Patty and Vatty

Timothy Williamson argues that knowledge is a purely mental state. Furthermore, Williamson argues that knowledge is factive but believing or hoping is not. One can only know that p if p is true; one can believe or hope that p regardless of the truthfulness or falsehood of p. 

Suppose a girl, Patty, and a brain in a vat, Vatty, are mental duplicates except for knowledge—they have same beliefs, hopes, intuitions, desires, and so on, but they do not have same knowledge. It follows that Patty and Vatty are also normative duplicates because there seems to exist a corresponding relationship between mental states and normative properties. For example, one’s belief about charity can correspond to one’s moral character. Intuitively, there is a sense of mental that if two things are normative duplicates, then they are mental duplicates in the full sense. So in this case, Patty and Vatty would be mental duplicates in the full sense. Given factivity of knowledge, however, Patty and Vatty are not knowledge duplicates. Patty knows, for example, that she now sits on a chair. Vatty may have same belief that she sits on a chair, but Vatty cannot be said to know so—factually speaking, Vatty floats in a vat. Thus, we have shown that two things that are mental duplicates in the full sense are not knowledge duplicates. It follows that knowledge is not a purely mental state.

Reference: Williamson, Timothy. "A State of Mind (excerpts)." Knowledge and its Limits (2000).: 21-41.