Varieties of misrepresentation and homomorphism

Abstract

This paper is a critical response to Andreas Bartels' (2006) sophisticated defense of a structural account of scientific representation. We show that, contrary to Bartels' claim, homomorphism fails to account for the phenomenon of misrepresentation. Bartels claims that homomorphism is adequate in two respects. First, it is conceptually adequate, in the sense that it shows how representation differs from misrepresentation and non-representation. Second, if properly weakened, homomorphism is formally adequate to accommodate misrepresentation. We question both claims. First, we show that homomorphism is not the right condition to distinguish representation from misrepresentation and non-representation: a "representational mechanism" actually does all the work, and it is independent of homomorphism -as of any structural condition. Second, we test the claim of formal adequacy against three typical kinds of inaccurate representation in science which, by reference to a discussion of the notorious billiard ball model, we define as abstraction, pretence, and simulation. We first point out that Bartels equivocates between homomorphism and the stronger condition of epimorphism, and that the weakened form of homomorphism that Bartels puts forward is not a morphism at all. After providing a formal setting for abstraction, pretence and simulation, we show that for each morphism there is at least one form of inaccurate representation which is not accommodated. We conclude that Bartels' theory -while logically laying down the weakest structural requirements -is nonetheless formally inadequate in its own terms. This should shed serious doubts on the plausibility of any structural account of representation more generally.

Preschool Children’s Reasoning about Sound from an Inferential-Representational Approach

“…The inferential approach can be characterized by factors such as intentionality (referring to the subject's awareness of the purpose or finality of their representation). Interpretation implies recognizing elements that give meaning to the representation, and surrogate reasoning is based on the representation elements to create a hypothesis or explanation that can be applied to what is intended to be represented [35,37,38].…”

“…It is important to emphasize that, in this approach, the established representations (by the subject or others) constitute a tool or epistemic artefact, referring to an intentionally built entity materialized through some medium (object, image, or expressed symbol) and used in multiple ways [30][31][32][33][34][35][36][37][38][39][40][41]. The epistemic tool implies that a subject can build new representations whose level of functionality will be determined merely by the form of expression and by the possibilities given by the theoretical, empiric, and contextual elements that the subject provides.…”

The Representational Semantic Conception

“…The reason why the constituents of representation cannot be structural is related to the inherent diversity of scientific modeling, which is ubiquitously idealization ridden. Scientific representations may idealize in at least three different ways (Pero and Suárez 2016): by abstracting, by pretending, or by simulating-where the third is a combination of the former two. No morphism can account for all these forms of idealization.…”

“…And the question then remains whether there is a further weakening of homomorphism that could do this. Pero and Suárez (2016) canvass the different options and answer negatively.…”

Models and Representation

“…(For detailed discussions of homomorphism and partial isomorphism see Suárez's (2003, pp. 239-241) and Pero and Suárez's (2016); Mundy (1986) discusses general constraints one may want to impose on morphisms. )…”