How can the mind (a non-physical mind) emerge from something physical? If it comes from something physical, is it not, too, physical?
100% false. The whole is not defined by the pieces. However, I wanna stress the word "metaphysical," as it defines what I'm speaking of as being borne <of> the physical, entering the realm of the metaphysical (things that do not occur in nature without the intervention of human thought; synthetic truths).
The reason it can be performed mathematically and not physically? I don't know, but it can, clearly. Why you think it means our mind is non-physical is a definite mystery to me. I don't need to answer why our brain can do it, because as far as anyone can tell, our brain is entirely physical, performing entirely physical processes.
Well, if you don't know, then why were you arguing? That's the type of "I don't know" answer I take issue with, as I said to BPC. It strikes me as escapist, and is brazenly indifferent to possible alternate explanations for the sake of ideological preservation. It's like saying "I don't know why I believe this, but I know I don't believe what you're saying."
If you don't really know why you're arguing, then that tells me that you have an unexamined belief set regarding the topic at hand that you're not willing to critically examine. The reason I say that is because you argued against my viewpoint without really knowing why. That disjunction that even you conceded by saying there was a clear difference between mathematics and physicalities is the kind of suggestion that a curious, discerning mind should investigate instead of eschewing it.
Sometimes it's the best answer, this, in my opinion, being one of those cases. It's not escapism, it's the truth. Sometimes admitting you don't know something prevents you from coming up with inaccurate answers which will potentially prevent you from discovering the true answers. A scenario (shout out to qualiasoup):
Imagine if we went back in time, say... 500 years ago, and showed some people a very convincing projection of a man sprouting wings and flying to the heavens. It's reasonable to assume that many, if not all of these people, would immediately describe this as a miracle and as evidence to god. They would end it there and never find out the truth. They have boxed themselves in ignorance because they have attempted to explain something that, at the time, is unexplainable.
So, I think about the origins of the universe. With our current technology, we cannot definitively know the answers. Some people said "hey, maybe it's this thing that's, like, beyond our universe. Like a god or something." Well, that works. Done! Well, no, because we still don't know. Just because an answer fits doesn't make it any more right. In fact, it probably just hurts.
I think it has its place in some scientific contexts
In a scenario where "I don't know" is a useful answer that doesn't needlessly gamble, then yes, it's a good answer. However, a lot of people mistake that to mean that everything should be an "I don't know." In contexts such as these, "I don't know" is more often apathy from what I've noticed.