Indiscrete Thoughts

ROTA, Gian-Carlo. Indiscrete Thoughts. Edited by Fabrizio Palombi. Boston: Birkhauser, 1997. xxii + 280 pp. Cloth, $36.00; paper, $19.00-This is a collection of vivid and stimulating writings in various literary forms by a well-known mathematician who is having an increasing influence as a (phenomenological) philosopher. It contains a core of papers that will change the face of the philosophy of mathematics and one of the most important papers on philosophical logic of this closing century, one that enables a fully effective transcendental logic. Indiscrete Thoughts, together with the previous anthology (Mark Kac, Gian-Carlo Rota, Jacob T. Schwartz, Discrete Thoughts [Boston: Birkhauser, 1985]), makes Rota's philosophical writing accessible.

Robert Sokolowski writes in a Foreword to Indiscrete Thoughts, "[Rota's] writings [here] have much of Socrates' irony and wit, and the occasional barb is also Socratic, meant to illuminate and to sting the reader into looking at things afresh. In these essays, mathematics is restored to its context in being and in human life" (p. xvii). Part 1, "Persons and Places," contains vivid characterizations of mathematicians and the recent history of mathematics. Part 2, "Philosophy," will be featured in this review. Amusingly, part 3 is safely titled "Readings and Comments" in the Contents, but it is titled "Indiscrete Thoughts" on the title page of part 3 (p. 194), and it deserves the pun on "indiscreet," as for example the one-line review of J. Passmore's Recent Philosophers, "When pygmies cast such long shadows, it must be very late in the day" (p. 257). (Most of part 3, however, is addressed to a mathematical audience.)

The three main essays of part 2, "The Phenomenology of Mathematical Truth," "The Phenomenology of Mathematical Beauty," and "The Phenomenology of...