Syntactic knowledge is widely held to be partially innate, rather than learned. In a classic example, it is sometimes argued that children know the proper use of anaphoric "one," although that knowledge could not have been learned from experience. Lidz et al. [Lidz, J., Waxman, S., & Freedman, J. (2003). What infants know about syntax but couldn't have learned: Experimental evidence for syntactic structure at 18 months. "Cognition," 89, B65-B73.] pursue this argument, and present corpus and experimental evidence that appears to support it; they conclude that specific aspects of this knowledge must be innate. We demonstrate, "contra" Lidz et al., that this knowledge may in fact be acquired from the input, through a simple Bayesian learning procedure. The learning procedure succeeds because it is sensitive to the "absence" of particular input patterns--an aspect of learning that is apparently overlooked by Lidz et al. More generally, we suggest that a prominent form of the ''argument from poverty of the stimulus'' suffers from the same oversight, and is as a result logically unsound.