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:

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> 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?
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My question is on the following sentence:

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> 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. 
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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!