For our purposes, the main interest of the Neo-Fregean approach is that it leads to a conception of ontological commitment more liberal than any yet considered. This conception arises from the Neo-Fregean's particular way of understanding Hume's Principle. First, since Hume's Principle is to define the concept of number, the left- and right-hand sides of the principle must at least have the same truth conditions.  Second, sentences with the same truth conditions have the same ontological commitments. This second assumption amounts to a sense in which being supervenes on truth: circumstances cannot differ with respect to what there is without differing with respect to what is true. It follows from these two assumptions that the left- and right-hand sides of Hume's Principle have the same ontological commitments. But that still leaves open three different ways that Hume's Principle can be viewed (Wright 1990). First, one might reject it on the grounds that the left- and right-hand sides clearly do not have the same ontological commitments: the numerical identity on the left-hand side is committed to numbers; the claim that two concepts are equal on the right-hand side is not. On this view, only a conditionalized version of Hume's Principle could be accepted: “if there are numbers, then …” (Field 1984). In response, the neo-Fregean can say that this confuses “having the same truth conditions” with some more fine-grained equivalence such as “expressing the same thought”. Only the latter requires that both sides refer to the same objects, where reference is a kind of explicit ontological commitment.[45]