[I wasn't able to use the symbol for the necessity operator in this piece.]
The x in ∃x occurs free in the scope of necessarily in ∃Fx therefore the statement is de re. On the other hand, no variable or constant is free in the scope of necessarily in the formula necessarily ∃x Fx, therefore it is a de dicto statement. [The logical symbolism in the above doesn't make sense. This needs to be revised.] So the de re statement reads:
There is at least one x, such as that x is necessarily F.
The de dicto statement reads:
Necessarily there is at least one x, such that that x is F.
The de re statement ascribes a necessary property to an object. Whereas the de dicto statement ascribes necessity to the formula itself. That is, necessarily at least one object is F. The de dicto statement is saying that there is necessarily at least one x such as that x is F. Whereas the de re statement says that there is at least one object (though not necessarily one object), such that the object is necessarily F. In the former case, the necessity operator works on the object, whereas in the latter case the operator works on a property of the object.
In terms of possible worlds, the de re statement says that all x’s have the property F at all possible worlds. And if a = x, then a has the property F at all possible worlds.
The de dicto statement, on the other hand, says that there is at least one x such that this x is F. However, x's aren’t necessarily F at all possible worlds. So x, or an x, on the de dicto reading, need not be F in all possible worlds.
Quine on De Re Modality
‘9 = the number of planets’ in Quine’s scheme because he was an extensionalist. That is, he didn’t believe in possible worlds. However, he didn't accept that that the number of planets necessarily is more than 7 because the number of planets does not necessarily equal 9. But if we don’t except that the definite description equals 9 because of possible world scenarios, then we have no “clear meaning” what the description ‘the number of planets’ refers to. It could be 10 in possible world w1 and 1000000 at another possible world. In fact if possible worlds are infinite in number, ‘the number of planets’ could equal any number. If this is the case, then the definite description ‘the number of planets’ quite evidently “lacks a clear meaning”. So the number of planets can either have no de re meaning or it has a different meaning at every possible world.
Quine must accept, and I think he did accept, Necessarily (9 > 7). Though, according to Marcus, the description ‘the number of planets’ can't be a proper name precisely because it designates different numbers at different possible worlds. However, the name ‘Tony Blair’ does indeed designate the same object at all possible worlds. Though what, precisely, does that mean? It doesn’t mean that Tony Blair is called ‘Tony Blair’ at all possible worlds. It does mean that our name ‘Tony Blair’ designates the object Tony Blair at all possible worlds, whether or not Tony Blair is actually called ‘Tony Blair’ at all these possible worlds.
Kripke’s necessary a posteriori means:
If a and b are identical, then necessarily a = b at all possible worlds.
No mention of actual names is mentioned here. The a and b designate objects, not names. So the person Tony Blair could be named ‘Frank Parsons’ at one possible world, just as Cicero was also named ‘Tully’ at our world. Therefore Tony Blair couldn't be two different entities at different worlds; though he could have two or more different names at other possible worlds.
De Re & De Dicto Modality
The first de dicto statement means that part of the concept [British monarch] includes or contains the concept [head of the British government]. Of course it could be the other way around. That is, the concept [head of the British government] contains or includes the concept [British monarch]. We could say that one is more of a definite description than the other. However, [British monarch] is still descriptive in that different individuals could fulfil that role at different possible worlds.
The de re reading applies an essential or necessary property to a res – to a person. It could be read this way: Ma necessarily ∃Ba. Here the necessity operator is applied to the person who is a British monarch. It says that if this is the case, then he or she must be head of the British government.
In the de dicto reading, the necessity operator is placed differently. Here we have: necessarily (Ma necessarily Ba) ¸ (Ba necessarily Ma) (Ma ≡ Ba). Here the necessity operator has as its scope the whole statement, including all the constituent concepts or predicates. It reads:
Necessarily, if a is M, then a is B and necessarily if a is B then a is M. Therefore a is M if and only if a is B.
It could be said that the biconditional in and of itself entails necessity.