1995 Articles

Variable-Binders as Functors

Varzi, Achille C.

The second part of Ajdukiewicz’s classic paper on Syntactic Connexion is devoted to a
discussion of languages involving variable-binding operators such as quantifiers, integrals,
and the like. Ajdukiewicz argues that such operators are not genuine functors,
and consequently that those languages run afoul of the basic functor/argument schema.
At most he suggests that all variable-binders might be restricted to one kind only, or to
the combination of ordinary functors with a “circumflex” operator (the terminology is
from Whitehead and Russell’s Principia Mathematica). And that suggestion has ever
since become quite popular, particularly under the impact of Church’s Lambda Calculus.