Mathematical Logic

by R.O. Gandy, C.E.M. Yates

Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.

416 pages, Kindle Edition

First published December 5, 2001

Reviews

[Jeff Cliff · Rating 4 out of 5]

I had a high bar coming into this book, and it lived up to what I expected of it. I have been coming back to it off and on for awhile as some of the proofs are *quite* involved. Some of the proofs build on top of other work (especially Alonzo Church), and generally -- you get a sense of who's shoulders Saint Turing was standing on with this book especially. Some of the chapters I'd encountered before and read, before I purchased this book, and some of the proofs I've seen (and glazed over) before, but they are becoming more clear, and more obviously sound the more passes I get of them. This book gives deep insight into Saint Turing and his thought - although the order is chronological, it would make a lot of sense to read in a slightly different order -- things like the "dots as brackets", if you're going to read the meat of the rest of his work, should probably be read nearer to the beginning of your journey into his work.

It also gives a fuller sense of what the world was robbed by, when he was de facto murdered by the British government, and a clue of what was still secret as of 2001 ( differential analysis, enigma-related work, early FVEY agreement on mass surveillance ). Turing was not a one-trick pony, he went in depth into a variety of topics and this book captures him at his best.