Binding without variables: Solving the under-generation problems

The variable-free semantics of Jacobson (1999, 2000, 2014) derives binding relations by the local application of the z-rule. This rule, however, under- generates binding. This paper makes two contributions: (i) replacing the z-rule with a more flexible rule called i (a la the W-combinator of Szabolcsi 1992), which allows for more binding relations; (ii) enriching Jacobson’s variable-free system and proposing a two-dimensional analysis to account for the interactions between scoping and binding. Issues to be covered include binding into adjuncts, possessor binding, scope ambiguity, inverse linking, weak crossover, and ‘paycheck pronouns’.