On the Formal Contextuality of Nontrivial Propositional Knowledge

Abstract This paper provides a rigorous model-theoretic account of the contextuality of propositional knowledge. We demonstrate that any nontrivial propositional sentence in a first-order language has a truth value that depends intrinsically on the choice of structure and valuation. Building on this elementary semantic fact, we argue that knowledge claims about such propositions are necessarily context-dependent. The treatment uses minimal formal machinery, specifically Tarski-style semantics, to clarify the logical foundations of the philosophical claim that “all knowledge is contextual.” Examples from mathematics, science, and ordinary language illustrate the practical implications of this result.