The Linguistic Foundations of Mathematical Abstraction

This paper argues that the abstract nature of mathematics persists even in its applied forms because mathematics functions fundamentally as a linguistic system. Since linguistic structures are inherently abstract, any discipline that operates through such structures inherits this abstraction. This perspective synthesizes insights from mathematical philosophy, linguistic theory, and epistemology. The argument suggests a conceptual shift in understanding the ontology of applied mathematics and its relation to cognitive and linguistic frameworks.

The author acknowledges using OpenAI’s language model solely for minor editorial assistance, including grammar correction, phrasing refinement, and clarity improvement. All philosophical arguments, conceptual developments, theoretical frameworks, logical structures, conclusions, and original ideas presented in this work were entirely conceived and developed by the author.