Classical causal models for Bell and Kochen-Specker inequality violations require fine-tuning.

Nonlocality and contextualityare at the root of conceptual puzzles in quantum mechanics, and are key resources for quantum advantage in information-processing tasks. Bell nonlocality is best understood as the incompatibility between quantum correlationsand the classical theory of causality, applied to relativistic causal structure. Contextuality, on the other hand, is on a more controversial foundation. In this work, I provide a common conceptual ground between nonlocality and contextualityas violations of classical causality. First, I show that Bell inequalities can be derived solely from the assumptions of no-signalling and no- fine-tuningof the causal model. This removes two extra assumptions from a recent result from Wood and Spekkens, and remarkably, does not require any assumption related to independence of measurement settings -- unlike all other derivations of Bell inequalities. I then introduce a formalism to represent contextualityscenarios within causal modelsand show that all classical causal modelsfor violations of a Kochen-Specker inequality require fine-tuning. Thus the quantum violation of classical causalitygoes beyond the case of space-like separated systems, and manifests already in scenarios involving single systems.