This paper argues that both individual and collective human cognition exhibit finite coherence bandwidths: bounded capacities to jointly represent, compare, and propagate complex inferential structures. When the semantic dependency diameter or conjunction order of a physical theory exceeds these bandwidths, theory comparison and validation encounter structural barriers that are invisible from within first-order scientific practice. We develop this claim using a strongly typed representation of claims and reasoning processes together with a geometric model of conceptual space. We introduce a conditional theorem on evaluator-relative indistinguishability, present a worked typed toy example, and propose Second-Order Physics as a program that constrains the form of admissible physical theories rather than proposing a new first-order ontology. The approach is situated relative to existing literature on bounded rationality, underdetermination, computational verification limits, and categorical foundations of physics. We conclude by discussing implications for stalled areas of fundamental physics and for domains—such as existential risk—where evaluative structure may exceed civilizational coherence bandwidths.