The present work is a systematic study of five frameworks or perspectives articulating mathematical structuralism, whose core idea is that mathematics is concerned primarily with interrelations in abstraction from the nature of objects. The first two, set-theoretic and category-theoretic, arose within mathematics itself. After exposing a number of problems, the Element considers three further perspectives formulated by logicians and philosophers of mathematics: sui generis, treating struct...

Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially. There is something viscous about the continuous. It is a unified whole. This is in stark contrast with the prevailing contemporary account, which takes a continuum to be composed of an uncountably infinite set of points. This vlume presents a collective study of key...

With this third edition of Nelson Goodman's The Structure of Appear ance, we are pleased to make available once more one of the most in fluential and important works in the philosophy of our times. Professor Geoffrey Hellman's introduction gives a sustained analysis and appreciation of the major themes and the thrust of the book, as well as an account of the ways in which many of Goodman's problems and projects have been picked up and developed by others. Hellman also suggests how The Stru...

This book explores the research of Professor Hilary Putnam, a Harvard professor as well as a leading philosopher, mathematician and computer scientist. It features the work of distinguished scholars in the field as well as a selection of young academics who have studied topics closely connected to Putnam’s work.It includes 12 papers that analyze, develop, and constructively criticize this notable professor's research in mathematical logic, the philosophy of logic and the philosophy...