The evolution of understanding of syntactic structure and its mathematical representation in the structuralist school: From Saussure to set theory, graphs, and algebras

Evans Gesura Mecha

doi:10.51867/AQSSR.3.2.50

Authors

Evans Gesura Mecha Kisii University, Kenya Author https://orcid.org/0000-0002-1875-7998

DOI:

https://doi.org/10.51867/AQSSR.3.2.50

Keywords:

C-command, Linearization, Mathematical Structuralism, Merge, Model-Based Linguistics, Multidominance, Structural Realism, Structuralism, Syntactic Structure, X-Bar Theory

Abstract

What kind of mathematical object is a sentence? This article traces how structuralist linguistics has answered that question, from Saussure's sign-system through Bloomfieldian and Harrisian distributionalism to the labelled tree of early generative grammar, the unordered set of Minimalist Merge, and today's graph-theoretic and algebraic reformulations. The paper adopts a conceptual-historical and critical analytical approach, examining foundational and contemporary theoretical literature on linguistic structuralism, mathematical representation, and the philosophy of scientific modelling. Its research design involves a comparative analysis of successive models of syntactic structure, focusing on their underlying mathematical assumptions, explanatory capacities, and limitations. We disentangle theses often conflated under “structuralism”: the linguistic school, mathematical structuralism, structural realism, and the structuralist theory of science, drawing on Rickart, Hellman and Shapiro, Votsis, Balzer, Sneed and Moulines, and Nefdt's model-based reading of grammar. We then re-examine linearization, the deep/surface distinction, binarity, endocentricity, Merge, and Hopf-algebraic and graph-theoretic reformulations, arguing that this history isolates which relational properties of language are genuinely forced and which are formal artefacts of a chosen idiom. Findings reveal that c-command remains a relatively stable relational property across changes in syntactic representation, whereas the deep-surface structure distinction illustrates how theoretical commitments may arise from the formalism adopted. The paper contributes a critical framework for distinguishing descriptive adequacy, derivational economy, and formal overhead in evaluating competing mathematical representations of syntactic structure.

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