The representativeness heuristic constitutes a striking departure from Bayesian updating. According to a strong form of the heuristic, agents reverse a conditioning argument: for example inferring that a patient is more likely than not to have a rare disease, conditional on a positive test result. The correct inference is that a positive test result is more likely than not, conditional on disease. Recent research implicates representativeness in a wide range of financial market anomalies, with potential consequences for the real economy. However, the cognitive foundations of the representativeness heuristic (RH) remain unknown. Here, we show that the RH emerges from a theory of associative memory and recognition, leading to a cognitive foundation for the RH, and a means of integrating the RH into economic models involving decision-making under uncertainty.