How do humans develop the capacity to reason? In five studies, we examined infants’ emerging ability to make exclusion inferences using negation, as in the disjunctive syllogism (P or Q; not P; therefore Q). Inspired by studies of non-human animals and older children, Experiments 1–3 used an exclusion task adapted from Call’s (2004) 2-cup paradigm and Experiments 4–5 used an exclusion task adapted from the blicket detector paradigm (Sobel & Kirkham, 2006). In both tasks, we found failure to make exclusion inferences at 15 months, fragile success at 17 months, and robust success by 20 months of age. These data converge with some prior evidence that fails to find a capacity to represent negation in infants younger than 15 months of age and conflict with other evidence from different paradigms that suggests infants do have this capacity. We discuss three different resolutions of these conflicting data, and suggest lines of further work that might adjudicate among them.