Cantor Georg Ferdinand Ludwig Philipp

<mathematics, history of philosophy, biography> german mathematician. Cantor (1845-1918) developed modern set theory as the foundation for all of mathematics and used the "diagonal proof" to demonstrate that lines, planes, and spaces must all contain a non-denumerable infinity of points; that is, they cannot be counted in a one-to-one correspondence with the rational numbers. The reality of trans-finite quantities within the set of real numbers leads, in turn to "Cantor's paradox" - that every set has more subsets than members, so that there can be no set of all sets. Recommended Reading: Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers, tr. by Philip E. Jourdain (Dover, 1955); Keith Simmons, Universality and the Liar: An Essay on Truth and the Diagonal Argument (Cambridge, 1993); and Joseph Warren Dauben, Georg Cantor (Princeton, 1990).

[A Dictionary of Philosophical Terms and Names]

<2001-10-11>

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Cantorian set theory

set theory

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Cantor's theorem

<logic> The power set of a given set has a greater cardinality than the given set.

[Glossary of First-Order Logic]

<2001-03-16>

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