Sets are central to mathematics and its foundations, but what are they? In this book Luca Incurvati provides a detailed examination of all the major conceptions of set and discusses their virtues and shortcomings, as well as introducing the fundamentals of the alternative set theories with which these conceptions are associated. He shows that the conceptual landscape includes not only the naïve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.
New York Times bestseller • Finalist for the Pulitzer Prize“This is a book to shake up the world.” —Ann PatchettNicholas Carr’s bestseller The Shallows has become a foundational book in one of the mos
Can we can use the patterns and processes of convergent evolution to make inferences about universal laws of life, on Earth and elsewhere?In this book, Russell Powell investigates whether we can use t
In this Element, we extend our earlier treatment of biology's first law. The law says that in any evolutionary system in which there is variation and heredity, there is a tendency for diversity and complexity to increase. The law plays the same role in biology that Newton's first law plays in physics, explaining what biological systems are expected to do when no forces act, in other words, what happens when nothing happens. Here we offer a deeper explanation of certain features of the law, develop a quantitative version of it, and explore its consequences for our understanding of diversity and complexity.
