On definitions, especially of dimension

pp. 207-216

in: Karl Menger, Selected papers in logic and foundations, didactics, economics, Berlin, Springer, 1979

Abstract

Part I of this chapter is a translation of the pages in Chapter 2 of my book Dimensions-theorie [1928,9] that deal with definitions in general and defining dimension in particular - passages often quoted by philosophers. In notes (added in bold-face brackets) I bring some of my views on the subject up to date. Part II is a reprint of sections of [1943, 1], a paper from an interesting series that L. R. Ford arranged in the American Mathematical Monthly when he was editor of that journal. Each paper of the series had in the title a question beginning with the words What is… ? Ford asked me to answer the question for dimension. (As to the genesis of my ideas, See Chapter 21.) Part III summarizes some basic methodological ideas propounded in Chapter 1 of [1928, 9].