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The End of Infinity : Where Mathematics and Philosophy Meet.

By: Material type: TextTextPublisher: New York : Algora Publishing, 2018Copyright date: ©2018Edition: 1st edDescription: 1 online resource (200 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781628943412
Subject(s): Genre/Form: Additional physical formats: Print version:: The End of InfinityDDC classification:
  • 111/.6
LOC classification:
  • BD411 .P388 2018
Online resources:
Contents:
Intro -- Cast of Characters -- Introduction -- Prelude: Time -- Chapter 1: History -- The Pre-Socratics -- The Milesian School -- The Pythagorean Society -- The Eleatic School -- The Crisis -- Plato -- Schopenhauer -- Conclusion -- Chapter 2: Aristotle -- The Categories -- Potential Infinity -- Divine Ideas -- Conclusion -- Chapter 3: Language &amp -- Logic -- Place-Value Numbers &amp -- Letters -- Universals -- The Gaps -- Classical &amp -- Modern Logic -- The Logic of Geometry &amp -- Arithmetic -- Conclusion -- Chapter 4: The Numbers -- Visualizing the Numbers -- From Natural to Rational -- The Real Numbers -- Understanding the Real Numbers -- Conclusion -- Chapter 5: Static Infinity -- Countable Sets -- Take it to the Limit -- The Largest Natural Number -- Just Say Nein -- Color by the Numbers -- Conclusion -- Chapter 6: Dynamic Infinity -- Points of Continuity -- Infinitesimals -- The Algebra of Calculus -- The Power Set -- Conclusion -- Chapter 7: Counting the Real Numbers -- The Diagonal Argument -- Cardinality Redux -- Symmetry -- Conclusion -- Chapter 8: The End of Infinity -- Embodied Mathematics -- The Uncanny Correlation -- Non-discursive Thought -- Pattern Recognition -- Conclusion -- Appendix: Simplified Proofs -- Index -- _GoBack.
Summary: The idea of infinity stands at the intersection of mathematics and philosophy. As da Vinci said, "Arithmetic is a computational science in its calculations, but it is of no avail in dealing with continuous quantity."The End of Infinity reviews the philosophical history of infinity, mathematics, numbers, and logic to demonstrate that the modern conception of infinity involves a logical and metaphysical contradiction that argues for a return to Aristotle's conception of potential infinity.
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Intro -- Cast of Characters -- Introduction -- Prelude: Time -- Chapter 1: History -- The Pre-Socratics -- The Milesian School -- The Pythagorean Society -- The Eleatic School -- The Crisis -- Plato -- Schopenhauer -- Conclusion -- Chapter 2: Aristotle -- The Categories -- Potential Infinity -- Divine Ideas -- Conclusion -- Chapter 3: Language &amp -- Logic -- Place-Value Numbers &amp -- Letters -- Universals -- The Gaps -- Classical &amp -- Modern Logic -- The Logic of Geometry &amp -- Arithmetic -- Conclusion -- Chapter 4: The Numbers -- Visualizing the Numbers -- From Natural to Rational -- The Real Numbers -- Understanding the Real Numbers -- Conclusion -- Chapter 5: Static Infinity -- Countable Sets -- Take it to the Limit -- The Largest Natural Number -- Just Say Nein -- Color by the Numbers -- Conclusion -- Chapter 6: Dynamic Infinity -- Points of Continuity -- Infinitesimals -- The Algebra of Calculus -- The Power Set -- Conclusion -- Chapter 7: Counting the Real Numbers -- The Diagonal Argument -- Cardinality Redux -- Symmetry -- Conclusion -- Chapter 8: The End of Infinity -- Embodied Mathematics -- The Uncanny Correlation -- Non-discursive Thought -- Pattern Recognition -- Conclusion -- Appendix: Simplified Proofs -- Index -- _GoBack.

The idea of infinity stands at the intersection of mathematics and philosophy. As da Vinci said, "Arithmetic is a computational science in its calculations, but it is of no avail in dealing with continuous quantity."The End of Infinity reviews the philosophical history of infinity, mathematics, numbers, and logic to demonstrate that the modern conception of infinity involves a logical and metaphysical contradiction that argues for a return to Aristotle's conception of potential infinity.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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