On the Expressive Limits of Formal Relational Languages: Pre-Relational Profiles and the Non-Uniformity of Relability

This paper develops a framework for analyzing the expressive limits of formal relational languages by focusing on the prior conditions of relation-formation rather than semantic self-reference. It introduces the notion of pre-relational profiles, class-specific sets of structural preconditions (such as distinguishability, syntactic formability, semantic meaningfulness, temporal orderability, informational difference, and causal interpretability) that must be satisfied for different classes of relations to be meaningfully formable. The central thesis is the non-uniformity of relability: distinct classes of relations require distinct pre-relational profiles. The framework distinguishes relability from both syntactic well-formedness and truth-evaluability, arguing that it operates at a level prior to Tarskian semantic hierarchy. The paper establishes a concrete result in the effective setting: there is no uniform computable procedure for determining membership in the closure generated by arbitrary effective profile-admission mechanisms. It further formulates a conditional conjecture concerning the possibility of total internal self-closure for stage-grounded mechanisms capable of diagonal self-application, and identifies the joint satisfiability of the conjecture’s hypotheses as an open problem. The work is positioned as a contribution to the philosophy of formal languages and formal ontology, shifting attention from what relational languages can express to what kinds of relations can become expressible in the first place. In this version, the epistemological framing is made more explicit by reconnecting the technical analysis of profile admission, closure, and self-reference to the guiding question of how formal relational languages can determine the conditions under which new classes of relations become relably formable.