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Large language models (LLMs) are increasingly used not only to retrieve information, but to answer questions, explain, teach, and support inquiry. In such settings, evaluation cannot be exhausted by accuracy or alignment alone. A system may give a correct answer while still narrowing users' access to alternative valid answers, explanations, or reasoning routes. Drawing on the broader notion of epistemic diversity in philosophy and social epistemology, we formalize it in the context of LLMs as the range of valid answers, explanations, and reasoning routes that an LLM exposes to users. We argue that epistemic diversity is a useful evaluation dimension for settings where LLMs are used to support knowledge-intensive tasks. We propose a preliminary framework for conceptualizing and measuring epistemic diversity in LLMs, and operationalize it in two domains. We find that frontier LLMs often exhibit epistemic narrowness, repeatedly collapsing large valid answer spaces onto small canonical subsets. These findings suggest that LLM evaluation should move beyond accuracy-oriented paradigms and treat epistemic diversity as an important dimension of model capability.