In his keynote address in 2015, George Lakoff said the following (at 22:10)
The whole idea of generative grammar fell apart. There were things that you could not do with it. Even if it was meaningless, you still couldn't do certain sentences... There are examples where there can't be a deep structure, for example. That was discovered in '74, and nobody's found a way to do it since then.
I find this confusing. According to Wikipedia
Generative Grammar considers grammar as a system of rules that generates exactly those combinations of words that form grammatical sentences in a given language.
Since the rules are arbitrary, shouldn't we be able to encode essentially anything with them?
So my question is: what are the limitations of generative grammar, and specifically what is Lakoff referring to here?