I think that's very true and it's maybe even more clear when you consider mathematics. You can maybe imitate but not effectively learn mathematics empirically. There is an infinite number of mathematical expressions or sequences that can be generated, so learning can never be done, you cannot compress yourself to mathematical understanding. (which is obvious if you try to feed language models simple arithmetic, they…
I'd say you're underselling modern AIs. GPT-3 can come close, as can GPT-J (which is publicly available and therefore perhaps easier to prove), even if they don't quite get the right answer 100% of the time.
I gave GPT-J the following prompt (which you can try yourself at https://6b.eleuther.ai/ just wait a few min for an answer)
What is 1 + 1?
2.
What is 3 + 2?
5.
What is 6984 + 120?
7104.
What is 3792 + 29382?
And it responded with 33374
What is -0.084435 + -0.3?
-0.384435
What is -4.1 + -0.4?
-4.5
... [more of the same omitted]
Note that it got almost the right answer! Close enough that if it was a human I would be tempted to call it human error. GPT-3 can do even better.EDIT: On another try GPT-J got the answer! Not bad (and GPT-3 is an even more powerful model).
33174
-3 + -91.4
-94.4
What is -1.6 + 13.81?
12.21