Inverse Operations with Transfinite Numbers and the Kalam Cosmological Argument

International Philosophical Quarterly 35 (2):219-221 (1995)
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Abstract

William Lane Craig has argued that there cannot be actual infinities because inverse operations are not well-defined for infinities. I point out that, in fact, there are mathematical systems in which inverse operations for infinities are well-defined. In particular, the theory introduced in John Conway's *On Numbers and Games* yields a well-defined field that includes all of Cantor's transfinite numbers.

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Graham Oppy
Monash University

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