 Nonetheless two distinct positions emerge from the material Frege works over, doctrines which Resnik (1980: 54), and likewise Shapiro (2000: 41–48) describe as term formalism and game formalism, respectively. The term formalist views the expressions of mathematics, arithmetic for example, as meaningful, the singular terms as referring, but as referring to symbols such as themselves, rather than numbers, construed as entities distinct from symbols. Thus Heine writes: