Selected Works of Giuseppe Peano


Book Description

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.




The Great Formal Machinery Works


Book Description

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.




Selected Works


Book Description




Peano


Book Description

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.







Critical Rationalism, Metaphysics and Science


Book Description

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.




Principia Mathematica


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The First Moderns


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A lively and accessible history of Modernism, The First Moderns is filled with portraits of genius, and intellectual breakthroughs, that richly evoke the fin-de-siècle atmosphere of Paris, Vienna, St. Louis, and St. Petersburg. William Everdell offers readers an invigorating look at the unfolding of an age. "This exceptionally wide-ranging history is chock-a-block with anecdotes, factoids, odd juxtapositions, and useful insights. Most impressive. . . . For anyone interested in learning about late 19th- and early 20th- century imaginative thought, this engagingly written book is a good place to start."—Washington Post Book World "The First Moderns brilliantly maps the beginning of a path at whose end loom as many diasporas as there are men."—Frederic Morton, The Los Angeles Times Book Review "In this truly exciting study of the origins of modernist thought, poet and teacher Everdell roams freely across disciplinary lines. . . . A brilliant book that will prove useful to scholars and generalists for years to come; enthusiastically recommended."—Library Journal, starred review "Everdell has performed a rare service for his readers. Dispelling much of the current nonsense about 'postmodernism,' this book belongs on the very short list of profound works of cultural analysis."—Booklist "Innovative and impressive . . . [Everdell] has written a marvelous, erudite, and readable study."-Mark Bevir, Spectator "A richly eclectic history of the dawn of a new era in painting, music, literature, mathematics, physics, genetics, neuroscience, psychiatry and philosophy."—Margaret Wertheim, New Scientist "[Everdell] has himself recombined the parts of our era's intellectual history in new and startling ways, shedding light for which the reader of The First Moderns will be eternally grateful."—Hugh Kenner, The New York Times Book Review "Everdell shows how the idea of "modernity" arose before the First World War by telling the stories of heroes such as T. S. Eliot, Max Planck, and Georges Serault with such a lively eye for detail, irony, and ambiance that you feel as if you're reliving those miraculous years."—Jon Spayde, Utne Reader




Practical Foundations of Mathematics


Book Description

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.




Language and Mathematics


Book Description

This book explores the many disciplinary and theoretical links between language, linguistics, and mathematics. It examines trends in linguistics, such as structuralism, conceptual metaphor theory, and other relevant theories, to show that language and mathematics have a similar structure, but differential functions, even though one without the other would not exist.