This academic paper challenges the traditional dichotomy of aleatoric and epistemic uncertainty within the context of large language model (LLM) agents, arguing that these established definitions are insufficient for complex, interactive AI systems. The authors assert that the existing frameworks often contradict each other and fail to account for the dynamic nature of human-computer interaction. They propose three new research directions to enhance uncertainty quantification in LLM agents: underspecification uncertainties, which arise from incomplete user input; interactive learning, enabling agents to ask clarifying questions; and output uncertainties, advocating for richer, language-based expressions of uncertainty beyond simple numerical values. Ultimately, the paper seeks to inspire new approaches to making LLM agents more transparent, trustworthy, and intuitive in real-world applications.