We marry three frameworks: (1) non-linguistic thought as geometric dynamics on Intentional Manifolds, (2) mathematical structure as a semantic language with internal grammar, and (3) topological gaps as phase transitions in cognitive systems.
We prove that mathematical operations (permutation, collapse, genus, singularity) are not descriptions of external reality but semantic objects with internal grammatical structure. This metamathematical perspective provides testable predictions for cognitive neuroscience, legal interpretation, and AI safety. The theory establishes that thought is geometry, mathematics is language, and topology is grammar.
Abstract.
We marry three frameworks: (1) non-linguistic thought as geometric dynamics on Intentional Manifolds, (2) mathematical structure as a semantic language with internal grammar, and (3) topological gaps as phase transitions in cognitive systems.
We prove that mathematical operations (permutation, collapse, genus, singularity) are not descriptions of external reality but semantic objects with internal grammatical structure. This metamathematical perspective provides testable predictions for cognitive neuroscience, legal interpretation, and AI safety. The theory establishes that thought is geometry, mathematics is language, and topology is grammar.