Comment by no_wizard

Your first sentence is a non-sequitur. The fact that we can't explain human behavior does not mean that our minds are more than mathematics.

While absence of proof is not proof of absence, as far as I know, we have not found a physics process in the brain that is not computable in principle.

Note that what you claim is not a fact, but a (highly controversial) philosophical position. Some notable such "non-computationalist" views are e.g. Searle's biological naturalism, Penrose's non-algorithmic view (already discussed, and rejected, by Turing) and of course many theological dualist views.

Your reasoning is invalid.

For your claim to be true, it would need to be provably impossible to explain human behavior with mathematics.

For that to be true, humans would need to be able to compute functions that are computable but outside the Turing computable, outside the set of lambda functions, and outside the set of generally recursive functions (the tree are computationally equivalent).

We know of no such function. We don't know how to construct such a function. We don't know how it would be possible to model such a function with known physics.

It's an extraordinary claim, with no evidence behind it.

The only evidence needed would be a single example of a function we can compute outside the Turing computable set, which would seem to make the lack of such evidence make it rather improbably.

It could still be true, just like there could truly be a teapot in orbit between Earth and Mars. I'm nt holding my breath.

I mean some people have a definition of intelligence that includes a light switch, it has an internal state, it reacts to external stimuli to affect the world around it, so a light switch is more intelligent than a rock.

Leaving aside where you draw the line of what classifies as intelligence or not , you seem to be invoking some kind of non-materialist view of the human mind, that there is some other 'essence' that is not based on fundamental physics and that is what gives rise to intelligence.

If you subscribe to a materialist world view, that the mind is essentially a biological machine then it has to follow that you can replicate it in software and math. To state otherwise is, as I said, invoking a non-materialistic view that there is something non-physical that gives rise to intelligence.

>Because whats inside our minds is more than mathematics,

uh oh, this sounds like magical thinking.

What exactly in our mind is "more" than mathematics exactly.

>or we would be able to explain human behavior with the purity of mathematics

Right, because we understood quantum physics right out of the gate and haven't required a century of desperate study to eek more knowledge from the subject.

Unfortunately it sounds like you are saying "Anything I don't understand is magic", instead of the more rational "I don't understand it, but it seems to be built on repeatable physical systems that are complicated but eventually deciperable"