Natalia Carrillo Giraldo

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.