Martin (1992: 109):
This scale is in certain respects a natural development in a language like English which has developed the definite/indefinite articles the way it has. Prior to the development of this system there was no need to mark every nominal group as "given" or "new". But "newness" could be made explicit, as it can be in many languages (see Martin 1983:60-62 for discussion), with the cardinal one or, in the plural, a quantifier like some. In Tagalog, for example isa 'one' and ilan 'few' can even be used to over-ride the very strong association of Theme with definiteness noted above in 3.2. The use of related items to realise [particular] reference in English reflects this pattern.
 This is a bare assertion, unsupported by evidence, or argument (see below). As previously demonstrated, the scale itself confuses (interpersonal) non-specific Deictics and post-Deictics with (textual) reference items, and these with what is claimed to be the centrality of (experiential) participants to a text.
 The English definite and indefinite articles — in SFL theory, the 'weak' specific and non-specific determiners (Halliday & Matthiessen 2014: 368) — did not, and do not, mark nominal groups as given or new (with or without scare quotes). Deixis and information are distinct grammatical systems, the former an interpersonal system of the nominal group, the latter a textual system of the information unit.
 Here Martin uses a claim about Theme to argue a claim about New, as an argument about deixis misunderstood as reference.
 Trivially, this confuses the numeral 'one' with the non-specific determiner 'one'.
 This is a bare assertion, unsupported by evidence, or argument. Moreover, it confuses a misunderstanding of deixis ('particular') rebranded as reference with given and new information.
 To be clear, Martin has made a (false) claim about two determiners, a(n) and the, and claimed, without evidence or argument, that the claim holds for different determiners: any, some, one, this. In terms of logical fallacies, this might be considered a fallacy of composition: assuming that something true of part of a whole must also be true of the whole.
Derrida (1998) referred to the rhetorical use of multiple inconsistent arguments to defend a point as Kettle logic (la logique du chaudron).