Induction --the ability to generalize from existing knowledge-- is the cornerstone of intelligence. Large language models have been shown to be capable of certain types of reasoning, however, they are limited in their ability to mimic human induction. In this paper, we combine representations obtained from large language models with theories of human inductive reasoning developed by cognitive psychologists. Our approach can capture several benchmark empirical findings on human induction, and generate human-like responses to natural language arguments with thousands of common concepts and properties. These findings shed light on the cognitive mechanisms at play in human induction, and show how existing theories in psychology and cognitive science can be integrated with leading methods in artificial intelligence, to successfully model high-level cognition.