The Square Circle

Abstract

AbstractThis article shows that there are square circles (or equivalently, round squares) in the sense that there are mathematical objects that are at the same time both perfectly circular and perfectly square. The philosophical significance of this is discussed, especially in view of philosophy's widespread use of “square circle” as a typical example of an impossibility. In particular, the focus is on what the existence of square circles means for the possibility of conceptual analysis, and more generally what we can learn about the nature of non‐formal concepts and their use in philosophy.