The spiritus asper as used by Frege in a letter to Russell from 1904 bears resemblance to Church’s lambda. It is natural to ask how they relate to each other. An alternative approach to functional abstraction developed by Per Martin-Löf some thirty years ago allows us to describe the relationship precisely. Frege’s spiritus asper provides a way of restructuring a unary function name in Frege’s sense such that the argument place indicator occurs all the way to the right. Martin-Löf’s alternative (...) approach shows that this is only half of what lambda does. The other half is the deletion of the argument place indicator, resulting in what Frege would have called an isolated function name. (shrink)

It is argued that the source of complexity in language is twofold: repetition, and syntactic embedding. The former enables us to return again and again to the same subject across many sentences, and to maintain the coherence of an argument. The latter is governed by two forms of complexification: the functor-argument structure of all languages and the operator-bound-variable mechanism of familiar formal languages. The former is most transparently represented by categorial grammar, and an extension of this can adequately describe the (...) syntax of variable binders. Both developments have roots within the work of the Lvov-Warsaw School. (shrink)