Abstract
The semantic view of theories is normally considered to be an account of theories congenial to Scientific Realism. Recently, it has been argued that Ontic Structural Realism could be fruitfully applied, in combination with the semantic view, to some of the philosophical issues peculiarly related to biology. Given the central role that models have in the semantic view, and the relevance that mathematics has in the definition of the concept of model, the focus will be on population genetics, which is one of the most mathematized areas in biology. We will analyse some of the difficulties which arise when trying to use Ontic Structural Realism to account for evolutionary biology.
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- 1.
Magnus (2010, p. 804).
- 2.
Cf. French and Ladyman (2003, p. 45): “structural realism is supposed to be realist enough to take account of the no-miracles argument”.
- 3.
See Frigg and Votsis (2011) for a survey on SSR. For a definition of structure, cf., e.g., Ibidem, p. 229: “A structure S consists of (a) a non-empty set U of objects, which form the domain of the structure, and (b) a non-empty indexed set R (i.e. an ordered list) of relations on U, where R can also contain one-place relations”.
- 4.
For technical details and examples, see (Halvorson 2012). Here the room suffices just to sketch Halvorson’s argument in five points: (1) given that, according to the semantic view, a theory is a class of models, if we have two classes of models , \({\mathcal{M}}\) and \({\mathcal{M}}^{\prime }\), under which conditions should we say that they represent the same theory? (2) Semanticists (e.g., Giere , Ladyman , Suppe , van Fraassen ) have not offered any sort of explicit definition of the form: (X) \({\mathcal{M}}\) is the same theory as \({\mathcal{M}}^{\prime }\) if and only if (iff)… (3) “Suppe ’s claim that ‘the theories will be equivalent just in case we can prove a representation theorem showing that \({\mathcal{M}}\) and \({\mathcal{M}}^{\prime }\) are isomorphic (structurally equivalent)’ […] just pushes the question back one level—we must now ask what it means to say that two classes of models are ‘isomorphic’ or ‘structurally equivalent’” (Halvorson 2012, p. 190). (4) He then considers the following three proposals for defining the notion of an isomorphism between \({\mathcal{M}}\) and \({\mathcal{M}}^{\prime }\): (a) Equinumerous: \({\mathcal{M}}\) is the same theory as \({\mathcal{M}}^{\prime }\) iff \({\mathcal{M}} \simeq {\mathcal{M}}^{\prime } ;\) that is, there is a bijection \(F:{\mathcal{M}} \to {\mathcal{M}}^{\prime }\). (b) Pointwise isomorphism of models: \({\mathcal{M}}\) is the same theory as \({\mathcal{M}}^{\prime }\), just in case there is a bijection \(F:{\mathcal{M}} \to {\mathcal{M}}^{\prime }\) such that each model \(m \in {\mathcal{M}}\) is isomorphic to its paired model \(F\left( m \right) \in {\mathcal{M}}^{\prime }\). (c) Identity: \({\mathcal{M}}\) is the same theory as \({\mathcal{M}}^{\prime }\), just in case \({\mathcal{M}} = {\mathcal{M}}^{\prime }\). (5) Finally, he tests such proposals and shows how they all fail, and thus makes it clear that it is impossible to formulate good identity criteria for theories when they are considered as classes of models .
- 5.
Lloyd (1984, p. 244).
- 6.
At least in the measure in which Psillos doesn’t give a different account of how to consider a theory to be empirically confirmed.
- 7.
French (2014, p. 195, fn 7).
- 8.
French (2014, pp. 274–275).
- 9.
To understand Fisher’s understanding of the FTNS, we have to accept Fisher’s view of ‘environment’: any change in the average effects constitutes an ‘environmental’ change. On the constancy of environment, cf. Okasha (2008, p. 331): “For Fisher, constancy of environment from one generation to another meant constancy of the average effects of all the alleles in the population. Recall that an allele’s average effect (on fitness) is the partial regression of organismic fitness on the number of copies of that allele.” Cf., also, Ibidem, p. 324: “an allele’s average effect may change across generations, for it will often depend on the population’s genetic composition”.
- 10.
See Otsuka (2014) for a survey.
- 11.
Matthen and Ariew (2009, p. 222).
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Sterpetti, F. (2016). Scientific Realism, the Semantic View and Evolutionary Biology. In: Ippoliti, E., Sterpetti, F., Nickles, T. (eds) Models and Inferences in Science. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-28163-6_4
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