Formal metatheorem for the synthetic-mathematics slogan

Determine whether the claim that only synthetic mathematics can be formalized can be formulated and proved as a metatheorem.

Background

The paper presents the slogan that the only mathematics that can be formalized is synthetic and connects it to the role of synthetic models in proof assistants. It leaves unresolved whether this informal claim can be given a precise metamathematical formulation and proof.

References

Is it possible to turn the slogan of section \ref{3.2} into a (meta)theorem ?

— Retro-synthetic Riemannian geometry in Rocq I : Taylor series of a metric  (2609.20127 - Clemente et al., 17 Sep 2026) in Section 4, item 5 (Linguistic aspects of formalization)