This paper offers some historical and conceptual remarks on the philosophical and logical procedures of abstraction, based on an account of the notions of concept and function. In order to provide a complete analyis, one should start by considering Plato’s theory of Ideas, which provides the first interpretation of “abstract terms” in the history of philosophy1. The nature of the most general F...

The purpose of the series is to make available to specialists and the interested public the results of research that, because of its unconventional or controversial nature, might otherwise go unpublished. The editor actively encourages younger, not yet well established, scholars and independent authors to submit manuscripts for consideration. Contributions in any of the major scholarly language...

We study translation covers of several triply periodic polyhedral surfaces that are intrinsically Platonic. describe their affine symmetry groups and compute the quadratic asymptotics for counting saddle connections cylinders, including count cylinders weighted by area. The mathematical was initiated Novikov, motivated electron transport. we consider particular interest as they admit different ...

We consider rotations A; B of nite order in SO(3), about axes separated by an angle of restricted type, and attempt to classify the possible group relations between A and B. We show that the relations responsible for the symmetries of the Platonic solids have consequencies far beyond that simple geometric setting.