Approaching Infinity

Approaching Infinity Addresses Seventeen Paradoxes Of The Infinite, Most Of Which Have No Generally Accepted Solutions. The Book Addresses These Paradoxes Using A New Theory Of Infinity, Which Entails That An Infinite Series Is Uncompletable When It Requires Something To Possess An Infinite Intensive Magnitude. Along The Way, The Author Addresses The Nature Of Numbers, Sets, Geometric Points, And Related Matters. The Book Addresses The Need For A Theory Of Infinity, And Reviews Both Old And New Theories Of Infinity. It Discussing The Purposes Of Studying Infinity And The Troubles With Traditional Approaches To The Problem, And Concludes By Offering A Solution To Some Existing Paradoxes. -- Provided By Publisher. The Need For A Theory Of Infinity. The Prevalence Of The Infinite -- Six Infinite Regresses -- Seveteen Paradoxes Of The Infinite -- Old Theories Of Infinity. Impossible Infinite Series : Two False Accounts -- Actual And Potential Infinities -- The Cantorian Orthodoxy -- A New Theory Of Infinity And Related Matters. Philosophical Preliminaries -- Sets -- Numbers -- Infinity -- Space -- Some Paradoxes Mostly Resolved -- Assessing Infinite Regress Arguments -- Conclusion. Michael Huemer. Includes Bibliographical References And Index. Front Matter....Pages i-xiii Front Matter....Pages 1-1 The Prevalence of the Infinite....Pages 3-8 Six Infinite Regresses....Pages 9-16 Seventeen Paradoxes of the Infinite....Pages 17-38 Front Matter....Pages 39-39 Impossible Infinite Series: Two False Accounts....Pages 41-48 Actual and Potential Infinities....Pages 49-70 The Cantorian Orthodoxy....Pages 71-90 Front Matter....Pages 91-91 Philosophical Preliminaries....Pages 93-107 Sets....Pages 108-118 Numbers....Pages 119-142 Infinity....Pages 143-161 Space....Pages 162-175 Some Paradoxes Mostly Resolved....Pages 176-228 Assessing Infinite Regress Arguments....Pages 229-246 Conclusion....Pages 247-260 Back Matter....Pages 261-275