Review by Choice Review
Simmons's task is to provide a unified approach to the entire family of semantic paradoxes: the liar paradox, the definability paradoxes, and Russell's paradox. All of these paradoxes rest on some form of self-reference, but simply avoiding self-reference is not an option because it crops up in unexpected ways. Simmons (Univ. of Connecticut) demonstrates that these paradoxes are fundamentally difficult to resolve in that they will keep reappearing in any attempted resolutions. Currently the most popular treatment is invoking Tarskian-type metalanguages, so that the paradoxes are resolved by sorting sentences into levels. Simmons rejects the metalanguage method. He asserts that any resolution has to use standard logic and ordinary common reasoning and language, since these give rise to the paradoxes. Nothing artificial (e.g., metalanguages) is allowed. Simmons's approach is based on a comment by Kurt Gödel, which is that the paradoxes can be viewed as giving rise to undefined singularities, like dividing by zero. At certain points, which Simmons is careful to specify, the values of the paradoxical sentences are undefined. Simmons defends his theory with intense vigor. His arguments are lengthy, detailed, and highly technical. Summing Up: Recommended. Graduate students, researchers, faculty. --Stephen P. Schwartz, emeritus, Ithaca College
Copyright American Library Association, used with permission.
Review by Choice Review
