This paper examines the inferential framework employed by Palaeolithic cognitive archaeologists, using the work of Wynn and Coolidge as a case study. I begin by distinguishing minimal-capacity inferences from cognitive-transition inferences. Minimal-capacity inferences attempt to infer the cognitive prerequisites required for the production of a technology. Cognitive-transition inferences use transitions in technological complexity to infer transitions in cognitive evolution. I argue that cognitive archaeology has typically used cognitive-transition inferences informed by minimal-capacity inferences, and that this reflects a tendency to favour (...) cognitive explanations for transitions in technological complexity. Next I look at two alternative explanations for transitions in technological complexity: the demographic hypothesis and the environmental hypothesis. This presents us with a dilemma: either reject these alternative explanations or reject traditional cognitive-transition inferences. Rejecting the former is unappealing as there is strong evidence that demographic and environmental influences play some causal role in technological transitions. Rejecting the latter is unappealing as it means abandoning the idea that technological transitions tell us anything about transitions in hominin cognitive evolution. I finish by briefly outlining some conceptual tools from the philosophical literature that might help shed some light on the problem. (shrink)