  In response, a correspondence theorist will point out: (a) The identity theory is defensible only for propositions as truthbearers, and only for propositions construed in a certain way, namely as having objects and properties as constituents rather than ideas or concepts of objects and properties; that is, for Russellian propositions. Hence, there will be ample room (and need) for correspondence accounts of truth for other types of truthbearers, including propositions, if they are construed as constituted, partly or wholly, of concepts of objects and properties. (b) The identity theory is committed to the unacceptable consequence that facts are true. (c) The identity theory rests on the assumption that that-clauses always denote propositions, so that the that-clause in “the fact that snow is white” denotes the proposition that snow is white. The assumption can be questioned. That-clauses can be understood as ambiguous names, sometimes denoting propositions and sometimes denoting facts. The descriptive phrases “the proposition…” and “the fact…” can be regarded as serving to disambiguate the succeeding ambiguous that-clauses—much like the descriptive phrases in “the philosopher Socrates” and “the soccer-player Socrates” serve to disambiguate the ambiguous name “Socrates” (cf. David 2002).