Hypotheses are "based" on data in the sense that via imagination we simulate ways the world might be, and then "data" is a clue to a contradiction.

Deep learning models are data: they are just associations between points.

Train a NN on data generated from an exponential function, and the model produced is not exponential.

Train a NN on the covid pandemic, and you will never obtain the SIR model.

AI is just associative statistical modelling. The model is the data.

Proving any given AI architecture can't do something doesn't prove all AI architectures forever will never be able to do something. Neural networks aren't all AI, they're not even "neural networks" since the terms wraps up a huge amount of architectural and design choices and algorithms.

Unless you believe in the soul, then the human brain is just a very complicated learning architecture with a specific structure (which we freely know doesn't operate like existing systems...sort of, of course we also don't know that it's not just a convoluted biological path to emulating them for specific subsystems either).

But even your original argument is focused on just playing with words to remove meaning: calling something data doesn't meaningfully make your point, because mathematical symbols are just "data" as well.

Mathematics has no requirement to follow any laws you think it does - 1 + 1 can mean whatever we want, and its a topic of discussion as to why mathematics describes the physical world at all - which is to say, it's valid to say we designed mathematics to follow observed physics.

I know this discussion is a bit old at this point, but I came across this[1] essay for the first time today, and this shows more of what I was trying to get across earlier in the thread. Hopefully you'll find it interesting. Essentially, they trained a GPT on predicting the next move in a game of Othello, and by analyzing the weights of the network, found that the weights encode an understanding of the game state. Specifically, given an input list of moves, it calculates the positions of its own pieces and that of the opponent (a tricky task for a NN given that Othello pieces can swap sides based on moves made on the other side of the board). Doing this allowed it to minimize loss. By analogy, it formed a theory about what makes moves legal in Othello (in this case, the positions of each player's pieces), and found out how to calculate those in order to better predict the next move.

[1] https://www.neelnanda.io/mechanistic-interpretability/othell...