9.5 Transport, forgetting, and conceptual loss

Every transformation creates a continuity question. Given \(J:\mathbb S\to \mathbb S^+\) and a compatible comparison \(\delta _{\mathfrak D}\) between the old and new preservation doctrines, restriction induces, when well-defined,

The fiber test of Section 5.6 now has an epistemic use: it separates a conservative elaboration from a genuinely new choice and from a proposal that rejects or reinterprets an old model. In a transformational trace, that classification belongs in the admission record; it cannot be inferred from the novelty of the proposed syntax.

Not all loss is a defect. A successful theory can abandon an assumption, identify formerly distinct descriptions, or restrict models that conflict with evidence. The requirement is to make that loss explicit. The extension record should state:

• which old objects and equations are preserved;

• which are reinterpreted, quotiented, weakened, or discarded;

• which old results can be transported and by what map;

• which observations become newly expressible; and

• which countermodels distinguish the new theory from the old.

This makes transformational creativity cumulative without requiring every new theory to contain its predecessor literally.