The Axiom of Constructibility


Book Description




Constructibility


Book Description

A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.







Foundational Studies Selected Works


Book Description

Foundational Studies Selected Works




Construction of Architecture


Book Description

Buildings don't just appear. While the aesthetics and theory of architecture have their glamour, architecture would not exist without the hands-on, nuts-and-bolts process of construction. Construction of Architecture gives architects, contractors, managers, trade workers, and anyone else involved in a building project a thorough overview of the process of taking or converting a fine design concept from a paper exercise to a finished, full-sized, occupiable and usable building. In an easy-to-read, conversational style, Ralph Liebing distills the often-complex procedures in the construction of architecture into clear, understandable phases. Connecting each phase to the next, he takes you step-by-step from project inception and documentation to code compliance to bidding and the contract through finalization of the project and occupancy of the completed building. This book is enhanced with features such as: Drawings and photographs of the building process. Samples of documents used in construction. A concise narrative of the construction of a typical commercial building, from start to finish. An Instructor Companion Site with an expanded glossary and additional resources. With this primer in hand, every aspiring building professional will have the solid foundation in the concepts and skills needed to bring any building project to fruition, from inception to occupancy.




A Structural Account of Mathematics


Book Description

Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems areapplied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true.Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show howsuch systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalisticoutlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.A Structural Account of Mathematics will be required reading for anyone working in this field.







Ruler and the Round


Book Description

An intriguing look at the "impossible" geometric constructions (those that defy completion with just a ruler and a compass), this book covers angle trisection and circle division. 1970 edition.




The Logic of Infinity


Book Description

Few mathematical results capture the imagination like Georg Cantor's groundbreaking work on infinity in the late nineteenth century. This opened the door to an intricate axiomatic theory of sets which was born in the decades that followed. Written for the motivated novice, this book provides an overview of key ideas in set theory, bridging the gap between technical accounts of mathematical foundations and popular accounts of logic. Readers will learn of the formal construction of the classical number systems, from the natural numbers to the real numbers and beyond, and see how set theory has evolved to analyse such deep questions as the status of the continuum hypothesis and the axiom of choice. Remarks and digressions introduce the reader to some of the philosophical aspects of the subject and to adjacent mathematical topics. The rich, annotated bibliography encourages the dedicated reader to delve into what is now a vast literature.