Martin (1992: 111):
Where more experiential meaning is required, a common noun will be selected as Thing, and Numerative, Epithet, Classifier and Qualifier elements added as appropriate… . The choices that are relevant to the discussion at this point have to do with the Deictic function. If the interlocutor/non-interlocutor opposition is relevant to identifying the participant in question then demonstrative reference will be selected… . This opposes participants near (in the sense of what Halliday 1985: 160) calls "associated with") the interlocutors (this/these) with those less proximate (that/those). Where "proximity" to the interlocutors is not relevant the definite article the can be used to mark the identity of the participants as recoverable.
 To be clear, this confuses the (structurally realised) system of the nominal group that realises a participant (experiential metafunction) with the (non-structurally realised) system of reference (textual metafunction).
 To be clear, this confuses the (structurally realised) deictic system of the nominal group (interpersonal metafunction) with the (non-structurally realised) system of reference (textual metafunction).
 To be clear, this misunderstands the deictic distinction between these determiners and misrepresents it as a distinction in the system of reference. The determiner distinction is between non-selective (the) and selective: near (this/these) vs far (that/those) specific deixis.