Principles of Mathematical Logic

by David Hilbert, Wilhelm Ackermann

David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. It lays the groundwork for his later work with Bernays. This translation is based on the second German edition, and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.

Genres: Logic, Mathematics, Science, Philosophy

172 pages, Hardcover

First published June 1, 1938

About the author

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory).

Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century.

Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic.

Reviews

[Douglas · Rating 4 out of 5]

This is a classic of Mathematical Logic. It is commonly referred as Hilbert-Ackermann or just HA. The book is infused with Hilbert's Formalist philosophy of Mathematics. The book contains the first formulations of important aspects of modern logic. It should be read anyone study logic at a high level. It is not a difficult book, if you took logic 101 in college you can probably handle it.

[Mkawass · Rating 4 out of 5]

A tour do force to learn logic. The only problem is that a lot had been discovered since Hilbert authored the book.