Models and Representation

Vincent Ardourel (KU Leuven), Anouk Barberousse (Paris Sorbonne Université), Cyrille Imbert (CNRS)
Scientific models need to be investigated if they are to provide valuable information about the systems they represent. Surprisingly, the epistemological question of what enables this investigation has hardly been investigated. Even authors who consider the inferential role of models as central, like Hughes (1997) or Bueno and Colyvan (2011), content themselves with claiming that models contain "mathematical resources" that provide "inferential power". We claim that these notions require further analysis and argue that mathematical formalisms contribute to this inferential role. We characterize formalisms, illustrate how they extend our mathematical resources, and highlight how distinct formalisms offer various inferential affordances.

James Nguyen (University of Notre Dame)
It is commonly assumed that idealised models misrepresent their target systems. And as such the role(s) of idealisations in science seem mysterious: how can misrepresentations accurately predict, explain, or generate understanding about, target system behaviour? In this paper I argue that this mystery is mistaken. That models are distortions of their target systems does not entail that they misrepresent them. By drawing on interpretational accounts of scientific representation -- accounts that diverge from the idea that models are `intended copies' of their targets -- I argue that models which distort aspects of their target systems, even with respect to essential features of the target behaviour, can nevertheless be considered accurate representations, even with respect to those very features, assuming that they are interpreted correctly. I illustrate this way of thinking about idealisation in science with the example of interpreting flat 2D maps of the earth's surface as well as models involving taking some parameter to a limit, both of which are commonly assumed to contain `essential idealisations'.

Guilherme Sanches de Oliveira (University of Cincinnati)
A powerful idea put forward in the recent philosophy of science literature is that scientific models are best understood as instruments, tools or, more generally, artifacts. This view ('artifactualism') is independent from the traditional philosophical approach of analyzing models as representations. Current artifactual accounts recognize this independence but still incorporate representational elements, treating models as representational tools or instruments. This article argues that a leaner version of artifactualism, free of representationalist assumptions, is both desirable and viable. Taking seriously the idea that models are artifacts elucidates a number of philosophical issues concerning scientific modeling while also dissolving puzzles about representation.

Yoichi Ishida (Ohio University)
Weisberg and others argue that equations are not mathematical models; equations are statements describing a model. I argue that equations function as iconic representations of physical systems. In the qualitative analysis of ordinary differential equations (ODEs), scientists rely on graphical/visual techniques to analyze ODEs. Using this example and Peirce's and Haugeland's theories of representation, I explain the iconicity of ODEs and show that my account makes better sense of the role of ODEs in mathematical modeling. Equations are like diagrams rather than sentences, and it is not a mistake to regard equations as models.

Armond Duwell (University of Montana)
This paper has two aims. One aim is to argue against the view that explanations of phenomena are essential to understanding them, as suggested by the received view associated with Strevens (2013), Grimm (2014), or Khalifa (2017), among others. The second is to argue that the modal view of understanding phenomena developed in Le Bihan (2017) and Duwell (forthcoming), a non-explationist view of understanding, doesn't succumb to objections that can be leveled at it.