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Beyond Infinity: Georg Cantor and Leopold Kronecker's Dispute over Transfinite Numbers
Adviser: Patrick Byrne
ABSTRACT: In the late 19th century, Georg Cantor opened up the mathematical field of set theory with his development of transfinite numbers. In his radical departure from previous notions of infinity espoused by both mathematicians and philosophers, Cantor created new notions of transcendence in order to clearly described infinities of different sizes. Leading the opposition against Cantor's theory was Leopold Kronecker, Cantor's former mentor and the leading contemporary German mathematician.
In their lifelong dispute over the transfinite numbers emerge philosophical disagreements over mathematical existence, consistency, and freedom. This thesis presents a short summary of Cantor's controversial theories, describes Cantor and Kronecker's philosophical ideas, and attempts to state clearly their differences of opinion.
In the end, the author hopes to present the shock caused by Cantor's work and an appreciation of the two very different philosophies of mathematics represented by Cantor and Kronecker.
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SUGGESTED CITATION:
Patrick Hatfield Carey, B.A. (Awarded in 2005)
College Honors Program; Philosophy
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Philosophy (0422)
Cantor, Kronecker, Transfinite Numbers, Philosophy of Mathematics, Infinity, Formalism
Patrick Hatfield Carey (2005) Beyond Infinity: Georg Cantor and Leopold Kronecker's Dispute over Transfinite Numbers, B.A. Thesis, Boston College, Philosophy, 52 pages.
