 Goodman and Quine tried early on to bite the bullet: they embarked on a project to reformulate theories from natural science without making use of abstract entities (Goodman &amp; Quine 1947). The nominalistic reconstruction of scientific theories proved to be a difficult task. Quine, for one, abandoned it after this initial attempt. In the past decades many theories have been proposed that purport to give a nominalistic reconstruction of mathematics. (Burgess &amp; Rosen 1997) contains a good critical discussion of such views.