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An exposition of second- and higher-order logic and type theory. It includes the syntax and semantics of classical second-order logic and a discussion of higher-order logic based on the concept of a type. Also explored are origins and nature of type theory, its relationship to set theory, and descriptions of contemporary forms of type theory.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled 'The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages, ' reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks, the elements of early Chinese, India...

Bell explores the psalms and what they might yield in relation to the challenges of everyday life.

This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy.  Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages, ’  reviews the work of Plato, Aristotle, Epicurus, and other  Ancient Greeks, the elements of early Chinese, In...

For over twenty-five years, this book has guided student writers through the struggles that come with writing dissertations and theses. It offers guidance to students through all the essential steps, including defining topics, selecting faculty advisors, and conducting, analysing, writing, presenting, and publishing research.

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The nature of expressing sorrow and despair as both acceptable to God and essential for mental and spiritual health is reflected on in this book and CD guide to the consolations of faith in periods of grief.

Logical Options introduces the extensions and alternatives to classical logic which are most discussed in the philosophical literature: many-sorted logic, second-order logic, modal logics, intuitionistic logic, three-valued logic, fuzzy logic, and free logic.

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Explains and investigates the paradoxes and puzzles that arise out of conceptual oppositions in physics and mathematics. In the process, John L. Bell not only motivates abstract conceptual thinking about the paradoxes at issue, he also offers a compelling introduction to central ideas in such otherwise difficult topics as non-Euclidean geometry, relativity, and quantum physics.

While intuitionistic (or constructive) set theory IST has received a certain attention from mathematical logicians, so far as I am aware no book providing a systematic introduction to the subject has yet been published. This may be the case in part because, as a form of higher-order intuitionistic logic - the internal logic of a topos - IST has been chiefly developed in a tops-theoretic context. In particular, proofs of relative consistency wi...

Details economic dislocations in North Carolina during the severest years of the depression. Separate chapters cover agriculture, banking, industry, labor, unemployment relief, government finances, blacks, transportation, and education.

A rigorous, axiomatically formulated presentation of the 'zero-square', or 'nilpotent' infinitesimal.

This book presents an overview of the development of the Axiom of Choice since its introduction by Zermelo at the beginning of the last century. The book surveys the Axiom of Choice from three perspectives. The first, or mathematical perspective, is that of the "working mathematician". This perspective brings into view the manifold applications of the Axiom of Choice-usually in the guise of Zorn`s Lemma- in a great variety of areas of mathemat...