Putnam's ``model-theoretic'' argument against metaphysical realism presupposes that an ideal scientific theory is expressible in a first order language. The central aim of this paper is to show that Putnam's ``first orderization'' of science, although unchallenged by numerous critics, makes his argument unsound even for adequate theories, never mind an ideal one. To this end, I will argue that quantitative theories, which dominate the natural sciences, can be adequately interpreted and evaluated only with the help of so-called theories of measurement (...) whose epistemological and methodological purpose is to justify systematic assignments of quantitative values to objects in the world. And, in order to fulfill this purpose, theories of measurement must have an essentially higher order logical structure. As a result, Putnam's argument fails because much of science turns out to rest on essentially higher order theoretical assumptions about the world. (shrink)