# A question regarding semantics of "only"

I have a question regarding semantics of only provided by Beaver & Clark (2009) and Chierchia (2013).

for something like "Sandy only met [Bush]F" (let this proposition be called p). Beaver & Clark's semantics would come out as -->

{Sandy only met [Bush]F}I (w) = ∀x meet(w, S, x) → x = B

Note: {p}I (w) ~ intensional value of p evaluated at some w

Chierchia's semantics for only would be --->

OnlyC (Sandy met [Bush]F)(w) = OnlyC (p(w)) = p(w) ∧ ∀q(w) ∈ C[ q(w) → q(w) ⊆ p(w)]

where, ⊆ = entails, C is the context set of alternatives provided by Focus which is used to calculate alternatives to p.

My problem is that the Beaver & Clark denotation doesn't seem to get at the meaning of "only" we want. which is captured by Chierchia due to the exhaustivity clause introduced by "only" i.e. p and its entailments are the only true propositions from the set of active alternatives.

to me, the Beaver & Clark denotation reads as "at world w, every x such that x met Sandy is Bill" which seems like a roundabout way to get at the semantics. moreover, instead of exhaustivity it relies on what looks very much like the uniqueness presupposition of "the".

I think the exhaustivity clause is crucial to the meaning of "only" and saying something akin to uniqueness presupposition is not the right way to get at semantics of "only". is my intuition wrong? do the two semantics come out to be equivalent?

References:

Beaver, David I., and Brady Z. Clark. Sense and sensitivity: How focus determines meaning. Vol. 12. John Wiley & Sons, 2009.

Chierchia, Gennaro. Logic in grammar: Polarity, free choice, and intervention. OUP Oxford, 2013.

• Could you please provide a full reference to the original papers? Commented Aug 28, 2021 at 16:07
• @lemontree I will edit the question with proper references. sorry Commented Aug 28, 2021 at 16:08
• Could you also point out where exactly in those books to find the relevant definitions? Commented Aug 28, 2021 at 16:19
• I'm not sure I understand the issue you're having with Beaver & Clark's definition. In what way is it roundabout? The resemblance to the uniqueness presupposition of the definite determiner is no surprise, given that "only" is part of the meaning of "the": "the P" = "there is at least one P and only one P". Commented Aug 28, 2021 at 16:21
• @lemontree I am not sure why we need to quantify over all individuals and then say if the predicate is true of them then they are Bush. that's not the intuition I get for meaning of "only". when I utter only(p) I seem to be saying that merely p is the case and nothing else. I am not saying everything that is the case is p. I guess I am hung up on the conventional understanding of "only" and to me it seems that Beaver & Clark's definition does not capture it while Chierchia's does Commented Aug 28, 2021 at 19:26