Metaredundancy is not "the lexicogrammar construing the semantics construing the context" (Bartlett 2022). Metaredundancy, as the name implies, is a redundancy on a redundancy. Halliday uses the term for the three strata of language: semantics, lexicogrammar and phonology:
- the redundancy of semantics and lexicogrammar is redundant with phonology, or
- semantics is redundant with the redundancy of lexicogrammar and phonology.
One reason why Halliday took up Lemke's term was that it allowed him to explain that stratification is not a temporal (or causal) chain relation, as in 'semantics is realised in lexicogrammar, which is then realised in phonology'.
To be clear, the relation between strata is not enhancing (temporal or causal), but elaborating, and identifying, with the higher stratum of two as Value and the lower stratum as Token. Metaredundant relations in stratification can thus be expressed by either of the following:
For Halliday:
- the realisation of semantics in lexicogrammar is realised in phonology, or
- semantics is realised in the realisation of lexicogrammar in phonology.
On the other hand, the notion of lexicogrammar construing semantics is the notion that semantics is intellectually constructed by lexicogrammar, and the notion of semantics construing context is the notion that context is intellectually constructed by semantics.