Natalia Carrillo

This chapter discusses the question of how models and theories relate. Its main contention is that there is no such thing as “the” relation between models and theories: models can stand in a multiplicity of relations to theories. After a brief review of how the relation between models and theories is analysed in the Syntactic View and the Semantic View of theories, the chapter discusses cases in which models are independent from theories, designed to explore properties of theories, live in a symbiotic relation with theories by completing them, aid the application of abstract theories to concrete target systems, and serve as mediators between theory and the world. The chapter then discusses where the line between models and theories should be drawn, and it ends with a short conclusion.

This chapter discusses the question of how models and theories relate. Its main contention is that there is no such thing as “the” relation between models and theories: models can stand in a multiplicity of relations to theories. After a brief review of how the relation between models and theories is analysed in the Syntactic View and the Semantic View of theories, the chapter discusses cases in which models are independent from theories, designed to explore properties of theories, live in a symbiotic relation with theories by completing them, aid the application of abstract theories to concrete target systems, and serve as mediators between theory and the world. The chapter then discusses where the line between models and theories should be drawn, and it ends with a short conclusion.

In this chapter we put the work of Finnish conceptual and environmental artist, Lauri Anttila (1938–2022), in dialogue with discussions of the practices of scientific and mathematical representation. We are interested in the counterintuitive claim that abstraction crucially involves concreteness: instead of thinking about abstraction in opposition to the concrete, we focus on the importance of concrete actions, methods, and instruments in achieving abstract representations. In particular, we study the process of abstraction as a chain of “material translations” that engages with our cognitive abilities, representational and other artefacts, and diverse epistemic contexts in various ways. To examine and illustrate abstraction as material translation, we study Anttila’s work, Homage to Werner Holmberg (1985–1986), which parodies scientific representation in seeking to render with scientific methods the landscapes in the paintings of Werner Holmberg, a Finnish landscape artist from the 19th century. We study the striking parallels between Anttila’s artwork and the writings on scientific representation by Bruno Latour and Michael Lynch. The comparison of these analyses of scientific abstraction, rendered both artistically and through scholarly discussion, allows us to widen the scope of the philosophical discussion of abstraction in science that has so far been too narrowly focused on omission.

En este trabajo defiendo la importancia de tomar en cuenta el papel de las normas implícitas en las prácticas en una noción de objetividad científica. Expongo la noción tradicional de objetividad según la cual la ciencia es objetiva en la medida en que nos proporciona representaciones absolutas del mundo tal como es “independientemente de nuestra mente”. Después discuto las limitaciones de esta perspectiva y propongo en su lugar la objetividad dialéctica, que se caracteriza como una cuestión de grado que se asocia con la evolución de los sistemas de compromisos: un sistema es más objetivo mientras más cerca esté del equilibrio reflexivo. Esta alternativa deja en la incertidumbre el papel de las normas implícitas en las prácticas. Para fortalecerla propongo ampliar la noción de equilibro reflexivo para que pueda gestionar mejor los sesgos que conllevan este tipo de normas.

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as they apply to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all.

New mechanical philosophy posits that explanations in the life sciences involve the decomposition of a system into its entities and their respective activities and organization that are responsible for the explanandum phenomenon. This mechanistic account of explanation has proven problematic in its application to mathematical models, leading the mechanists to suggest different ways of aligning abstract models with the mechanist program. Initially, the discussion centered on whether the Hodgkin-Huxley model is explanatory. Network models provided another complication, as they apply to a wide number of materially diverse systems. In this article, we examine the various attempts to integrate abstract models within the mechanist program, also presenting a further challenge: the Heimburg-Jackson model, which was introduced as an alternative to the Hodgkin-Huxley model. We argue that although the notion of abstraction as the omission of irrelevant mechanistic details appears to give a mechanistic solution for accommodating abstract models, this notion does not suit models whose epistemic strategy is not decompositional. As a result, the mechanist has to choose whether to dilute the mechanistic approach nearly beyond recognition or to claim that many, if not most, abstract theoretical models do not deliver mechanistic explanations, or qualify as explanatory at all.

In philosophy of science, abstraction tends to be subsumed under representation, often being described as the omission of a target’s features when it is represented. This approach to abstraction sidesteps cognitive aspects of abstraction processes. However, cognitive aspects of abstraction are important in understanding the role of historically grounded epistemic criteria supporting modeling in science. Drawing on recent work on the relation between metaphor and abstraction, we introduce the concept of paths of abstraction, and use historical and contemporary examples to point to their role in guiding the development of relevance criteria which support modeling strategies in science.

Natalia Carrillo and Tarja Knuuttila claim that there are two traditions of thinking about idealization offering almost opposite views on their functioning and epistemic status. While one tradition views idealizations as epistemic deficiencies, the other one highlights the epistemic benefits of idealization. Both of them treat idealizations as deliberate misrepresentations, however. They then argue for an artifactual account of idealization, comparing it to the traditional accounts of idealization, and exemplifying it through the Hodgkin and Huxley model of the nerve impulse. From the artifactual perspective, the epistemic benefits and deficiencies introduced by idealization frequently come in a package due to the way idealization draws together different resources in model construction. Accordingly, idealization tends to be holistic in that it is not often easily attributable to some specific parts of the model. They conclude that the artifactual approach offers a unifying view into idealization in that it is able to recover several basic philosophical insights motivating both the deficiency and epistemic benefit accounts, while being simultaneously detached from the idea of distortion by misrepresentation.

Idealization is commonly understood as distortion: representing things differently than how they actually are. In this paper, we outline an alternative artifactual approach that does not make misrepresentation central for the analysis of idealization. We examine the contrast between the Hodgkin-Huxley (1952a, b, c) and the Heimburg-Jackson (2005, 2006) models of the nerve impulse from the artifactual perspective, and argue that, since the two models draw upon different epistemic resources and research programs, it is often difficult to tell which features of a system the central assumptions involved are supposed to distort. Many idealizations are holistic in nature. They cannot be locally undone without dismantling the model, as they occupy a central position in the entire research program. Nor is their holistic character mainly related to the use of mathematical and statistical modeling techniques as portrayed by Rice (2018, 2019). We suggest that holistic idealizations are implicit theoretical and representational assumptions that can only be understood in relation to the conceptual and representational tools exploited in modeling and experimental practices. Such holistic idealizations play a pivotal role not just in individual models, but also in defining research programs.

Discussion of modeling within philosophy of science has focused in how models, understood as finished products, represent the world. This approach has some issues accounting for the value of modeling in situations where there are controversies as to which should be the object of representation. In this work I show that a historical analysis of modeling complements the aforementioned representational program, since it allows us to examine processes of integration of analogies that play a role in the generation of criteria of relevance, which are important for the configuration of the object of research. This, in turn, shows that there are norms in modeling practices whose historical reconstruction is relevant for their philosophical analysis.