Halliday & Matthiessen (1999: 429):
In Fawcett’s model, there is only one system–structure cycle within the content plane: systems are interpreted as the semantics, linked through a “realisational component” to [content] form, which includes items and syntax, the latter being modelled structurally but not systemically; […] in our model there are two system-structure cycles, one in the semantics and one in the lexicogrammar. Terms in semantic systems are realised in semantic structures; and semantic systems and structures are in turn realised in lexicogrammatical ones.
… grammatical metaphor is a central reason in our account for treating axis and stratification as independent dimensions, so that we have both semantic systems and structures and lexicogrammatical systems and structures. Since we [unlike Fawcett] allow for a stratification of content systems into semantics and lexicogrammar, we are in a stronger position to construe knowledge in terms of meaning. That is, the semantics can become more powerful and extensive if the lexicogrammar includes systems.
Halliday & Matthiessen (2004: 25):
The stratification of the content plane had immense significance in the evolution of the human species — it is not an exaggeration to say that it turned Homo … into Homo sapiens. It opened up the power of language and in so doing created the modern human brain.