Variable-Binders as Functors
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.
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- Poznan Studies in the Philosophy of the Sciences and the Humanities
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- November 21, 2014