Then again math is hard for us. So I think there are nuances.
It is reasonable to believe that written language is easier to train on a neural net that is trained on both images and words so it can form visual links between words. Maybe that takes more computational grunt than we have at the moment. The failure so far proves nothing.
You do realize we can train a neural network to perform this task? It is a binary classification problem. When I look at a grammatically incorrect sentence I don't do much symbolic reasoning - it just feels "wrong" to me. It does not match any patterns I have in my head for grammatically correct sentences. There's a lot of pattern matching in our thinking process.
What's missing in the current generation of neural networks is efficient information storage and ability to recall that information (e.g. lookup) or update it (direct write).
I'm doing a master's in deep learning for NLP and I'm not sure we can. Language modelling can't do this because grammatical yet semantically implausible combinations of words yield very low perplexity, like the classic being Noam Chomsky's "Colorless green ideas sleep furiously".
What would be a training set for this? I assume we would first try to do parsing to extract the grammatical role of each word. Then what would be the dataset? A massive attempt at generating the set of all possible trees that are grammatical?
I guess we could use massive textual datasets from reputable sources and extract their grammatical role tree, and learn from that. Generating negative examples with sufficient coverage would be very hard. Strict generative modelling without negative examples with good coverage would see the same problem as with language modelling, where acceptable but unlikely examples would have low perplexity despite being good.
It would seem to me that in order to generate negative examples with good coverage, your would need to have a man made program with a definition of what grammaticality means, which would make making a neural network useless to begin with.
Seems like the experts agree with my take: https://linguistics.stackexchange.com/a/1108
Unlike current DL models, humans have a world model (common sense) which is formed through an ability to create/update/lookup explicit rules/facts. Once we figure out how to incorporate that into a learning algorithm and/or a model architecture, AI will become a lot smarter.
I’d encourage you to read a little more about the topic with an open mind. You might learn something.
That isn't a problem of scale, it's a problem of architecture. This is one of the reasons Deepmind decided to tackle Starcraft. It's very difficult to solve Starcraft without your AI having some ability to develop and then manipulate a mental model of the game, because that's what you need to construct and unfold original, non-linear strategies.
It is completely plausible that when neural nets get scaled up to something approaching human-brain numbers of connections they will well approximate a human brain or be a few tweaks away. Obviously it won't be knowable until state of the art gets there, but there is no reason to think human intelligence is going to be complicated. It is one evolutionary step up from some pretty basic animals.