The Essence of Scott's "Continuous Lattices"

Following Fernando Zalamea's call for mathematical criticism [4], we engage in an immersion and reflection on Dana Scott's seminal paper Continuous Lattices [3]. During that process, we turn to making mathematics by extracting the essence of Scott's arguments, thereby engaging in what we might call mathematical praxis. We reveal that Scott's construction of a model of λ-calculus actually happens in a more general setting than it first seems, which includes the use of a particular geometric context [1] to then construct a poset-enriched semicartesian monoidal category in which the inverse system constructions actually take place. We ponder the philosophical implications of this approach.