 Analogous “no conceptual analysis” objections can be made if we accept that the concept of logical truth has some other strong modal notes unrelated to analyticity; for example, if we accept that it is part of the concept of logical truth that logical truths are true in all counterfactual circumstances, or necessary in some other strong sense. Sher (1996) accepts something like the requirement that a good characterization of logical truth should be given in terms of a modally rich concept. However, she argues that the notion of model-theoretic validity is strongly modal, and so the “no conceptual analysis” objection is actually wrong: to say that a formula is or is not model-theoretically valid is to make a mathematical existence or non-existence claim, and according to Sher these claims are best read as claims about the possibility and necessity of structures. (Shalkowski 2004 argues that Sher's defense of model-theoretic validity is insufficient, on the basis of a certain metaphysical conception of logical necessity. Etchemendy 2008 relatedly argues that Sher's defense is based on inadequate restrictions on the modality relevant to logical truth. See also the critical discussion of Sher in Hanson 1997.) García-Carpintero (1993) offers a view related to Sher's: model-theoretic validity provides a (correct) conceptual analysis of logical truth for Fregean languages, because the notion of a set-theoretical structure is in fact a subtle refinement of the modal notion of a possible meaning assignment. Azzouni (2006), ch. 9, also defends the view that model-theoretic validity provides a correct conceptual analysis of logical truth (though restricted to first-order languages), on the basis of a certain deflationist conception of the (strong) modality involved in logical truth.