Review by Choice Review
While Godel's fame rests on his 1931 incompleteness theorems, his long career produced many diverse achievements. Here, top experts survey these accomplishments. A shocking start to the work is Angus Macintyre's chapter, in which he argues that the incompleteness theorems themselves have had "restricted" mathematical impact beyond logic; students of number theory should note that Macintyre's appendix has the latest information on the possibility of proving Fermat's last theorem within Peano arithmetic. Harvey M. Friedman, the late Paul J. Cohen, and W. Hugh Woodin, all major logicians, cast summaries of their own work against the context Godel established. Many will have heard that Godel dabbled in relativistic cosmology, but Wolfgang Rindler demonstrates the importance and ingenuity behind Godel's construction and surprising continuity with his general intellectual orientation. Petr Hajek justifies attention accorded lately to Godel's ontological proof of the existence of God, published only in 1995, decades after Godel's death. Of course, the incompleteness theorems receive ample commentary; several articles concern their historical context, initial reception, and synergy with the birth of practical computing (even though Godel himself did not take much interest). Two leading pundits, philosopher Hilary Putnam and physicist Roger Penrose, update their thoughts on the implications of incompleteness concerning the nature of consciousness. Summing Up: Recommended. Upper-division undergraduates and above. D. V. Feldman University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
