[skyechurch]

This is a really good question. Wittgenstein himself didn't think much of it, and it is generally believed he didn't really understand it:

https://plato.stanford.edu/entries/wittgenstein-mathematics/...

Talking about the Tractatus, I would suggest that Godel's work would be considered "nonsense", in that it attempts to use (mathematical) language to describe language, which is an invalid operation. This opinion went very much out of fashion, I suspect because computers do these operations with great success, but I believe he is saying something deep about meaning here, not about symbolic manipulation at all. But Wittgenstein didn't publish anything after the Tractatus (except a spelling dictionary for rural Austrian schoolchildren), and what has been published posthumously is extremely difficult, so this is probably a question for a very small number of subject matter experts. So not me. I'd ve very interested in better-informed opinions.

[beezlebroxxxxxx]

Later Wittgenstein is not really "extremely difficult". But it does present an understanding of meaning and language and philosophy that is quite different from the TLP, many would say it is fundamentally different although there are disagreements. I don't really know if he would have much to say about Godel's work based on his later writings. He would probably have to much to say about how others have used Godel's work and concepts, though, to make questionable connections to other things.

If anything he would probably be very critical of the idea that it has profound insight into anything beyond niche questions of higher order math and computation. It makes sense in that context, but then it would be similar to the philosophers he criticized as constructing houses of cards out of "language games" if you were to apply it to something to which it has no contextual relationship at all, in which you case you could say it is "nonsense" when it outsteps the bounds of sense. Later Wittgenstein is not really concerned with fundamental, Platonic, truth. In fact, he is outright critical of the very idea. His later writings are more about method. He's far more interested in clarification as the goal of philosophy. He wants to dissolve seemingly intractable questions to reveal how they are the product of nonsensical language games filled with mistaken assumptions.