A typical example of what makes theory unformalizable is the horizontal relation between epistemorphization and the diegesis.
It’s neither the case that both the truth and the untruth can be rendered apparent; nor that rendition-to-the-apparent (literally: e-vidence) reveals truth. In the rigorous language of Rudolf Willie’s “Formal Concept Analysis”, this structure of horizontal relation is termed “orthogonality”. In this way (and at least for this special problem of truth/experience — an important one) the unformalizeability of theory can be formalized.
Ça veut dire: any formalization of theory is forced to “break ties” at horizontal/orthogonal relations. This matches the subjective experience of mathematical training, where one learns to produce proofs by tie-breaking between equally valid derivation subtrees. It also neatly characterizes just what’s the “petty bourgeois” step we refuse to do.