The universal approximator approach is another big one that people lean on from the opposite direction (I suppose you could call it the "anti-deep learning" school of thought). Most people don't take the time to consider what a universal approximator actually is.

Are humans universal approximators? Absolutely not. The mere proof that a nn with an infinite number of hidden nodes (which isn't practical, which could end the discussion there) can find a statistical mapping between any two input and outputs is hardly a benefit. There is something so much more to intelligence --- the ability to generalize well (aka not overfitting) is first and foremost.

I'd push you to ask why you perceive that stacking RBMs produces "eerily human-like" results. I'd argue that they don't: http://blog.keras.io/how-convolutional-neural-networks-see-t...