Re-thinking the Arbitrary Mapping of Signier and Signied: A Symmetry and Symmetry-Breaking Perspective

Ferdinand de Saussure's axiom that the bond between signifier and signified is arbitrary has anchored structural linguistics for over a century, yet arbitrariness itself has never been furnished with a principled physical or mathematical basis. This gap has concrete consequences: it leaves unexplained both the constitutive difficulty of recovering natural language from biological signals and the absence of a physically grounded account of the mind-language relation. This paper addresses both problems by invoking spontaneous symmetry breaking from theoretical physics and group theory. We make the following contributions: (i) Saussurean arbitrariness is formalised as maximal symmetry over the space of signifier--signified mappings, elevating it from an empirical axiom to a structural theorem., (ii) The intervention of any interpretive system is modelled as a symmetry-breaking event that selects a semantic vacuum, condensing meaning from a degenerate possibility space., (iii) We prove that this breaking is generically irreversible, providing a structural basis for the hermeneutic circle and constitutive untranslatability., (iv) Neural encoding and natural language are shown to be two independent symmetry breakings, making biosignal-to-language decoding constitutively non-unique., (v) A gauge-theoretic programme is sketched in which neural-linguistic interfaces target gauge-invariant semantic content, stable across all admissible decoding choices, via fibre bundle formalism.