MATH ACROSS THE CURRICULUM:

HOW MANY ANGELS?

PHILOSOPHY, MATHEMATICS
AND THE INFINITE

 

Professor Groszek

1997

 

Contents of Selected Readings

Chapter One: Infinity, from Infinity and the Mind, by Rudy Rucker.

Chapter Two: A Contemporary Look at Zeno's Paradoxes, from Space, Time, and Motion, a Philosophical Introduction, by Wesley C. Salmon.

What the Tortoise Said to Achilles, by Lewis Carroll, in Mind.

What Achilles Should Have Said to the Tortoise, by J. F. Thomson, in Ratio.

Why "Oughts" are not Facts (or What the Tortoise and Achilles Taught Mrs. Ganderhoot and Me about Practical Reasoning), by G. F. Schueler, in Mind.

The Ways of Paradox, from The Ways of Paradox and other Essays, by W. V. Quine.

Chapter Two: Aristotle, from The Infinite, by A.W. Moore.

Extracts from The Mathematical Works of Isaac Newton.

The Analyst (and Editor's Introduction), from The Works of George Berkeley Bishop of Cloyne, edited by A. A. Luce.

Discourse on the Method for Rightly Conducting One's Reason and for Seeking Truth in the Sciences (parts one through four), by RenÉ Descartes, translated by Donald A. Cress.

On the Infinite, by David Hilbert, from Philosphy of Mathematics, Selected Readings, edited by Paul Benacerraf and Hilary Putnam.

The Extraordinary Hotel, from In Search of Infinity, by N. Ya. Vilenkin, translated by Abe Shenitzer. (This excerpt has elsewhere been identified as written by Stanislaw Lem.)

Chapter Six: Cantor's Philosophy of the Infinite, from Georg Cantor, His Mathematics and Philosophy of the Infinite, by Joseph Warren Dauben.

Chapter Nine: Reactions, from The Infinite, by A. W. Moore.

Disputation, by Arend Heyting, from Philosphy of Mathematics, Selected Readings, edited by Paul Benacerraf and Hilary Putnam.

Chapter One: Realism, from Realism in Mathematics, by Penelope Maddy.

Mathematical Models, Computers, and Platonism, in Chapter Eight, Mathematical Reality, from The Mathematical Experience, by Philip J. Davis and Reuben Hersh.

Infinity, or The Miraculous Jar of Mathematics, in Chapter Four, Inner Issues, from The Mathematical Experience, by Philip J. Davis and Reuben Hersh.

Infinity in God and Mathematics, by Jill Le Blanc, in Religious Studies.

Copyright Issue