 All this might seem a lot of extra work for little. What do we really gain from these ‘canonical notations’ in determining ontological commitment? One attempt to answer this, which partly motivates the above way of doing things, is based on the following consideration: We might wonder why we should think that quantifiers are of great importance for making ontological commitments explicit. After all, if I accept the apparently trivial mathematical fact that there is a number between 6 and 8, does this already commit me to an answer to the ontological question whether there are numbers out there, as part of reality? The above strategy tries to make explicit that and why it in fact does commit me to such an answer. This is so since natural language quantifiers are fully captured by their formal analogues in canonical notation, and the latter make ontological commitments obvious because of their semantics. Such formal quantifiers are given what is called an ‘objectual semantics’. This is to say that a particular quantified statement ‘\(\exists x\,Fx\)’ is true just in case there is an object in the domain of quantification that, when assigned as the value of the variable ‘x’, satisfies the open formula ‘\(Fx\)’. This makes obvious that the truth of a quantified statement is ontologically relevant, and in fact ideally suited to make ontological commitment explicit, since we need entities to assign as the values of the variables. Thus (L1) is tied to (O1). The philosopher most closely associated with this way of determining ontological commitment, and with the meta-ontological view on which it is based, is Quine, in particular his (Quine 1948). See also van (Inwagen 1998) for a presentation sympathetic to Quine.