Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is that reflexive (...) and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

In Epiphany Term, 1942, C.S. Lewis delivered the Riddell Memorial Lectures in the Physics Lecture Theatre, King's College, Newcastle, which was then a constituent college of the University of Durham. The Riddell Memorial Lectures were founded in 1928 in memory of Sir John Buchanan Riddell of Hepple, onetime High Sheriff of Northumberland, who had died in 1924. His son, Sir Walter, was, like his father, a devout Christian, active throughout his life in public affairs. He was Fellow, and subsequently (...) Principal, of Hertford College, Oxford, and Secretary, and subsequently Chairman, of the University Grants Committee---at a time when the interventions of the UGC in academic affairs were entirely benign. I myself have a special personal interest in the founder of the Riddell Lectures. Sir Walter and my father were contemporaries at Oxford and close friends. Owing to his untimely death I never knew him, though I am credibly assured that he must have viewed me when I was taken to Hepple in a Moses' basket at the age of six months. In being invited to give this lecture on the Riddell Lectures, I am not only honoured but enabled to discharge a debt of family.. (shrink)