 One can ‘internalize’ this functional approach. This is done in the case of various property theories, formal theories for reasoning about properties as metaphysical objects (Bealer 1982, Zalta 1983, Menzel 1986, 1993, and Turner 1987). This kind of theory is employed in certain metaphysical investigations where properties are metaphysical entities to be investigated. In these theories, metaphysical relations are (or are among) the objects of interest; just as we add term-building symbols + and \(\times\) in formal theories of arithmetic to build numbers, \(\lambda\) is used in property theory to build relations. This approach contrasts with the approach above. There, \(\lambda\) was added to the grammar of first-order logic by making it a recipe for building atomic formulas; it was a new formula-building operator, like \(\vee\) or \(\rightarrow\) or the other connectives. In the case of property theories, the \(\lambda\) plays a role more like + and \(\times\) in formal theories of arithmetic: it is used to construct relations (which, in this setting, are to be understood as a kind of metaphysical object). Unlike + and \(\times\), though, the \(\lambda\) binds variables.