I articulate and defend the thesis that first-order logic is algebraic, in the sense that it does not have a single canonical application to reality. If correct, this thesis supports a flexible conception of ontology. Suppose we have a first-order language that purports to talk about certain objects, say Fs, whose conditions for correct use are expressed in terms that are already assumed to be in good standing and thus, in particular, involve no talk about Fs. Suppose further that these assertability conditions respect the laws of logic. Finally, suppose that the assertability conditions involve a criterion of identity that licenses the use of non-trivial identity statements. Then, according to the flexible conception, there really are Fs. I also defend this algebraic conception of logic, and the conception of ontology to which it gives rise, against the objection that this approach involves a problematic form of anti-realism.