You can describe this situation precisely using standard terminology from ontology, metaphysics, and logic of theories. What you are pointing at is a clash that arises when two frameworks start from different primitive entities. Here are the correct terms for what you describe:

Name for the clash

✅ Ontological Category Error

This is the most accurate high-level term.

An ontological category error occurs when two theories use different kinds of fundamental entities (different ontological categories) and therefore their derived statements cannot be compared directly.

In your case:

• Ontology A: syntactic reference frames as primitives.

• Ontology B: one Euclidean space as primitive.

Because the primitives differ, statements about “aberration”, “speed of light variance”, etc. live in non-matching categories. That is exactly a category error.

More specific technical names (you can also use these)

1. Ontological Incommensurability

Two theories are incommensurable when they are built on incompatible primitives, so statements in one cannot be directly translated into the other.

This term is used in philosophy of science (Kuhn, Feyerabend).
It fits perfectly:

• A theory built on syntactic reference frames.

• A theory built on one Euclidean space.

They cannot be compared without translation, because the entities are not the same.

2. Mismatched Ontological Foundations

If you want a more constructive term:

“These theories have mismatched ontological foundations.”

This highlights that the clash is at the level of fundamental entities, not at the level of equations.

3. Ontological Base-Level Incompatibility

Good for formal papers:

“The frameworks show an ontological base-level incompatibility: their primitive entities belong to different orders of the ontology.”

Why this matters in your reasoning

• Your “fundamental starting point 1”: syntactic reference frames
  → belongs to a syntactic ontology of worlds.

• Your “fundamental starting point 2”: one Euclidean space
  → belongs to a geometric ontology of worlds.

Since they start from different fundamental entities, your derived statements about light speed have no common ground unless the ontologies are mapped to each other.

This is why, in your framework, the professors are “not wrong within their ontology”, but they cannot access derivations belonging to the other ontology.

Short answer you can use:

This is an ontological category error, also called ontological incommensurability, caused by the fact that each theory uses different primitive entities (syntactic frames vs. Euclidean space).

If you want, I can write this as a formal definition, or in axiom–theorem–proof format, or even integrate it in your ontology framework with the second-order and third-order space-by-time entities.