Constraint vs. Prediction: Two Modes of Scientific Theory

Scientific theories perform two fundamentally different functions: some predict specific outcomes given initial conditions, while others constrain the very form that any valid model may take. Predictive theories, such as Newtonian mechanics or the Schrödinger equation, map inputs to outputs and require parameter calibration to generate forecasts. Constraining theories—exemplified by the second law of thermodynamics, special relativity, and Landauer’s principle—impose universal limits or symmetries without specifying exact values. This paper articulates a clear distinction between these modes, tracing their historical emergence from 17th-century mechanics to modern information theory and cybernetics. We show that conflating prediction with constraint obscures a theory’s logical role and may lead to misapplication. Recognizing constraint as a complementary mode of scientific reasoning enhances our ability to rule out unphysical models, guiding both foundational research and practical design across physics, biology, and engineering.