Existential commitments of First Order Logic

In First Order Logic (FOL), we have two oddities: (a) if "b" is a name, then it's a theorem that b exists, and that (b) it's a theorem that something or other exists. We might conclude that since theorems hold necessarily, everything that exists, exists necessarily. Or we might be embarrassed and reject FOL, going for some version of free logic.

Maybe, though, what we should say is that just as ordinary language sentences have presuppositions, a language can have presuppositions. Presuppositions make communication easier. Instead of a nurse's making the convoluted request "If you have an age, please tell me your age; otherwise, please tell me that you're ageless", the nurse can simply presuppose that you have an age and ask: "How old are you?" It's not particularly surprising that presuppositions might also make reasoning easier. It can be easier to reason on the presupposition that there is something, and on the presupposition that names have reference. So FOL has presuppositions. No need for embarrassment: the presuppositions make things simpler for us, much as it's easier to work with commutative groups than groups in general.

Of course, if a language L has presuppositions, then we shouldn't expect its theorems to hold necessarily. Rather, a theorem is something that necessarily follows from the presuppositions. We can without embarrassment say that it's a theorem of an appropriate dialect of FOL that Obama exists, since the only modal conclusion we can make is that, necessarily, if the presuppositions of the dialect are true, Obama exists.

We could search for a logic without presuppositions. That's a worthwhile quest, and leads to exploring various free logics. But we shouldn't go overboard in worrying about the metaphysical consequences if we don't find a good one. Likewise, we shouldn't worry too much if we can't find a satisfactory quantified modal logic. These are just tools. Nice to have, but people have done just fine with modal and other arguments for centuries without much of a formal logic.