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.
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Text: English, German (translation)
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23 of 24 people found the following review helpful:
5.0 out of 5 stars
classic,
By A Customer
This review is from: Principles of Mathematical Logic (Hardcover)
Brief though it is, _Priniciples_ manages to cover not only the usual topics (sentential calculus, first-order predicate calculus, completeness, decidability), but also: the monadic predicate calculus in relation to Aristotelian logic; second-order logic; set theory and the Fregean concept of number; and the theory of types (logics of higher order). You might say that Hilbert covers the same ground in 160 pages that Russell and Whitehead labor over for 3 volumes. The bottom line: a treat for anyone interested in logic, especially in the period from Frege to Godel.
6 of 6 people found the following review helpful:
4.0 out of 5 stars
Good old book,
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This review is from: Principles of Mathematical Logic (Hardcover)
I learned logic from this book, and so I am very fond of it. As a presentation of what was known at that time, it cannot be beaten. The only problem with it is that a lot more has been discovered, so a modern treatment of the subject is better for the beginner who wants to be properly informed. For this I suggest the books by Copi or even Kleene. But if you don't care about modernity, or have an interest in the way things used to be done, I strongly recommend this book. Also, I might mention that Hilbert's "Geometry and the Imagination" is good even for the modern mathematician.
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First Sentence:
A first and indispensable part of mathematical logic consists of the so-called sentential calculus (calculus of sentences). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Rule of Implication, Physik Vol, Principia Mathematica New!
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A first and indispensable part of mathematical logic consists of the so-called sentential calculus (calculus of sentences). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Rule of Implication, Physik Vol, Principia Mathematica New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
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44
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- Introduction to Mathematical Logic by Alonzo Church in Front Matter, page 70, and Back Matter
- Introduction to Mathematical Philosophy by Bertrand Russell on page 139, and Back Matter
- Mathematical logic by W. V Quine in Front Matter, and Back Matter
- Introduction to Logic by Alfred Tarski in Back Matter
- The Logical Syntax of Language (Open Court Classics) by Rudolf Carnap in Back Matter
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- Philosophy of Science, Logic and Mathematics in the 20th Century: Routledge History of Philosophy Volume 9 by Stuart G. Shanker in Front Matter, page 19, and page 40
- Philosophy's Second Revolution: Early and Recent Analytic Philosophy by Clarke on page 38, Back Matter (1), and Back Matter (2)
- The Blackwell Guide to Philosophical Logic (Blackwell Philosophy Guides) by Lou Goble on page 32, and page 53
- A New Stoicism by Lawrence C. Becker in Back Matter (1), and Back Matter (2)
- Metalogic: An Introduction to the Metatheory of Standard First Order Logic by Geoffrey Hunter on page 254, and Back Matter
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