Halliday & Matthiessen (1999: 504):
A stratified semiotic defines three perspectives, which (following the most familiar metaphor) we refer to as ‘from above’, ‘from roundabout’, and ‘from below’: looking at a given stratum from above means treating it as the expression of some content, looking at it from below means treating it as the content of some expression, while looking at it from roundabout means treating it in the context of (i.e. in relation to other features of) its own stratum.
Halliday (2008: 141):
When we are observing and investigating language, or any other semiotic system, our vision is essentially trinocular. We observe the phenomenon we want to explore — say, the lexicogrammar of language — from three points of vantage. We observe it from above, in terms of its function in various contexts. We observe it from below, in terms of its various modes of expression. And thirdly, we observe it from its own level: from within, or from round about, according to whether we are focussing on the whole or some of its parts.Halliday & Matthiessen (2004: 31):
We cannot expect to understand the grammar just by looking at it from its own level; we also look into it ‘from above’ and ‘from below’, taking a trinocular perspective. But since the view from these different angles is often conflicting, the description will inevitably be a form of compromise.
Halliday (2008: 6):
The boundaries of any grammatical category are likely to be fuzzy […] — such indeterminacy is a general property of the grammar. The grammarian attempts to define each category as accurately as possible, looking at it from three different angles: its systemic environment (contrast with other term or terms in the system, and the relationship of that system to other systems); its meaning (proportionality in semantic terms), and its form. In other words, the grammarian adopts a “trinocular” perspective on the stratal hierarchy so that every category is viewed “from round about”, “from above” and “from below”. And since the views from these different angles often conflict, assigning instances to a particular category involves some degree of compromise, where criteria will depend on the purposes of the description.