Epstein and Carnielli, both logicians who have been collaborating on computability theory for two decades, introduce the philosophical aspects of recursion theory and logic. Opening with a discussion of the philosophical foundations of mathematics, and a presentation of the ideas of whole number, function, proof, and real number, the book continues with an exploration of computability and recursive functions. Part III presents a full development of G÷del's theorems, and the book concludes with a look at the technical side of these ideas by reviewing Church's Thesis. Annotation c. Book News, Inc., Portland, OR (booknews.com)