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Introduction to Mathematical Logic
Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics S...
The Collected Works of Alonzo Church
Writings, including articles, letters, and unpublished work, by one of the twentieth century's most influential figures in mathematical logic and philosophy. Alonzo Church's long and distinguished career in mathematics and philosophy can be traced through his influential and wide-ranging writings. Church published his first article as an undergraduate at Princeton in 1924 and his last shortly before his death in 1995. This volume collects all of his published articles, many of his reviews, his monograph The Calculi of Lambda-Conversion, the introduction to his important and authoritative textbook Introduction to Mathematical Logic, a substantial amount of previously unpublished work (includi...
The Calculi of Lambda-conversion
The classic book that inspired Alan Turing and helped to lay the foundation for theoretical computer science This book provides a concise introduction to the calculi of lambda-conversion first discovered by Alonzo Church and developed by him in collaboration with his students, S. C. Kleene and J. B. Rosser. The first four chapters present the calculus of lambda-conversion in detail, with subsequent chapters discussing the calculus of λ-K-conversion, the calculus of restricted λ-K-conversion, and the calculus of λ-δ-conversion, as well as the applications of the latter to symbolic logic. Gödel numbers are presented using simplified notation, and the fundamental Church-Rosser consistency ...
Logic, Meaning and Computation
This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields.
The Turing Guide
Alan Turing has long proved a subject of fascination, but following the centenary of his birth in 2012, the code-breaker, computer pioneer, mathematician (and much more) has become even more celebrated with much media coverage, and several meetings, conferences and books raising public awareness of Turing's life and work. This volume will bring together contributions from some of the leading experts on Alan Turing to create a comprehensive guide to Turing that will serve as a useful resource for researchers in the area as well as the increasingly interested general reader. The book will cover aspects of Turing's life and the wide range of his intellectual activities, including mathematics, code-breaking, computer science, logic, artificial intelligence and mathematical biology, as well as his subsequent influence.
On Quine
A collection of essays which critically evaluate the writings of Quine.
Alan Turing's Systems of Logic
A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influentia...
