While the various axiomatic systems of set theory saved mathematics from its immediate peril, they
failed to satisfy a great many people. In particular, many who were sensitive to the elegance and
universality of mathematics were quick to point out that the creations of Zermelo and von Neumann
must be regarded as provisional solutions—as expedients to solve a temporary problem; they will
have to be replaced, sooner or later, by a mathematical theory of broader scope, which treats the
concept of “set” in its full, intuitive generality
While the various axiomatic systems of set theory saved mathematics from its immediate peril, theyfailed to satisfy a great many people. In particular, many who were sensitive to the elegance anduniversality of mathematics were quick to point out that the creations of Zermelo and von Neumannmust be regarded as provisional solutions—as expedients to solve a temporary problem; they willhave to be replaced, sooner or later, by a mathematical theory of broader scope, which treats theconcept of “set” in its full, intuitive generality
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