 It is a logical truth in (standard) first order logic that something exists, i.e., ‘\(\exists x\,x=x\)’. Similarly, it is a logical truth in (standard versions of) second order logic that ‘\(\exists F\forall x\,(Fx \vee \neg Fx)\)’. These are existentially quantified statements. Thus, one might argue, logic is not neutral with respect to what there is. There are logical truths that state that something exists. However, it would be premature to conclude that logic is not neutral about what there is, simply because there are logical truths in (standard) first or second order logic which are existential statements. If we look more closely how it comes about that these existential statements are logical truths in these logical systems we see that it is only so because, by definition, a model for (standard) first order logic has to have a non-empty domain. It is possible to allow for models with an empty domain as well (where nothing exists), but models with an empty domain are excluded, again, by definition from the (standard) semantics in first order logic. Thus (standard) first order logic is sometimes called the logic of first order models with a non-empty domain. If we allow an empty domain as well we will need different axioms or rules of inference to have a sound proof system, but this can be done. Thus even though there are formal logical systems, in the sense of (L1) in which there are logical truths that are existential statements, this does not answer the question whether or not there are logical truths, in the sense of (L2), that are existential statements. The question rather is which formal system, in the sense of (L1), best captures the logical truths, in the sense of (L2). So, even if we agree that a first order logical system is a good formal system to represent logical inferences, should we adopt the axioms and rules for models with or without an empty domain?