The End of Infinity : Where Mathematics and Philosophy Meet.
Patton, Anthony C.
The End of Infinity : Where Mathematics and Philosophy Meet. - 1st ed. - 1 online resource (200 pages)
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 & -- Logic -- Place-Value Numbers & -- Letters -- Universals -- The Gaps -- Classical & -- Modern Logic -- The Logic of Geometry & -- 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.
9781628943412
Infinite.
Electronic books.
BD411 .P388 2018
111/.6
The End of Infinity : Where Mathematics and Philosophy Meet. - 1st ed. - 1 online resource (200 pages)
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 & -- Logic -- Place-Value Numbers & -- Letters -- Universals -- The Gaps -- Classical & -- Modern Logic -- The Logic of Geometry & -- 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.
9781628943412
Infinite.
Electronic books.
BD411 .P388 2018
111/.6