Is intelligence general or is it a system of specific abilities? This debate revolves around the interpretation of a single construct g, the general factor of intelligence. g accounts for half of the covariance between cognitive tests. According to g-theory, g represents a general mechanism causal to all kinds of tests. We present a simulation study motivated by process overlap theory, a new theory of intelligence, that proposes that the covariance between tests is the result of the overlap of the processes they tap, and that g is the consequence, not the cause of such covariance. Our results demonstrate that it is possible to fit a higher-order g model, the most commonly used model in studies of intelligence, to data generated without a general mental ability. Therefore, fitting such models cannot decide between g-theory and process overlap theory and does not provide evidence for the existence of general intelligence.