Meaning, Opacity, and Function: An Observer-Relative Classification of Artifacts

Whether an artifact is understood, merely apprehended, or functional depends on the observer confronting it rather than on the artifact alone. We take three binary predicates over a domain of artifacts – structured meaning M, residual opacity C, and functionality K, each read relative to an agent – and study the finite datum they induce: which of the seven regions they carve are inhabited for that agent. Two modelling choices are stipulated before anything is derived: the semantic predicates need not exclude one another, and denotation is confined to their overlap Θ = M ∩ C. The admissible data are then exactly the covers of the predicate set, so their number – 109 labelled, 34 up to relabelling – is the classical cover count of a three-element set and not a new enumeration. Three results follow. The types with empty symbolic carrier are exactly those omitting the two overlap cells, seventeen in number; since a query's denoting token must lie in that carrier – a requirement that is definitional – an agent of such a type poses no query whatever architecture it carries. The six-coordinate structural profile that a type fixes is realizable if and only if it satisfies four explicit Boolean conditions, whence 39 of the 64 profiles occur. And architectures inducing the same compositional closure may still differ in the generation depth they assign its elements and in the pairs on which their composition is defined, two being the least size of the functional set at which this can happen. The predicates are supplied model data throughout: identifying the intended assignment from external evidence lies outside the present formalism.