Halliday & Matthiessen (1999: 97-8):
The semantic categories are themselves construed by means of realisation; they are constructed within the grammar and lexis of a language. If we model the ideation base as a semantic space, we are foregrounding one aspect of the construction of meaning in language, namely the way in which lexicogrammar construes our experience of the world in the guise of multidimensional matrices or grids. This is an important feature of language as a semiotic system, an inevitable consequence of the principle of arbitrariness: since the forms of expression are arbitrary, they impose discontinuity on the content. […] But the semantic categories themselves (seen from above, as it were) are much more fluid and indeterminate than their realisations in wording imply. The notion of semantic space allows us to adopt a complementary standpoint from which we can view these phenomena topologically, bringing out the inherently elastic quality of the dimensions involved, and gaining a deeper insight into the semogenic processes by which the meaning potential is ongoingly remoulded in the history of the system [phylogenesis], of the user [ontogenesis], and of the text [logogenesis].