Supposing an objector were to suggest, by way of criticism, that there is an equivocation in the Modal Ontological argument. Notice that the very first premise is that it is logically possible that a maximally great being exists. Following this defenders of the argument help themselves to the Axiom S5 in Modal Logic which demonstrates that anything which is possibly necessary is necessary. However, here’s a possible (no pun intended) objection:
One might deny the first premise, which says that it is logically possible that a maximally great being exists, by responding that the word possible is here not being used as an epistemic term, but as reflecting or predicating a modal status: namely the status of being contingent. When we say that something is possible what we mean is just that something has a modal status which differs from either ‘impossibility’ or ‘necessity’. All of modal logic is in one sense an exercise in classifying propositions, or that which propositions signify, into one of these three categories: ‘possible’ ‘impossible’ or ‘necessary’. Thus, when we say that something is possible we mean to predicate of it this intermediate modal status. However, the concept of a maximally great being just involves predicating the modal status of ‘necessity’, it is literally incorrect to say that a maximally great being is ‘possible’. Thus, we can imagine somebody using this argument to deny the first premise of the modal-Ontological argument.
We can avoid this argument by more clearly defining possible in our modal vocabulary: we can say that something is logically possible if and only if it obtains in one logically possible world. Then we would say that the word possible is not being used epistemically, but it also isn’t predicating any modal status, except insofar as it is eliminative of one modal status: being impossible. For something to be contingent, therefore, more is required than that it is possible. It must also be possible for the thing to fail to instantiate/obtain. That is to say, X is contingent iff there is at least one logically possible world in which ~X and one logically possible world in which X. Therefore possibility is a necessary but not sufficient condition of contingency. This definition is more modest in that it doesn’t take predicating possibility to predicate a definite modal status along with it. Also, consider how plausible this definition of possibility is in light of the fact that the definition of necessary is just that it exists in all logically possible worlds, and ‘impossible’ that it exists in none.