 That is, informally, if there could be something satisfying any given description \(\varphi,\) then there is something that could satisfy that description, a thing that is possibly \(\varphi.\) The validity of BF in SQML rests on two facts:  first,  that in the model theory of SQML (as in all varieties of possible world semantics), the possibility operator \(\Diamond\) is literally an existential quantifier ranging over all possible worlds; and  second,  that, in evaluating an existentially quantified formula \(\exists\nu\varphi\) at a possible world \(w,\) the initial occurrence of \(\exists\nu\) in the formula ranges unrestrictedly over all individuals. Hence, switching the order of adjacent occurrences of \(\Diamond\) and \(\exists\nu\) in a formula will not alter its truth value; to say that some world and some object are thus and so is to say no more and no less than that some object and some world are thus and  so.[44]  And this is what warrants, in particular, the inference from  (2)  to  (4).  Letting “\(\sfB\)” represent the predicate “is Bergoglio’s child”, the logical form of  (2)  is \(\Diamond\exists \sfx\, \sfB\sfx\). Expressed semantically in SQML: some world and some individual are such that, in that world, that individual is Bergoglio’s child. But that is to say no more and no less than that some individual and some world are such that, in that world, that individual is Bergoglio’s child, \(\exists \sfx\,\Diamond \sfB\sfx,\) i.e.,  (4).