The Twin Earth thought experiment invites us to consider a liquid that has all of the superficial properties associated with water (clear, potable, etc.) but has entirely different deeper causal properties (composed of “XYZ” rather than of H2O). Although this thought experiment was originally introduced to illuminate questions in the theory of reference, it has also played a crucial role in empirically informed debates within the philosophy of psychology about people’s ordinary natural kind concepts. Those debates have sought to accommodate an apparent fact about ordinary people’s judgments: Intuitively, the Twin Earth liquid is not water. We present results from four experiments showing that people do not, in fact, have this intuition. Instead, people tend to have the intuition that there is a sense in which the liquid is not water but also a sense in which it is water. We explore the implications of this finding for debates about theories of natural kind concepts, arguing that it supports views positing two distinct criteria for membership in natural kind categories – one based on deeper causal properties, the other based on superficial, observable properties.