 In the contemporary philosophical literature, a number of books and papers have investigated a form of abstraction that doesn’t depend on mental processes. We may call this the way of abstraction principles. Wright (1983) and Hale (1987) have developed an account of abstract objects on the basis of an idea they trace back to certain suggestive remarks in Frege (1884). Frege notes (in effect) that many of the singular terms that appear to refer to abstract entities are formed by means of functional expressions. We speak of the shape of a building, the direction of a line, the number of books on the shelf. Of course, many singular terms formed by means of functional expressions denote ordinary concrete objects: ‘the father of Plato’, ‘the capital of France’. But the functional terms that pick out abstract entities are distinctive in the following respect: where \(f(a)\) is such an expression, there is typically an equation of the form: