In Chapter 6 of Our Idea of God (1991), Thomas Morris provides a brief but helpful explanation of different types of necessity in relation to divine attributes.
Morris explains three different types or levels of necessity.

Let’s use claims about the divine attribute of omnipotence as examples of the three types of necessity. I think this might help with further discussion about the paradox of the stone and the divine attribute of omnipotence.

de dicto necessity
(1) Necessarily, God is omnipotent.

This means that nothing gets to count as being ‘God’ unless it is omnipotent, just as nothing gets to count as being a ‘bachelor’ unless it is unmarried. Having the property of omnipotence is a necessary condition or conceptual requirement for something to be (correctly) called ‘God’, just as having the property of being unmarried is a necessary condition or conceptual requirement for something to be (correctly) called a ‘bachelor’ . Something is ‘God’ only if it is omnipotent, just as something is a ‘bachelor’ only if it is unmarried.

de re necessity
(2) God is necessarily omnipotent.

This means that the being who in fact is God is not only omnipotent, but has omnipotence as an essential property, just as the being who in fact is Bradley Bowen is not only a person, but has personhood as an essential property. If the being referred to by the name ‘God’ ceases to be omnipotent, that being will cease to exist, just as if the being referred to by the name ‘Bradley Bowen’ ceases to be a person, then that being will cease to exist.

Note that with de re necessity, the possession of the essential property need not be logically implied the key word or phrase used in the statement. Thus, we could replace the word ‘God’, which might logically imply omnipotence, with another expression which did not have this implication, and still have a (potentially) true claim:

(3) The creator of the universe is necessarily omnipotent.

If (2) were true, then presumably (3) would also be true, even though the expression ‘the creator of the universe’ does not logically imply omnipotence. What matters is not the logical implications of the name or concept, but the nature of the thing to which the name or concept refers.

Because de re necessity concerns essential properties, the following is another way of asserting this type of necessity:

(4) Omnipotence is an essential property of the being who is God.

Similarly, personhood is an essential property of the being who is writing this blog post. If I cease to be a person, I will cease to exist. If God ceases to be omnipotent, he will cease to exist, according to claims (2) and (4).

Most theologians agree with (1), and many agree with (2). But many theologians want to make an even stronger claim:

(5) Necessarily, God is essentially omnipotent.

This claim involves a combination of de dicto and de re necessity. It means that nothing gets to count as being ‘God’ unless it is essentially omnipotent. Having the property of omnipotence as an essential property is a necessary condition or conceptual requirement for something to be (correctly) called ‘God’.

To be continued…