I have yet to take my own advice and dig into the field of innate idea literature – but here’s a few more thoughts on the topic.
Like I mentioned before, the Lockean ‘blank-slate’ theory doesn’t hold a lot of water with me. I don’t see how experience of sensory-data alone provides an adequate account of reality – I mentioned the law of non-contradiction before as a brief example. This is something that is not derived, so far as I can tell, from any sense data, nor can one arrive at the law of non-contradiction by reason alone in a non-circular way. Other things like logic seem to me to be in roughly the same category – it’s not something we learn from any sensory experience, nor can we justify the use of logic in a non-circular way.
This is certainly not, however, a ‘non-contradiction or logic of the gaps’ argument – but so far I have yet to hear a convincing account of such phenomenon. I’d certainly welcome one, however.
With regards to language, I can see both options as viable (and, for all I know, given my lack of interaction with recent literature on the topic the two ideas may have been synthesized) and compatible. I see no reason why innate ideas, or innate abilities to grasp things like grammar can’t coexist with a Wittgenstein-ian public-speech theory. I haven’t begun really putting the two together in a coherent way, but it’s definitely something I’m thinking on.