Elliott Mendelson

The author tells us that this book was originally intended to be part of a larger work, with the provisional title God and Infinity, but that he opted instead for a separate and independent treatment of the notion of infinity in philosophy and related areas. The original purpose is very well-hidden, showing itself clearly only in the Preface and a few other places. The book begins with a chapter describing some known alleged difficulties having to do with the infinitely large and infinitely small . This is followed by a chapter on some basic mathematical notions and facts, including sketchy references to Zermelo-Fraenkel set theory , ordinal and cardinal numbers, Cantor's diagonal method, some special set-theoretic statements , analysis, non-standard analysis, model theory, internal set theory , Conway numbers, and the ‘finite mathematics’ of Mycielski and Lavine. Of course, readers will obtain very little solid information about these matters, but at least they will be introduced to some of the terminology. Chapter 3 returns to the problems and conundrums introduced in Chapter 1 and tries to resolve them or show that they are illusory. In some cases, the trouble arose because an infinite sequence of experiments was imagined which would be physically impossible . Other apparent difficulties arose only because of unfamiliarity with the …