It is a commonplace that “the map is not the territory.” The phrase goes back to Alfred Korzybski, while the insight—formulated by insisting on an apparent triviality—is surely older and has received poetical expressions from Lewis Carroll and Jorge Luis Borges among others. The difference between map and territory is a difference of categories and is at the base of the representation relation. Hence maps play a prominent role in the discourse about representation which takes place in a number of (...) disciplines and from different perspectives. Three of them are of special interest for the present paper.One influential view has been put forward by historian of art Ernst Gombrich in his classical lecture on.. (shrink)

As an illustration of the complexities involved in connecting physics and molecular biology at the nanoscale, in this paper I discuss two case studies from nanoscience. The first examines the use of a biological structure to build nanostructures in a controlled way. The second discusses the attempt to build a single molecular wire, and then decide whether such a wire is indeed conducting. After presenting the central features of each case study, I examine the role played in them by microscopic (...) imaging, the different styles of reasoning involved, and the various theoretical, methodological, and axiological differences. I conclude by arguing that, except for the probe microscopes that are used, there is very little in common between the two cases. At the nanoscale, physics and molecular biology seem to meet in a non-unified way. (shrink)

A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. (...) In this paper, we discuss the shortcomings of this account, and show how these shortcomings can be overcome by a broader view of the application of mathematics: the inferential conception. (shrink)