Overview

This book is about “diamond”, a logic of paradox. In diamond, a statement can be true yet false; an “imaginary” state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued boolean logic. Diamond is a new way to solve the dilemmas of higher mathematics. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book consists of two sections: Elementary; which covers the classic paradoxes of mathematical logic and shows how they can be resolved in this new system; and Advanced, which relates diamond to Boolean logic, three-valued logic, Gödelian meta-mathematics and dilemma games.

Full Product Details

Author:   Nathaniel S Hellerstein (City College Of San Francisco, Usa)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   14
Dimensions:   Width: 16.10cm , Height: 2.00cm , Length: 22.00cm
Weight:   0.494kg
ISBN:  

9789810228507

ISBN 10:   9810228503
Pages:   272
Publication Date:   04 January 1997
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Part 1 Paradoxes: Russell's paradox; Heap paradoxes; game paradoxes. Part 2 Diamond: diamond values; harmonic functions; diamond circuits; Brownian forms. Part 3 Diamond laws. Part 4 Self-reference: re-entrance and fixed points; phase order; the outer fixed points. Part 5 Fixed point lattices: relative lattices; shared fixed points. Part 6 Limit logic: limit fixed points; diamond computation. Part 7 Paradox resolved: Russell's paradox; Santa sentences; antistrephon; Heap paradoxes; game paradoxes. Part 8 The continuum: Cantor's paradox; Dedekind splices; Zeno's theorem. Part 9 Analytic functions - harmonic analysis - 3-logic metamathematics - dilemma: prisoner's dilemma; dilemma as diamond metric; banker's dilemma. Part 10 Speculations: diamond types?; null quotients?; general lattices?; general waves?.

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