  How does one formalize the structure of structures necessary for the
foundations of physics? This work is an attempt at conceptualizing the
metaphysics of pregeometric structures, upon which new and existing notions of
quantum geometry may find a foundation. We discuss the philosophy of
pregeometric structures due to Wheeler, Leibniz as well as modern
manifestations in topos theory. We draw attention to evidence suggesting that
the framework of formal language, in particular, homotopy type theory, provides
the conceptual building blocks for a theory of pregeometry. This work is
largely a synthesis of ideas that serve as a precursor for conceptualizing the
notion of space in physical theories. In particular, the approach we espouse is
based on a constructivist philosophy, wherein ``structureless structures'' are
syntactic types realizing formal proofs and programs. Spaces and algebras
relevant to physical theories are modeled as type-theoretic routines
constructed from compositional rules of a formal language. This offers the
remarkable possibility of taxonomizing distinct notions of geometry using a
common theoretical framework. In particular, this perspective addresses the
crucial issue of how spatiality may be realized in models that link formal
computation to physics, such as the Wolfram model.
