The model of human intelligence that is most widely adopted derives from psychometrics and behavioral genetics. This standard approach conceives intelligence as a general cognitive ability that is genetically highly heritable and describable using quantitative traits analysis. The paper analyzes intelligence within the debate on natural kinds and contends that the general intelligence conceptualization does not carve psychological nature at its joints. Moreover, I argue that this model assumes an essentialist perspective. As an alternative, I consider an HPC theory of intelligence and evaluate how it deals with essentialism and with intuitions coming from cognitive science. Finally, I highlight some concerns about the HPC model as well, and conclude by suggesting that it is unnecessary to treat intelligence as a kind in any sense.