Analogy, Identity, Equivalence

Category theory, possibly more than any other mathematical theory, has a rich philosophical significance. The reason why it has not been so far exploited by philosophers is that they know it, if at all, only superficially. In the present essay, I shall explore only one aspect of this theory, namely the way it contributes to our understanding of such concepts as: analogy, identity, equivalence. It goes without saying that these concepts play a paramount role not only in many scientific disciplines, but also in philosophy of science and in some fundamental ontological questions. They are notoriously difficult to be defined, and most often are used intuitively or only with the help of purely verbal clarifications. Within the category theory their meaning can be rigorously determined, and their definitions are not arbitrary but imposed, so to speak, by the mathematical context. And even more importantly, these definitions often reveal the variety of meanings never suspected outside the categorical context the meanings that can doubtlessly be adapted to enrich many traditional philosophical discussions.