Numbers, Properties, and Frege

An attempt is made to situate, clarify, & interpret G. Frege's arguments against a nominalist, abstractionist version of the property analysis of number. Based on C. Lambros's critique of Frege's theory of number ("Are Numbers Properties of Objects," Philosophical Studies, 1976, 29, 6, 381), it is argued that Lambros misinterprets the central arguments of Die Grundlagen der Arithmetic (The Foundations of Arithmetic). For example, rather than viewing the green/thousand argument of 28e as analogical, it is argued that it is a dilemma, requiring the nominalist either to maintain that an individual can be a one thousand or to show how one can abstract properties from objects that do not have these properties & in some cases from objects that do not even exist. Frege's other arguments against this view are analyzed & defended. Modified AA