In the decade before 1900, the Italian mathematician Giuseppe Peano was one of the most original and influential pioneers of modern mathematical logic. He made significant contributions to the development of the foundations of mathematics and the axiomatic method (for example, his postulates for the natural numbers), dimension theory (including the space-filling curve), measure theory, vector analysis, differential equations, and the rigorization of analysis. Several of Peano's works have been translated into other languages; here for the first time is a generous selection of works translated into English. Fifteen articles, one booklet, and parts of two books and one monograph, published between 1883 and 1921, chosen with the interests of mathematicians and logicians in mind, are included. Each selection is preceded by an introductory note. The volume also contains a biographical sketch, a chronological list of Peano's publications (larger by one fifth than any previously published list), and a bibliography on the life and work of Peano. This selection will appeal especially to historians of mathematics and logic, but also to those mathematicians and logicians who wish to know more about how their subject came to be.

All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.

Calcolo Geometrico, G. Peano's first publication in mathematical logic, is a model of expository writing, with a significant impact on 20th century mathematics. Kannenberg's lucid and crisp translation, Geometric Calculus, will appeal to historians of mathematics, researchers, graduate students, and general readers interested in the foundations of mathematics and the development of a formal logical language. The book has never been reprinted in its entirety, and only two chapters have ever been translated into English. Readers of this valuable translation will gain insight into the work of a distinguished mathematician and founder of mathematical logic.

I suppose Joseph Agassi's best and dearest self-description, his cher ished wish, is to practice what his 1988 book promises: The Gentle Art of Philosophical Polemics. But for me, and for so many who know him, our Agassi is tough-minded, not tender, not so gentle. True to his beloved critical thinking, he is ever the falsificationist, testing himself of course as much as everyone else. How, he asks himself, can he engage others in their own self-critical exploration? Irritate? Question their logic, their facts, their presuppositions, their rationales? Subvert their reasoning, uncover their motives? Help them to lose their balance, but always help them, make them do it to, and for, themselves. Out of their own mouths, and minds, and imagination. A unique teacher, in classroom and out; not for everyone. Agassi is not quite a tight textual Talmudist disputant, not quite the competitor in the marketplace of ideas offered for persuasive sale, not quite the clever cross-examining lawyer advocate, not quite a philosopher-scientist, not a sceptic more than necessary, not quite embat tled in the bloody world but not ever above the battle either . . . but a good deal of all of these, and steeped in intelligence and good will.

Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.