Inconsistent mathematics

by Mortensen, Chris

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Title Statements

Full title :Inconsistent mathematics / by Chris Mortensen.

Summary

The theory of inconsistency has been growing steadily over the last two decades. One focus has been philosophical issues arising from the paradoxes of set theory and semantics. A second focus has been the study of paraconsistent, or inconsistency-tolerant, logics. A third focus has been the application of paraconsistent logics to problems in artificial intelligence. This book focuses on a fourth aspect, the construction of mathematical theories in which contradictions occur, and the investigation of their properties. The inconsistent approach provides a distinctive perspective on the various number systems, order, differential and integral calculus, discontinuous changes, inconsistent systems of linear equations, projective geometry, topology and category theory. The final chapter outlines several known results concerning paradoxes in the foundations of set theory and semantics.

The book begins with an informal chapter which summarises the main results nontechnically, and draws philosophical implications from them. This volume will be of interest of advanced undergraduates, graduate students and professionals in the areas of logic, philosophy, mathematics and theoretical computer science.

Edition Statements

Publication Date:©1995.

Publication Statements

Publisher(s):Kluwer Academic
Place of Publication:Dordrecht
Language:eng
Publication Date:©1995.

The Physical Object

Description:ix, 155 pages : : illustrations ; : 25 cm

Edition Identifiers

ISBN:0792331869, 9780792331865, 9789048144808, 9048144809
oclc:ocm31240354
LC Classification:QA9
Dewey Decimal:510/.1

1. Motivations -- 2. Arithmetic -- 3. Modulo Infinity -- 4. Order -- 5. Calculus -- 6. Inconsistent Continuous Functions -- 7. The Delta Function -- 8. Inconsistent Systems of Linear Equations -- 9. Projective Spaces -- 10. Topology -- 11. Category Theory / Chris Mortensen and Peter Lavers -- 12. Closed Set Sheaves and Their Categories / William James -- 13. Duality -- 14. Foundations: Provability, Truth and Sets / Chris Mortensen and Joshua Cole.

Subjects

Inconsistance (Logique) Inconsistency (Logic) Logic, Symbolic and mathematical logica Logique symbolique et mathématique mathematics Parakonsistente Logik