Earlier in this century, many philosophers of science (for example, Rudolf Carnap) drew a fairly sharp distinction between theory and observation, between theoretical terms like 'mass' and 'electron', and observation terms like 'measures three meters in length' and 'is _2° Celsius'. By simply looking at our instruments we can ascertain what numbers our measurements yield. Creatures like mass are different: we determine mass by calculation; we never directly observe a mass. Nor an electron: this term is introduced in order to explain what we observe. This (once standard) distinction between theory and observation was eventually found to be wanting. First, if the distinction holds, it is difficult to see what can characterize the relationship between theory :md observation. How can theoretical terms explain that which is itself in no way theorized? The second point leads out of the first: are not the instruments that provide us with observational material themselves creatures of theory? Is it really possible to have an observation language that is entirely barren of theory? The theory-Iadenness of observation languages is now an accept ed feature of the logic of science. Many regard such dependence of observation on theory as a virtue. If our instruments of observation do not derive their meaning from theories, whence comes that meaning? Surely - in science - we have nothing else but theories to tell us what to try to observe.

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"Examines the achievements of science that further our understanding of the natural universe, and the possible extent and limitations of those achievements." -- Preface.

This is a thorough and comprehensive treatment of the theory of NP-completeness in the framework of algebraic complexity theory. Coverage includes Valiant's algebraic theory of NP-completeness; interrelations with the classical theory as well as the Blum-Shub-Smale model of computation, questions of structural complexity; fast evaluation of representations of general linear groups; and complexity of immanants.

The first comprehensive exploration of the nature and value of understanding, addressing burgeoning debates in epistemology and philosophy of science.

This book is the first systematic treatment of measures on projection lattices of von Neumann algebras. It presents significant recent results in this field. One part is inspired by the Generalized Gleason Theorem on extending measures on the projection lattices of von Neumann algebras to linear functionals. Applications of this principle to various problems in quantum physics are considered (hidden variable problem, Wigner type theorems, decoherence functional, etc.). Another part of the monograph deals with a fascinating interplay of algebraic properties of the projection lattice with the continuity of measures (the analysis of Jauch-Piron states, independence conditions in quantum field theory, etc.). These results have no direct analogy in the standard measure and probability theory. On the theoretical physics side, they are instrumental in recovering technical assumptions of the axiomatics of quantum theories only by considering algebraic properties of finitely additive measures (states) on quantum propositions.

What is it to be scientific? Is there such a thing as scientific method? And if so, how might such methods be justified? Robert Nola and Howard Sankey seek to provide answers to these fundamental questions in their exploration of the major recent theories of scientific method. Although for many scientists their understanding of method is something they just pick up in the course of being trained, Nola and Sankey argue that it is possible to be explicit about what this tacit understanding of method is, rather than leave it as some unfathomable mystery. They robustly defend the idea that there is such a thing as scientific method and show how this might be legitimated. This book begins with the question of what methodology might mean and explores the notions of values, rules and principles, before investigating how methodologists have sought to show that our scientific methods are rational. Part 2 of this book sets out some principles of inductive method and examines its alternatives including abduction, IBE, and hypothetico-deductivism. Part 3 introduces probabilistic modes of reasoning, particularly Bayesianism in its various guises, and shows how it is able to give an account of many of the values and rules of method. Part 4 considers the ideas of philosophers who have proposed distinctive theories of method such as Popper, Lakatos, Kuhn and Feyerabend and Part 5 continues this theme by considering philosophers who have proposed naturalised theories of method such as Quine, Laudan and Rescher. This book offers readers a comprehensive introduction to the idea of scientific method and a wide-ranging discussion of how historians of science, philosophers of science and scientists have grappled with the question over the last fifty years.

Looks at religious, philosophical, and scientific theories surrounding the nature and origin of the universe, covering such topics as the Big bang theory, general relativity, quantum theory, evolution, and creationism.

The development of physical theory is one of our greatest intellectual achievements. Its products--the currently prevailing theories of physics, astronomy, and cosmology--have proved themselves to possess intrinsic beauty and to have enormous explanatory and predictive power. This anthology of primary readings chronicles the birth and maturation of five such theories (the heliocentric theory, the electromagnetic field theory, special and general relativity, quantum theory, and the big bang theory) in the words of the scientists who brought them to life. It is the first historical account that captures the rich substance of these theories, each of which represents a fascinating story of the interplay of evidence and insight--and of dialogue among great minds. Readers sit in with Copernicus, Kepler, and Galileo as they overturn the geocentric universe; observe the genius of Faraday and Maxwell as they "discover" the electromagnetic field; look over Einstein's shoulder as he works out the details of relativity; listen in as Einstein and Bohr argue for the soul of quantum mechanics in the Completeness Debate; and watch as Hubble and others reveal the history of the universe. The editors' approach highlights the moments of discovery that rise from scientific creativity, and the presentation humanizes the scientific process, revealing the extent to which great scientists were the first to consider the philosophical implications of their work. But, most significantly, the editors offer this as their central thesis: although each was ushered in by a revolution, and each contains counterintuitive elements that delayed its acceptance, these five theories exhibit a continuous rational development that has led them to a permanent place in the worldview of science. Accessible to the general reader yet sufficiently substantive that working scientists will find value in it, The Tests of Time offers an intimate look into how physical theory has been developed, by the brilliant people who have developed it.