2.Thanks to Ed, for the challenge presented by your reading of my diagram below as ‘(paradigmatic) "features" and (syntagmatic) "structures"’.The diagram is meant to show that structures are part of systems, not opposed to them as the system/structure and paradigmatic/syntagmatic terms might suggest. Structures don’t realise systems, but features in systems. Structures are perceivable tokens of the abstract values of features. Each instance of structure is recognisable by its similarity to other instances of the same structure, and its difference from other types of structure. Similarity is represented in the diagram by hexagons, and difference by the system. The entry condition to a system is a more general similarity that is shared by its structures, e.g. the structure +Subject;+Finite is shared by the structures Subject^Finite and Finite^Subject. These similarities and differences in structure realise similarities and differences in features, such as indicative: declarative/ interrogative. Hence the system of features is a mirror of the system of structures. They are two faces of a system. This is my understanding of MAKH’s axial breakthrough.
[1] Some of the problems with this diagram were identified in the earlier post David Rose Misunderstanding Generalisation And Abstraction.
[2] This is a very serious misunderstanding. Systems and structures are distinct levels of symbolic abstraction (elaboration + identity), whereas the relation that obtains between a whole and its parts is composition (extension). A part of a system is a subsystem, whereas a structure (e.g. of a group) is part of a larger structure (e.g. of a clause).
[3] This is a very serious misunderstanding. It is the entire system of a rank unit that specifies how its entire structure is realised, and this is achieved through realisation statements, not features.
[4] This confuses lower abstraction with perceivability. The structure of a nominal group cannot be perceived, unless, like its system, it is represented theoretically.
[5] This confuses the realisation (token-value) relation between structure and system with the instantiation (token-type) relation between instances and instance type.
[6] This confuses instance type (similarity) with paradigmatic order (difference).
[7] This confuses instance type (similarity) with the entry condition of a system. In the grammar, the first entry condition of a system is a formal unit on the rank scale.
[8] This is misleading, because it is untrue. Difference in system is difference between paradigmatic features, such as declarative vs interrogative, whereas difference in structure is difference in elements, such as Subject vs Complement.
[9] To be clear, the claim that "Halliday's axial breakthrough" is that system and structure are "two faces of a system" derives from the multiple misunderstandings identified above.
