Can I suggest when reading the various philosophers of language cited in this thread, to remember the one missing puzzle piece that lies at the heart of systemic functional semiotics... axis.
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To be clear, here Rose confuses axis with system. Axis is a local dimension with two orders: paradigmatic and syntagmatic. Halliday & Matthiessen (2014: 32):
System, on the other hand, is the dimension of the paradigmatic order of axis only. Halliday & Matthiessen (2014: 20):
