Intentional Semantic Geometry: Statements as Grammar-Mediated References into Determinable Spectra

Abstract

Non-trivial scientific meaning is not, in general, a proposition in a fixed logic-space. A statement is a pointer into a semantic geometry - a spectrum - and its interpretation is grammar-mediated: a grammar decides how the statement names regions or positions in the spectrum. Both the pointing (where does the statement land?) and the substrate (what is the spectrum, structurally?) are objects of research. We propose Intentional Semantic Geometry (ISG) as the discipline that makes this structure explicit: statements, grammars, spectra, references, and two irreducible modes of indeterminacy (pointing indeterminacy under a fixed substrate, substrate indeterminacy across candidate grammars). Under ISG, the operators DIA (which names the interpretive gap left by a partition) and REI (which reintegrates that gap) recover a natural position as the derived discipline for handling the double indeterminacy. We equip them with a typed calculus that separates the type of an operation from the direction in which it is applied and from its normative valence, and that identifies which reintegration routes transform a state and which only certify one. The same calculus types the two deployment effects of a separating criterion - excisive cutting and non-excisive classification, which refines the description of an intact spectrum - and states the typed interface through which classified, still-unnamed regions become inputs to symbolic reification in the companion MCK framework. The framework unifies substrates already studied independently in the programme (topological property classes over infinite traces; epistemic region cubes; capability lattices for threshold monitors; two-agent channel-based semantic bodies), and provides the language for a reflexive application: a paper's positioning statements about its own contribution are ISG operations on the contribution's admissible-readings spectrum, subject to the same double indeterminacy as any other statement about a geometrically-supported object. --- SCOPE AND STATUS. This is a preprint. It has not been peer reviewed and is not under journal acceptance. It is the foundational paper of the ISG cluster of the programme; companion papers are cited with their deposit status at each citation.