FC doesn't fit the scalar implicature pattern

...where [\phi]_classical is the conservative semanticist's (e.g. the Gricean's) analysis of sentence \phi, the free choice sentence isn't equivalent to anything of the `implicature-strengthened' form [\phi]_classical + p, except in the trivial case where p = the conclusion of the inference. NB that usually p = ~r, where r is some relevant stronger alternative to the proposition \phi expresses.

Examples of the pattern:

(1) A v B = [A v B]_classical + \neg(A & B)
("A & B" is a relevant alternative to "A v B" on the Horn-scale; obviously "A & B" is stronger than "A v B"_class)

(2) Three F G = [Three F G]_classical + \neg(more than three F G)
("n F G", for n greater than 3, are all relevant alternatives to "three F G" on the Horn-scale; each of these n would entail [three F G]_class, and hence are stronger relevant alternatives)

(3) Warm(a) = [Warm(a)]_classical + \neg[Hot(a)]_classical

(4) Mary likes SUE / Mary likes (only) Sue
= [Mary likes Sue]_classical + \forall x (x \neq Sue) -> neg(Mary likes x)

Possible response on behalf of (neo-)Gricean: maybe you could express the missing p = ~r if you used `only' in the specification of p?

(5?) Might(p v q) = [Might (p v q)]_classical + \neg(Might only p) ??

But that's very odd. In what sense is "Might only p" a relevant alternative to a part or whole of the original sentence? Plus, if you're allowed to use "only"s in the specification of the relevant alternatives, I could run disastrous symmetry arguments against the entire Neo-Gricean enterprise:

(6) A v B = [A v B]_classical + \neg(Only A) => A & B.

(!!!) Perhaps this is what Fox is working to avoid in his 2006 paper.