Computability Theory

Roles: algorithm, decision-procedure, undecidable-problem, oracle, reduction, halting, recursion, turing-machine

The mathematical study of what can and cannot be computed in principle, independent of time or resource constraints. As a source domain, computability theory supplies the concepts of undecidability (problems no algorithm can solve), the halting problem (can you predict whether a process will terminate?), and Turing completeness (the minimum threshold for universal computation). When someone says a question is “undecidable,” that a process “may never terminate,” or that a system is “Turing-complete,” they are borrowing from this frame. Its metaphorical power lies in establishing absolute limits on knowledge — not practical limits that better engineering might overcome, but proven impossibilities. Its danger lies in overextension: treating messy empirical questions as if they had the clean binary structure of formal decidability.

As Source Frame (1)