What they do argue against is the likelihood that infants are biologically endowed with cortically instantiated representational knowledge. If their arguments are correct, then it is hard to see how their position could be reconciled with there being an innate symbolic language of thought, such as Mentalese. In addition, if 'innate knowledge' entails innate representations, then knowledge of natural kinds, the principles of Universal Grammar, and innate knowledge in other domains would also be inconsistent with the book's central claim. Almost certainly not, since the erstwhile representational nativists would almost certainly join forces with those evolutionary psychologists who posit the existence of many highly specific innate mechanisms, eg. The hexagonal shape of the honey cells made by bees is quoted as one example of a universally occurring, species-specific phenomenon which is not specified in the genome, but rather results from the problem of maximising the use of limited space, combined with the physical properties of beeswax.
Spandrels provide another example.
I was not happy with all of the arguments proposed in the book. For example, I think the case for specificity at the level of architectural constraints is understated, and the case for brain plasticity correspondingly overstated. No doubt other readers, and especially any lingering representational nativists, and 'special-mechanism nativists', will find plenty of individual points to take issue with. However, this is a groundbreaking book, packed with clearly presented information and stimulating argument, and written with a combination of authority and modesty which is quite unusual and a very winning combination. The book's value will, I suspect, lie precisely in the arguments which it provokes, so criticism and controversy will testify to its importance rather than to its weaknesses.