Do mathematical things exist independently of the minds who conceive of them ? The ontological status of abstract things, right? My point is, materialists deny these kinds of things. That's disembodied spiritual bunkum and it has no place in modern thinking.
Then, later in the day they're perfectly happy to deal with things just as abstract and non-corpreal without feeling like they're cheating in any way.
The fact is the philosophy of science has not caught up to the advances in science as any good QM thread here will show.
>Does the law of non-contradiction exist?
The fact that neither of us can answer this (assuming we both agree to what it implies about the world, which actually, heh... I am not totally convinced of, but that's another matter) ... anyway the fact that neither us can answer this in the way you meant it is an interesting fact in the same family of interesting questions as raised in this discussion.
The quarks->atoms->molecules->neurons->brains->experience (consciouness) chain of causality, which is the standard model of reality and has been for a few hundred years now, is broken at both ends by which I mean the descriptive philosophical ideation at both ends is to no one's real satisfaction.
Sure, and they would have to provide some sort of naturalist account for mathematics. There are some proposals for this kicking around.
> is broken at both ends by which I mean the descriptive philosophical ideation at both ends is to no one's real satisfaction.
Indeed, there is no hole-free reduction along the chain you cite, but those holes are continuously shrinking. This is why I consider the special pleading around consciousness a god of the gaps. There are some very interesting puzzles around consciousness, but I think ascribing a special status to consciousness will ultimately be abandoned, just like vitalism.
Existence is a tricky as a proposition, as Kant famously argued. Does the following make sense to you: the law of non-contradiction exists.
Computation has similar logical character as other rules of logic. In fact, intuitionism ensures a 1:1 correspondence between the two. So computation is not a "non-corporeal thing" any more than any other form of logic. If you take rules of logic to also be non-corporeal things, well then this "problem" you speak of was present in functionalism from the start, and yet it doesn't seem to trouble anyone.