How to avoid Babelian confusion in theoretical physics?

Avril Emil wondered in discussion group of The Finnish Society for Natural Philosophy, how it is possible to deduce explanations from so different premises (see this). The discussion was related to the deepening crisis of cosmology caused by the findings of James Webb space telescope and suggesting that the big cosmic narrative is entirely wrong: even the origin of the CMB is challenged by FWST. I glue below my response.

Principles are needed, a mathematician would talk about an axiomatic approach. Otherwise, the result is a confusion of languages at Babel.

1. If we demand that the description of gravity and also other interactions be geometrized and that the classical conservation laws hold true as a consequence of Noether’s theorem, we end up to H=M⁴×CP₂ if we demand the symmetries of the standard model.
2. If we also demand a number-theoretic description complementary to the geometric one (the equivalent of Langlands duality), we end up with M⁸-H duality and classical number systems are an essential part of the theory. M⁸ corresponds to octonions. The dynamics in M⁸ are also fixed by the quaternionicity/associativity requirement. The symmetries of the standard model correspond to the number-theoretic symmetries of octonions.
3. If we demand a generalization of 2-D conformal symmetry to 4-dimensionality, we end up with holography= holomorphism vision. The dynamics of spacetime surfaces is unique everywhere except at singularities, regardless of the action principle, if it is general coordinate invariant and constructible using induced geometry. Spacetime surfaces are minimal surfaces (analogous to solutions of massless field equations) and the field equations reduce to purely algebraic local conditions. The theory is classically exactly solvable.
4. One can claim that the theory is uniquely determined simply because it exists mathematically. The requirement for the existence of a twistor gradient in the theory leads to H=M⁴×CP₂. Only these two 4-spaces in H have a twistor space with the Kähler structure needed to define the classical theory.

The 4-dimensionality of spacetime surfaces follows in several ways: as an extension of conformal invariance from 2 to 4 dimensions and also from the requirement that, assuming free fermion fields in H, one obtains a vertex on the spacetime surface geometrically corresponding to the creation of a fermion pair. The requirement that a free theory gives interactions sounds impossible to implement, but a special feature of 4-D spacetimes is the exotic diff structures, which are standard diff structures with defects corresponding to vertices. The creation of a fermion pair intuitively corresponds to the turning of a fermion line back in time and the edge associated with this turning corresponds to the defect, the vertex. For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.