Symbolisation for extended axiomatic functionalism

This article presents a set of symbols for the linguistic, and semiotic, theory of extended axiomatic functionalism. Section 2 provides a visual representation for one of the two components of the theory, the signum ontology, plus the ancillary areas of general phonetics and general semantics. Section 3 presents the proposed symbols for the signum ontology and ancillary areas. Sections 4-4.5 provide exemplification: Section 4.1 for general-phonetic notions, Section 4.2 for general-semantic notions, Section 4.3 for morphontic (non-meaning-related) only notions, Section 4.4 for semantic (meaning-related) only notions, and Section 4.5 for both morphontic and semantic notions. Sections 5-5.5 consider the principles adopted in drawing up these symbols, as follows: retention of existing linguistic symbols (Section 5.1), use of identical symbols for morphontics and semantics, and plain vs. italic text (Section 5.2), degree of abstraction (Section 5.3) – instantiation, i.e. direct model for speech events (level 1) (Section 5.3.1), immediate generalisation from speech events (level 2) (Section 5.3.2), secondary generalisation from speech events (level 3) (Section 5.3.3), and signum level (level 4) (Section 5.3.4), and degree of peripherality or centrality (Section 5.4). Section 6 provides a representation of (i) the second of the two components of extended axiomatic functionalism, the system ontology, and (ii) the overall theory, comprising the signum ontology and the system ontology (plus ancillary areas of general semantics and general phonetics). Section 6.1 considers the proposed symbols for the system ontology. Section 6.2 discusses issues involved in choosing appropriate symbols for the system ontology. Section 7 considers ways in which the symbols for both the signum ontology and system ontology can be simplified. Section 8 compares the symbols proposed in this article with those proposed by Mulder for ‘standard axiomatic functionalism’.