Inconsistent Mathematics

  • Chris Mortensen

Part of the Mathematics and Its Applications book series (MAIA, volume 312)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Chris Mortensen
    Pages 1-14
  3. Chris Mortensen
    Pages 15-32
  4. Chris Mortensen
    Pages 33-38
  5. Chris Mortensen
    Pages 39-42
  6. Chris Mortensen
    Pages 43-58
  7. Chris Mortensen
    Pages 59-66
  8. Chris Mortensen
    Pages 67-72
  9. Chris Mortensen
    Pages 73-82
  10. Chris Mortensen
    Pages 83-92
  11. Chris Mortensen
    Pages 93-100
  12. Peter Lavers
    Pages 101-114
  13. William James
    Pages 115-124
  14. Chris Mortensen
    Pages 125-128
  15. Joshua Cole
    Pages 129-146
  16. Back Matter
    Pages 147-158

About this book

Introduction

without a properly developed inconsistent calculus based on infinitesimals, then in­ consistent claims from the history of the calculus might well simply be symptoms of confusion. This is addressed in Chapter 5. It is further argued that mathematics has a certain primacy over logic, in that paraconsistent or relevant logics have to be based on inconsistent mathematics. If the latter turns out to be reasonably rich then paraconsistentism is vindicated; while if inconsistent mathematics has seri­ ous restriytions then the case for being interested in inconsistency-tolerant logics is weakened. (On such restrictions, see this chapter, section 3. ) It must be conceded that fault-tolerant computer programming (e. g. Chapter 8) finds a substantial and important use for paraconsistent logics, albeit with an epistemological motivation (see this chapter, section 3). But even here it should be noted that if inconsistent mathematics turned out to be functionally impoverished then so would inconsistent databases. 2. Summary In Chapter 2, Meyer's results on relevant arithmetic are set out, and his view that they have a bearing on G8del's incompleteness theorems is discussed. Model theory for nonclassical logics is also set out so as to be able to show that the inconsistency of inconsistent theories can be controlled or limited, but in this book model theory is kept in the background as much as possible. This is then used to study the functional properties of various equational number theories.

Keywords

Arithmetic Mathematica artificial intelligence calculus computer computer science geometry logic set theory theoretical computer science

Authors and affiliations

  • Chris Mortensen
    • 1
  1. 1.Centre for Logic, Department of PhilosophyUniversity of AdelaideNorth TerraceAustralia

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8453-1
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4480-8
  • Online ISBN 978-94-015-8453-1
  • About this book
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