Axis pairs perceivable forms with conceivable meanings, which makes semiosis possible. Turning your question around, what the others all have is axis. It’s also what makes SFL systemic.
I liked my bon mot ‘Axis pairs perceivable forms with conceivable meanings, which makes semiosis possible.’
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[1] This is misleading, because it is untrue. In SFL Theory, axis is the local dimension whose orders are paradigmatic and syntagmatic, with system as the dimension of paradigmatic order and structure as the dimension of syntagmatic order (Halliday & Matthiessen 2014: 20, 32).
Importantly, axis does not "pair forms with meanings". Form and meaning are located on both axes in the lexicogrammar. (There is meaning, but not form, on the semantic stratum, and form, but not meaning, on the expression plane.) Lexicogrammatical form is modelled as a rank scale, and rank units are interpreted in terms of their function in realising meaning. Paradigmatically, each formal rank unit is the entry condition to systems of such functions, and syntagmatically, each element of function structure is realised by a formal unit of the rank below.
With regard to "perceivabilty", lexicogrammar is 'a purely abstract level of representation "in between" the two faces of the sign' (Halliday & Matthiessen 1999: 613).
[2] This is misleading. To be clear, the 'others' here are those identified by Ed McDonald:
I noted the reference to axis, and I'm a bit puzzled as to how and why this seems to have become the theoretical fons et origo. Do we really to trace everything back to that single distinction? And if so, why paradigmatic/syntagmatic (and not and / or system/text, content/form, synchronic/diachronic...)? Does it have a privileged relation to realisation and / or instantiation?
[3] This is misleading. What makes SFL systemic is the priority it gives to system over structure, just as what makes SFL functional is the priority it gives to function over form.
