It is said by some (or most) logicians that logic must handle every possible state of affairs and hence it can't imply the existence of anything. That almost sounds like a non sequitur. Yes, we believe that logic must handle every possible state of affairs. Nonetheless, how does it follow from this that logic can't imply the existence of anything? Why can't we have it that logic must be able to handle every state of affairs and imply the existence of something or one thing?
I suppose if logic is applicable to everything, then implying the existence of something would pollute its ability to handle all states of affairs. Or is that the case? Would that this something, or these things, would somehow make logic contingent or perhaps empirical in nature. Nonetheless, implying or allowing the existence of something that is contingent or empirical is not the same as that logic itself being empirical or contingent. Logic can be applied to the empirical and the contingent. That's never been problematic.
Does it mean, instead, that if logic implies the existence of anything, or something, that it would somehow depend on that something? And, if it did, then its logical purity would somehow be sullied?
In that sense, quantificational logic is far from pure. Quantifiers in logic have existential import or commitments. That is, quantification logic implies the existence of something – many things, in fact. Even free logic accept abstract objects of various kinds. Even logical self-identity has existential import. That is, (x) (x = x) has existential implications and, more obviously, so does: (∃y) (y = y).
It seems to follow from the acceptance of quantification logic that an “ empty universe” is excluded – nay, it's logically impossible. However, do these facts about quantification logic necessarily apply to the more generic “logic” we began discussing? Perhaps quantification logic is actually “deviant logic”!