Colin McGinn challenges in his book Logical Properties the standard treatment of modality and proposes some rather provocative and unorthodox ideas on the nature of necessity and associated modal notions. There is much to argue about McGinn's positions, but I would like to focus on three particular issues:
The main objection of McGinn to the possible world semantics is that this approach reduces modal notions to quantifications over universes of possible worlds, and whether a world is possible or not is already dependent on the modal concept of possibility, thus engendering a circular reasoning. As I see it, the flaw in this argument stems from the wrong assumption that characterizing a world W as possible is a modal business; although McGinn does not put it explicitly, he seems to think that the statement "W is a possible world" is equivalent to something like "possibly W exists". But actually there is nothing modal about the concept of "possible world": a possible world is just a consistent (i.e. logically non-contradictory) state of affairs, of which the actual world we live in is just an example. Rephrase the whole possible worlds semantics formulation replacing "possible world" with "consistent world" and all the apparent circularities vanish away.
Later on, McGinn proposes a copula modifier theory to explain modality: basically, this theory contends that modal notions qualify the way that objects hold properties. So, "Socrates must be a man" means that Socrates holds the property of being a man in the mode of necessity. McGinn immediately realizes that adscribing modality to the copula of statements cannot cover uses of modality qualifying entire statements, as in "it is impossible that 2 + 2 = 5" (which, incidentally, is how modality operators work in formal modal logic). He solves the problem by postulating that in these cases the missing copula to qualify is that adscribing the truth property to the proposition at hand: so "it is impossible that 2 + 2 = 5" can be rephrased as "the proposition '2 + 2 = 5' cannot be true", which, according to the copula modifier theory, means that "2 + 2 = 5" holds the property of being true in the mode of impossibility. In the process, McGinn has forced us to accept propositions as first-class entities to talk about, an ontological extension that some (notably Quine) reject commiting to. Even admitting this unexpected guest, it is not clear to me how this theory sheds any light on the nature of modality: one can as well go the reverse way and formulate predicate-qualifying modal sentences as sentence-level modal utterances: for instance, "Socrates must be a man" is just a way of saying "necessarily Socrates is a man", which process does not involve the introduction of propositions and the "truth predicate". Why McGinn prefers one rewriting rule to the converse is unknown to me --furthermore, McGinn's formulation poses some perplexities when iterated modality is considered, as he readily acknowledges.
Finally, having stated that modality affects the way objects hold properties, McGinn renounces to further analyze what the exact nature of this relationship between objects and properties is. He gives in passing a Tarski-style semantic formulation of modality along the lines
x satisfies 'is necessarily F' iff x necessarily satisfies 'F',
only to admit that this does not add anything to our understanding of modality. Modal truth is left as a sort of primitive, epiphenomenal concept for which even a special entity status is set up within the confines of McGinn's exuberant ontology. It is difficult to see how this situation represents an improvement over the standard modal theory.