I don't think so, because in this case the "cave" is also anthropic. Prior to Plato, there was the view (by the elean philosophers, such as Parmenides and Zeno) that while a "real" world may exist, it would not be tied to our world. So in that model you would have a real cave, but the human cave wouldn't be tied to it. In Plato's model, by contrast, the "real" world is (albeit infinitesimally) tied to our world. The difference is, obviously, enormous.
I personally think it is pretty strange to try to examine if math is cosmic (more than human/human-similar), since even if it is only human it still won't be depleted nor fully understood. It is a nice angle on the ability to create real AI, though, since if math is only human, but still never fully to be known (even by humans with 3000 IQ etc), then no AI can be programmed with it (it can still generate it out of some bio matter, like humans do). Maybe for math to be actually cosmic it wouldn't even be enough that all intelligent organisms are built from the same elementary particles and arrangements (which is already assuming the divisions of particles end at some point, which they may well not do), since for all we know the emergence of mathematical thinking may be dependent on far more localized parameters than that.
By the way, I was happy to read by Conway (who is "of famous") a view I always had and even mentioned a number of times in CFC OT, but always was met with non-positive comments. Namely that it is quite suspicious that humans sense stuff in 3d, and that this may mean that 3d itself is not formed as an object but as a result of procedures that have nothing to do with dimensions. In other words that "3d" may just be human-sensespeak for "way of viewing", and have nothing to do with what it is being picked up as (and also, which is a different point, nothing to do with what it is analyzed as).
