Customer Reviews

Principles of Mathematical Logic

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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.

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.