The problem of adequately defining numbers
DeLong, D. Stephan
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Natural numbers, although they pervade much of mathematics, are among the most difficult entities for which to provide definitions. Although it is often overlooked, as the efforts of pure mathematics are directed toward the maximization of rigor, the development of sound definitions for numbers can be viewed as one of the most critical objectives of the discipline. This paper is an examination and a support for the efforts in this area of the German logician Gottlob Frege, and in particular of his landmark treatise die Grundlagen der Arithmetik. This work marked the first successful attempt to define numbers through appeal to pure logic alone, and stands as a significant achievement in the history of mathematical philosophy.