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.
Immunology is central to contemporary biology and medicine, but it also provides novel philosophical insights. Its most significant contribution to philosophy concerns the understanding of biological individuality: what a biological individual is, what makes it unique, how its boundaries are established and what ensures its identity through time. Immunology also offers answers to some of the most interesting philosophical questions. What is the definition of life? How are bodily systems delineated? How do the mind and the body interact? In this Element, Thomas Pradeu considers the ways in which immunology can shed light on these and other important philosophical issues. This title is also available as Open Access on Cambridge Core.
Why the social character of scientific knowledge makes it trustworthyDo doctors really know what they are talking about when they tell us vaccines are safe? Should we take climate experts at their wor
Scientific advances have transformed the world. However, science can sometimes get things wrong, and at times, disastrously so. Understanding the basis for scientific claims and judging how much confidence we should place in them is essential for individual choice, societal debates, and development of public policy and laws. We must ask: what is the basis of scientific claims? How much confidence should we put in them? What is defined as science and what is not? This book synthesizes a working definition of science and its properties, as explained through the eyes of a practicing scientist, by integrating advances from philosophy, psychology, history, sociology, and anthropology into a holistic view. Crucial in our political climate, the book fights the myths of science often portrayed to the public. Written for a general audience, it also enables students to better grasp methodologies and helps professional scientists to articulate what they do and why.
Scientific advances have transformed the world. However, science can sometimes get things wrong, and at times, disastrously so. Understanding the basis for scientific claims and judging how much confidence we should place in them is essential for individual choice, societal debates, and development of public policy and laws. We must ask: what is the basis of scientific claims? How much confidence should we put in them? What is defined as science and what is not? This book synthesizes a working definition of science and its properties, as explained through the eyes of a practicing scientist, by integrating advances from philosophy, psychology, history, sociology, and anthropology into a holistic view. Crucial in our political climate, the book fights the myths of science often portrayed to the public. Written for a general audience, it also enables students to better grasp methodologies and helps professional scientists to articulate what they do and why.
The practice of paleontology has an aesthetic as well as an epistemic dimension. Paleontology has distinctively aesthetic aims, such as cultivating sense of place and developing a better aesthetic appreciation of fossils. Scientific cognitivists in environmental aesthetics argue that scientific knowledge deepens and enhances our appreciation of nature. Drawing on that tradition, this Element argues that knowledge of something's history makes a difference to how we engage with it aesthetically. This means that investigation of the deep past can contribute to aesthetic aims. Aesthetic engagement with fossils and landscapes is also crucial to explaining paleontology's epistemic successes.
