I'll have to read the book, but in my mind, the (emprical) study of humans and their brains doesn't shed light on the metaphysical question of the nature of mathematics. What they find is how humans have developed to do mathematics. We could have evolved to be the way we are with or without mathematics being "out there". Survival in the physical world would lead us to "throw away the metaphors that don't work well". At any point in time a concrete human being would still be able to consider only a limited set of mathematical ideas i.e. for humans "mathematics bottoms out at "what goes on in human noggins"".
I'd say the patterns you mentioned in an earlier comment are a way for math (or parts of it e.g. some integers) to be "out there". If humans embody mathematics, then analogously so do those patterns.
> No, it's actually, "ta-da, we're not conscious! but here's why we think we are!"
And of course the "think" has a quality to it that the hard problem is about. It's interesting how illusionists and eliminativists explain away aspects of SE by invoking (other) aspects of SE. "You merely have an illusion of being conscious" - that illusion is the hard problem, so now explain that illusion. I could be having an illusion of an illusion of consciousness.
Imagine something that doesn't exist in the usual physical sense e.g. a dinner table on the Moon. Does that table exist? Not in the usual physical sense. Your thought or imagination of it does, though. What is that thought or image in your mind's eye "made of"? Sure, you might be able to correlate it precisely with certain neurons and yet you've not answered the question. You might call the mind's eye table an illusion, but you're not gonna deny that the picture of it exists in some sense. Three things exist: the physical table, your neurons and, separately, although not entirely independently from the neurons, (the picture of) the mind's eye table. Hence, the latter is part of the universe and the fundamental substrate of the universe must support if somehow, in a way that's different from the usual physical matter tables and neurons. Is your visual brain circuitry involved in the imagination, perhaps even generating the image in your mind's eye? Perhaps, but this doesn't answer the question. If we're nothing but our perceptions, then what the heck is that imaginary table that I'm visualizing quite well while there's no perception of an actual table? What are the physical laws characterizing such mind's eye objects, somehow coupled to ordinary physical matter and yet not of the same "stuff"?
Models like the one linked don't explain why SE exists in the universe. They posit certain physical/mathematical strucutures and claim that if this or that structure is present, then ta-da there is SE (or the illusion of it, which is the same thing). People in the stone age had a model of that kind: "this piece of matter, structured with two arms and legs - it's conscious". At some point we developed language and the model got a bit more precise by demanding the piece of matter emit certain sounds from a specific location on their body. What we have today is no different in kind. We've just become more precise at locating the pieces of human matter to verify the presence of conciousness (or illusions). None of that says why that configuration of neurons experiences or has illusions, only that it does. Science tells us that experience is in the nature of certain pieces of matter and we just have to accept that without further explanation, like the fact that electric charge exists and follows certain rules. Deeper "why" answers are out of the scope of current science.
> It's interesting how illusionists and eliminativists explain away aspects of SE by invoking (other) aspects of SE. "You merely have an illusion of being conscious" - that illusion is the hard problem, so now explain that illusion.
I've explained this elsewhere, but will repeat here: this argument relies on a definition of "illusion" that begs the question on the existence of a subject, just like Descartes. Define illusion as "a perception that directly entails a false conclusion", and there is no subject needed, and no hard problem remains.
It's like you're asking me to explain the dinosaur you saw while you were hallucinating. Sure, I agree we should explore the biochemistry and neurology involved in dream-like states that yield distorted perceptions that imply false conclusions about reality. Let's not go so far as to posit that those distorted perceptions are real if there's no corroborating evidence of their existence.
> It's like you're asking me to explain the dinosaur you saw while you were hallucinating.
No, it's not like that at all. We're not discussing the dinosaur. We're discussing the existence of hallucinations (and SE in general). The dinosaur is irrelevant; the fact that it was possible to have the experience is the central question.
Again, this comes back to my fundamental argument with Dennett (and one that he graciously conceded in an email back in the 90s; not sure he would do so now): trying to figure out what it is that we are conscious of, rather than how we are conscious of anything at all. I'm 110% ready to concede that everything we are conscious of is an illusion, an error, a projection, an intent-laden stance etc. I'm 110% ready to concede that everything we think we experience as a "self" is wrong.
None of that helps to explain how experience is possible. So you're either denying that SE exists, or like Dennett insisting that mysterious SE can be explained by non-mysterious stuff.
It can't be "literally everything". It is experience that enables us to correct those misconceptions in the first place. It is by experiencing that we discovered and experimentally confirmed quantum theory i.e. that "the world is not classical". It is by reflecting on his experiences that Dennett came to his conclusions.
It is reason that permits us to correct those errors, not phenomenal experience. Our perceptions and "experiences" deceive us all of the time, and through reason we have found many of those flaws. Consciousness is the final boss fight, and the battle has begun:
Build the thing on a sea platform. Launch the counterweight into water. Make it sharp-nosed like the payload, so it could potentially survive impact with water and be recovered.
Free labor - not with the portable scanner type of self-checkout. You put stuff directly in your bag instead of the cart, so no extra effort is necessary. Although tbh, even the scale-type machines are quicker to use than waiting in line. They do perform randomized checks, but very rarely and only 3 items ie 1-2 minutes total delay.
Plus with contactless payment my shopping is an essentially frictionless walk through the store building.
I've been thinking about this since I read about the Pirahã people. The concept of number enables engineering and business (accounting) (and perhaps timekeeping). Someone unfamiliar with numbers would find it very difficult to function in modern society and a group of such people wouldn't build modern civilization (unless they discovered numbers, which someone did at some point, of course). Now, here's an example of my crazy dream: imagine the possibility of currently inaccessible ways of perceiving or thinking, that, if they were to become available, would enable a four year old child to gain an understanding of, for example, elementary particle physics from zero to phd level in mere minutes. Of course, that way of thinking might be so different that said understanding might make no use of (our current) mathematics or the concept of elementary particle at all.
Hmm, I tend to think that what one can do with some objects is an essential part of what they are.
Two-dimensional vectors can just as well be thought of as points in the plane. What sets complex numbers apart is eg that we define complex multiplication of them.
A more general example: a group is not just some set G, but that set with a binary operation satisfying certain axioms.
