general and modeling a strategy to deal with insufficient epistemic success.
- 20.
Scholl and Räz adopt the distinction between “how possibly” and “how actually” from the discussion on mechanistic explanation (Machamer et al. 2000), a discussion that has been up until recently relatively disinterested in modeling and that considered models as explanation sketches only (see Knuuttila and Loettgers 2013).
- 21.
The “how-possible” may be a bit misleading expression in this context, since what Volterra accomplished was an alternative explanation for the prevailing explanations that attributed the fluctuations to external causes.
- 22.
A model template is an abstract conceptual idea concerning usually a certain kind of interaction and associated with particular mathematical forms and computational methods, see for further discussion Knuuttila and Loettgers (2014).
- 23.
Even though the differences between the three case studies with respect to Volterra’s work were more substantial, such underdetermination of theories by data would be a common feature of other scientific practices, too.
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Knuuttila, T., Loettgers, A. (2016). Contrasting Cases: The Lotka-Volterra Model Times Three. In: Sauer, T., Scholl, R. (eds) The Philosophy of Historical Case Studies. Boston Studies in the Philosophy and History of Science, vol 319. Springer, Cham. https://doi.org/10.1007/978-3-319-30229-4_8
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