 There are three crucial points to the DPL treatment here. (1) The existential quantifier is externally dynamic and hence may affect the interpretation of variables outside its scope, and in particular “x” in the consequent of (32a). (2) “\(\rightarrow\)” is internally dynamic and allows the interpretation of its antecedent to affect the interpretation of its consequent (just as is conjunction). 1 and 2 together mean that the quantifier in the antecedent of (32)/(32a) can semantically bind the variable in the consequent, even though it is not in the syntactic scope of the quantifier. But without doing anything further, we would be left with (32a) having the truth conditions of