some mathem- aticians (e.g. Mayberry 1994) have tried simply to deny that mathematics has a foundation. But plainly more needs to be said if this is to be anything more substantial than an indefinite refusal to address the question. Another response to these difficulties, more popular among mathematicians than among philosophers, has been to espouse a stricter formalism, a version, that is to say, of the view that the primitive terms of an axiomatic theory refer to nothing outside of the theory itself. The crudest version of this doctrine, pure formalism, asserts that mathematics is no more than a game played with symbols. Frege’s demolition of this view (1893–1903, II, §§86–137) is treated by most philosophers as definitive. Indeed it has become popular to doubt whether any of the mathematicians Frege quotes actually held a view so stu- pid. However, there are undoubtedly some mathematicians who claim, when pressed, to believe it, and many others whose stated views entail it