Work · Analytic Philosophy
What Is Cantor’s Continuum Problem?
Mathematical objects exist independently of us and are grasped by a kind of intuition; undecided questions such as the continuum hypothesis still have an answer.
Introduction
Gödel wrote this expository article for the American Mathematical Monthly in 1947 and published a revised version with a supplement in 1964. Cantor’s continuum hypothesis states that there is no set whose size lies strictly between that of the natural numbers and that of the real numbers. Gödel had shown in 1938–40 that it cannot be disproved from the standard axioms of set theory; he suspected that it could not be proved from them either – as Paul Cohen showed in 1963 – and himself thought it false. Such independence, he argues, does not make the question meaningless: new axioms, recognised as true, may settle it. The article is one of the classic statements of mathematical Platonism.
More works by Kurt Gödel
Sources: Wikidata
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