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zAbstract Cantor's theory of cardinality violates common sense. It says. for example. that all infinite sets of integers are the same size. This thesis criticizes the arguments for Cantor's theory and presents an alternative. The alternative is based on a general theory, called n(s.. (for "Class Size")- CS consists of all sentences in the first-order language with a subset predicate and a less-than predicate which are true in all interpretations oftti at 1an 9u age whose doma i n i s a fin i t epawe r set. Th us, CS says that less-than is a linear ordering with highest and lowest members and that every set is larger than any of its proper subsets. Because the language of CS is so restricted, (5 will have infinite interpretations. In particular, the notion of one-one correspondence cannot b