Is there a difference between "Who necessarily do not exist" or "who do not exist necessarily"?

This is from the English version of the book "The Name of the Rose" by Umberto Eco.

Brother William was arguing that the non-Christian people should also be given the right to rule. Here are some sentences before the one that I have question with:

And could it be denied that many Roman emperors - Trajan, for instance - had exercised their temporal power with wisdom? And who gave the pagans and the infidels this natural capacity to legislage and live in political communities?

My question is on the following sentence:

Was it perhaps their false divinities, who necessarily do not exist (or do not exist necessarily, however you understand the negation of this modality)? Certainly not.

I think here he used these two different expressions to express slightly different inferences. Is that true? So what is the difference? Also the clause "however you understand the negation of this modality", does it confirm the difference?

Thank you for your help!

Solution 1:

Yes, there is a difference.

"Who necessarily do not exist" means that those people do not exist due to some need or requirement. This is saying the "who" do not exist.

"Who do not exist necessarily" means that those people may not exist, that we can't logically conclude that they do exist. This is NOT saying that the "who" do not exist. Instead, it is saying that the "who" may or may not exist.

Solution 2:

The modality referred to is occasioned by the adverb necessarily. Apparently, Eco is considering two different statements, where the negation either does not, or does, span the modality, respectively:

• necessarily (not exist)

• not (necessarily exist)

These would indeed be understood differently (provided our understanding of "necessarily X" is different to "X" alone, of course. This may take some mind bending :))

The intuitive understanding (of some eminent philosophers) of the modality of necessity led to semantic models for modal statments, such as possible world semantics. Under this semantics, necessarily X is explained as "X holds in all possible worlds"; this explanation makes apparent the distinction of the two statements.

Philosophers' preoccupation with necessity (and the consequent need to develop a semantics for it) traditionally stemmed from considerations of a priori truths or ontological arguments, etc.