PHIL 29.02 The Infinite

Infinity is an indispensable concept for mathematics. Arithmetic deals with infinitely many natural numbers, geometry with infinitely long lines, calculus with infinitely small changes, and set theory with multiple levels of infinity. But the infinite raises distinctive philosophical problems. Just what is our concept of the infinite? A completed totality larger than any finite totality? Something that extends beyond all bounds? What justifies us in applying this concept? Are there larger and smaller levels of infinity? How many? Moreover, how are we to deal with the paradoxes that arise from the concept? The infinite also has a related, but arguably distinct use in certain philosophical debates where it is used to denote ideas of perfection or completeness, e.g. of the divine or human reason. What is the relationship between this notion of the infinite and its use in mathematics? Readings will include historical and contemporary sources, from Aristotle to Cantor to today.

Prerequisite

One Philosophy course, or permission of the instructor.

Degree Requirement Attributes

Dist:TMV

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