David Miller elegantly and provocatively reformulates critical rationalism—the revolutionary approach to epistemology advocated by Karl Popper—by answering its most important critics. He argues for an approach to rationality freed from the debilitating authoritarian dependence on reasons and justification."Miller presents a particularly useful and stimulating account of critical rationalism. His work is both interesting and con ...
This book is the sixth volume of reviews on advanced problems of phase transitions and critical phenomena, with the first five volumes appearing in 2004, 2007, 2012, 2015, and 2018. It aims to provide an overview of those aspects of criticality and related topics that have attracted much attention due to the recent contributions. The six chapters discuss criticality of complex systems, where the new, emergent properties appear via collective beh ...
A deeply skeptical and incisively analytical examination of exceptional breadth, this book explores the range of what we call the sciences, revealing the important things that we do not know about nearly everything that matters. ...
Truth used to be based on reason. No more. What we feel is now the truest source of reality. Despite our obsession with the emotive and the experiential, we still face anxiety, despair, and purposelessness.How did we get here? And where do we find a remedy? In this modern classic, Francis A. Schaeffer traces trends in twentieth-century thought and unpacks how key ideas have shaped our society. Wide-ranging in his analysis, Schaeffer examines ph ...
These counterexamples, arranged according to difficulty or sophistication, deal mostly with the part of analysis known as «real variables,» starting at the level of calculus. The first half of the book concerns functions of a real variable; topics include the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, uniform convergence, and sets and measure on the real axis. The second half, enco ...
Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, num ...
One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: «Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?» Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best trea ...
