Do you agree at least that a xor gate is doing math?
Right, but my point is that following a bunch of translation rules from one language to another is not the same thing as understanding a language. That's not what humans are doing when they use language.
> The solution probably isn't symbolic but numeric, but that hardly changes anything - you still need a lot of math to consciously solve such an equation numerically.
This is assuming the brain is doing math. Even deeper than that, it's assuming that math is something more than a specialized human language. That math exists in nature to be harnessed by neurons.
Also the Chinese room would express emotions, do word games etc, whatever's appropriate in the context. The people doing the lookups wouldn't know that they are writing a joke, but who cares about them?
> This is assuming the brain is doing math.
Well of course brain is doing math, see: 234-123=111 - this is math, my brain did this.
> Even deeper than that, it's assuming that math is something more than a specialized human language
If neurons arriving at solutions to math problems consciously is math, then why neurons arriving at these same solutions subconsciously isn't?
Yes. You need to decide where to put your hand, how to orient it, etc in reaction to the ball movement.
The answer is a solution to the differential equations, and you cannot consistently get a good answer to an equation if you don't solve it.
The solution probably isn't symbolic but numeric, but that hardly changes anything - you still need a lot of math to consciously solve such an equation numerically.
> Or the system knows how to translate from English to Chinese. Human language isn't simply about following translation rules, though. It's also about communication and expressing thought. Or participating in language games.
human doesn't get to decide what to do in Chinese room experiment - (s)he is just a dumb CPU that does table lookups in a huge book. Every possible response to a sequence of previous messages is already written in that book (so it must be quite big ;) ).
You could completely automate it, remove the human and nothing would change from the outside.