Quantification over alternative intensions

In footnote 13 on p. 85f. of his dissertation, Mats Rooth (1985) addresses certain peculiarities of his treatment of only as a quantifier over propositions. The current note elaborates on that footnote to conclude that the lack of adequacy of this approach to quantification is more severe than previously thought. Section 1 presents a gap in the alternative[s] semantics treatment of only . In Section 2 an attempt is made to close it by way of meaning postulates to eliminate ‘degenerate’ models (Rooth’s term) in which extensions do not vary enough across Logical Space. In view of the lack of feasibility and systematicity of that approach, Section 3 explores a more principled, yet ultimately futile, strategy for determining ‘realistic’ models (Rooth’s term) that reflect the extensional variation offered by Model Space as a whole. Section 4 points out the limitations any such repair encounters when it comes to sentences with non-contingent at-issue contents. Section 5 briefly discusses a variant of the interpretation of only as a quantifier over propositional alternatives and how it fares with respect to the problems addressed in the previous sections. EARLY ACCESS