The Concept And The Role Of The Model In Mathematics And Natural And Social Sciences

Proceedings of the Colloquium sponsored by the Division of Philosophy of Sciences of the International Union of History and Philosophy of Sciences organized at Utrecht, January 1960.

In this book Lee Rudolph brings together international contributors who combine psychological and mathematical perspectives to analyse how qualitative mathematics can be used to create models of social and psychological processes. Bridging the gap between the fields with an imaginative and stimulating collection of contributed chapters, the volume updates the current research on the subject, which until now has been rather limited, focussing largely on the use of statistics. Qualitative Mathematics for the Social Sciences contains a variety of useful illustrative figures, introducing readers from the social sciences to the rich contribution that modern mathematics has made to our knowledge of logic, structures, and dynamic systems. A beguiling array of conceptual systems, topological models and fractals are discussed which transcend the application of statistics, and bring a fresh perspective to the study of social representations. The wide selection of qualitative mathematical methodologies discussed in this volume will be hugely valuable to higher-level undergraduate and postgraduate students of psychology, sociology and mathematics. It will also be useful for researchers, academics and professionals from the social sciences who want a firmer grasp on the use of qualitative mathematics.

Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.

First published in 1968, this book explores the theme of geographical generalization, or model building. It is composed of seven of the chapters from the original Models in Geography, published in 1967. The first chapter broadly outlines this theme and examines the nature and function of generalized statements, ranging from conceptual models to scale models, in a geographical context. The following six chapters deal with socio-economic building in geography. They focus on demographic and sociological models as well as looking at special aspects of models in human geography in reference to economic development, urban geography and settlement location, industrial location, and agricultural activity. This book represents a robustly anti-idiographic statement of modern work in one of the major branches of geography.

Computer simulation has become an important means for obtaining knowledge about nature. The practice of scientific simulation and the frequent use of uncertain simulation results in public policy raise a wide range of philosophical questions. Most prominently highlighted is the field of anthropogenic climate change—are humans currently changing the climate? Referring to empirical results from science studies and political science, Simulating Nature: A Philosophical Study of Computer-Simulation Uncertainties and Their Role in Climate Science and Policy Advice, Second Edition addresses questions about the types of uncertainty associated with scientific simulation and about how these uncertainties can be communicated. The author, who participated in the United Nations’ Intergovernmental Panel on Climate Change (IPCC) plenaries in 2001 and 2007, discusses the assessment reports and workings of the IPCC. This second edition reflects the latest developments in climate change policy, including a thorough update and rewriting of sections that refer to the IPCC.

The 31st European Symposium on Computer Aided Process Engineering: ESCAPE-31, Volume 50 contains the papers presented at the 31st European Symposium of Computer Aided Process Engineering (ESCAPE) event held in Istanbul, Turkey. It is a valuable resource for chemical engineers, chemical process engineers, researchers in industry and academia, students and consultants in the chemical industries. Presents findings and discussions from the 31st European Symposium of Computer Aided Process Engineering (ESCAPE) event