Which term refers to the study of the nature, basis, and extent of knowledge?

The term that refers to the study of the nature, basis, and extent of knowledge is epistemology. This branch of philosophy explores questions related to belief, truth, and justification, seeking to understand how knowledge is acquired, and what constitutes justified belief. It delves into various sources of knowledge, such as perception, reason, memory, and testimony, and discusses the limits and scope of what can be known.

In contrast, logic deals with the principles of valid reasoning and argumentation, focusing on the structure of arguments rather than the nature of knowledge itself. Metaphysics, on the other hand, is concerned with the fundamental nature of reality, including concepts like being, existence, and the universe, but it does not primarily focus on knowledge as a subject. Aesthetics pertains to the nature of beauty, art, and taste, which again diverges from the study of knowledge.

Thus, the selection of epistemology is accurate because it directly addresses the foundational aspects of what knowledge is, how it can be obtained, and its limits.