It isnt.
Our bodies are the primary site of "causal analysis". Eg., when I touch the hot surface of a stove I do not infer that temperature is a cause of my hand being hot.
Such an inference, as the basis for our models of the world, would be -- as you/hume/etc. say -- deeply insufficient.
The operation of the world on our bodies is already laden with causal information. A hand striking a face does not just create a "painful sense impression"... rather the body encodes it as caused by the object you also saw.
It is the action of the world upon the body that is the bedrock of our causal model building. Scientific/inferential processes sit on top of that to disambiguate between possible distal causes.
A machine, as a person, given "mere data" cannot hope to do much.
Now I feed into the machine what data?
Here, it gets this: all gravitational, electomagnetic, etc data within 1km; all geometric information about all objects within 1km (, and all of their properties, etc.)
Now, machine, what caused the pot to boil?
It has no clue. There are an infinite number of antecedent temporal events.
The problem isn't the mathematics of causal inference. The problem is relevance. That isn't an inferential problem.
Right, determining the cause of the pot boiling given only local information about this one event is impossible. But that's not a good representation of learning from a real-world data set. A real training corpus might also have an example of a pot boiling in a campfire, a water heater heating up water using fire, someone touching an open flame and going "ouch!", fire burning down a house, etc. All these examples taken together can reasonably lead one to infer that fire causes things to become hot. This is the kinds of regularity found in real world datasets and a good learning algorithm will extract this regularity in the course of predicting the dataset.
You are just shifting relevance problem to the human to solve. That's my point.
The "regularity" isn't very hard to find when the data which exposes it is already selected.
events A then B then C do not imply C is caused by B is caused by A
This problem is worse the more data you have, as with my example above of giving the machine /every/ event within a 1km radius of a pot boiling.
Identifying a cause is a dynamic experimental process. A machine can only accept a highly prepared dataset which has already been chosen because the associations are known to be causal.
The body is a mechanism of relevance. The more data you feed a machine, the worse it performs.
The body isnt necessarily right about causation (though it often is) but it provides a minimal mechanism of relevance to enable inference.
Data itself contains no causal information.
This is not to say that we should expect some non-turing weirdness or anything 'mystical' like that, but that we just haven't taken the time to analyze the exact mechanisms and to model cells at this level well enough to be able to say that they are similar to any particular computational structure. Thus, to claim that the brain in its entirety is similar to any particular computational structure such as an NN is either wrong or trivial - the only level at which 'similarity' can be claimed is that they are both useful in computation, and likely turing complete. Anything more specific is fanciful thinking.
I'm sorry but this shows a profound misunderstanding of what a NN is, and what the brain is.
There are no "neural network"s. The NN algorithm is a method for optimizing the parameters of a piece-wise linear regression model.
These regression models have no homology to any brain structure and the process of producing them ("training") has no neurological analogue either. They can be produced with a variety of algorithms.
Here's one: f(x) = max(0, 2max(0, 3x - 0.1) - 0.5)
The phrase "neural network" is, as peddled by the media and poorly informed lecturers, a lie. It is neither neural nor a network. It's just gradient descent with more parameters.
A model of the brain would model, at least: neuroplasticity, biochemical signalling, activation frequency, etc.
There is nothing about a peice-wise linear regression model which does any of that. No matter how many circles and lines you draw. (NB. essentially any mathematical function can be drawn as a "neural network". The "network" is just a way of diagramming function application & dot-products).
Aside from all that, the body-brain system of animals is a physical process whose properties are not abstract. The reason we are intelligent is because we have bodies capable of causal analysis; and that capability is biophysical.
To put it another way, no algorithm which runs on a digital computer will turn it into gold. Not even one called, "the midas algorithm".