Abstraction, Structure, and Substitution: Lambda and its Philosophical
λ-calculi are of interest to logicians and computer scientists but have
largely escaped philosophical commentary, perhaps because they appear
narrowly technical or uncontroversial or both. I argue that even within
logic λ-expressions need to be understood correctly, as functors signifying functions in intension within a categorial or typed language.
λ-expressions are not names but pure variable binders generating functors,
and as such they are of use in giving explicit definitions. But l is
applicable outside logic and computer science, anywhere where the notions
of complex whole, substitution, abstraction and structure make sense. To
illustrate this, two domains are considered. One is somewhat frivolous:
the study of flags; the other is very serious: manufacturing engineering.
In each case we can employ λ-abstraction to describe substitutions within
a structure, and in the latter case there is even a practical need for
such a notation.