An interesting behavior in large language models (LLMs) is prompt sensitivity. When provided with different but semantically equivalent versions of the same prompt, models may produce very different distributions of answers. This suggests that the uncertainty reflected in a model's output distribution for one prompt may not reflect the model's uncertainty about the meaning of the prompt. We model prompt sensitivity as a type of generalization error, and show that sampling across the semantic concept space with paraphrasing perturbations improves uncertainty calibration without compromising accuracy. Additionally, we introduce a new metric for uncertainty decomposition in black-box LLMs that improves upon entropy-based decomposition by modeling semantic continuities in natural language generation. We show that this decomposition metric can be used to quantify how much LLM uncertainty is attributed to prompt sensitivity. Our work introduces a new way to improve uncertainty calibration in prompt-sensitive language models, and provides evidence that some LLMs fail to exhibit consistent general reasoning about the meanings of their inputs.