Abstract

Idealization in mathematics, by its very nature, generates a gap between the theoretical and the practical. This article constitutes an examination of two individual, yet similarly created, cases of mathematical idealization. Each involves using a theoretical extension beyond the finite limits which exist in practice regarding human activities, experiences, and perceptions. Scrutiny of details, however, brings out substantial differences between the two cases, not only in regard to the roles played by the idealized entities, but also in regard to appropriate criteria for justifying the use of such entities. The background information supplied and the examples chosen for analysis in this paper were selected from the areas of measurement theory, probability theory, mathematical logic, and philosophy of mathematics.