This paper is a critical response to Andreas Bartels’ 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. (shrink)

This volume of Metatheoria includes translations into Spanish of the three famous papers on the schools in foundations of mathematics, logicism, intuitionism and formalism, presented at the Königsberg’s Symposium on Foundations of Mathematics in September 1930 and finally published in the journal Erkenntnis in 1931. The three papers constituted a milestone in the Philosophy of Mathematics of the last century. In this introduction to the translations, the editors of the volume outline the historical context in which the original papers were (...) conceived and they include some details concerning their original publication. They also stress the decisive role played by the papers in the philosophy of mathematics in the last century. A summary of them is provided and the underlying ideas of the Vienna Circle on the nature of mathematics and the impact of Gödel theorems in the foundations programs are discussed. Moreover, they briefly introduce the original contributions to the volume that follow the translations. (shrink)