The author states (p. 11): ”Abstract entities are mysterious and must be avoided at all costs. They are especially pernicious in mathematics where they make understanding of the application of mathematics very unlikely, and hence cannot be part of acceptable truth conditions for the sentences of mathematics.” The first part of the book discusses the ontological commitments of formal languages in general and shows how their semantics can be developed with a maximum of ontological economy by using substitutional quantification. The second part gives a semantic interpretation of the mathematical theories of the integers and rational numbers which accounts for the practical application of these theories to counting and measurement without assuming that numbers exist. The author views this interpretation as providing strong support for nominalism, and suggests that all of predicative mathematics, which presumably includes all of applicable mathematics, may prove amenable to ”nominalization”.