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What's the role of "idealistic" philosophies of well-regarded scientists such as Max Tegmark's "Mathematical Universe Hypothesis"?
https://en.wikipedia.org/wiki/Our_Mathematical_Universe
It has been accused of being a form of Platonic idealism, a concern that I fully share.
But what's the purpose of speculating about such theories? Does it serve as an hypothesis for real science, as a motivation for undergrads or as a "cool" popular scientific thing?
Why develop or read such "theories"?
I will present a possible explanation for why the fiercest defenders of natural sciences often ended up with the most idealistic metaphysics in the history of the philosophy of science:
Science is incomplete without a metaphysical background, i.e. methodological and ontological reflections on its very possibility. Hellmuth Plessner delivers a nice argument within chapter two of his The Levels of the Organic and the Human [Die Stufen des Organischen und der Mensch; translation forthcoming] for the link between natural sciences and idealistic metaphysics (the only one I am aware of atm, tbh).
According to Plessner, the problem is that science (i.e. natural science, as opposed to humanities) has to methodologically rely on material reductionism, i.e. all that is scientifically accessible is that which is measurable, i.e. the physical world, and the world ends up looking like only the measurable [physical] stuff was actually existing (analoguous: If all you have as a tool is a hammer, stuff starts to look a nail).
In that mode of thought, there is a hidden Cartesian dualism underlying, a division of Being into res extensa (material world) and res cogitans (mind).
As there is no explicable transition possible between these dichotomic spheres, we end up with two basic possibilities for metaphysical foundations (without giving up the Cartesian divide and the standpoint of experience [Erfahrungsstellung] of natural sciences): Reduction of either the mental into the physical (abstracting from any qualia) or the physical into the mental (which includes both qualia and other data).
To paraphrase what this means as a matter of metaphysical consequences: Either we end up baffled, not being able to explain mental phenomena like "colour", "pain", or "intuitive understanding of other humans" at all (except as handwaving them as "epiphenomena" of some neuronal activity), or we end up with (absolute) Idealism, since the mental sphere is undoubtably existent and "nearer" to our consciousness than the outer world (the main line of argument of Descartes himself) and able to include all of this.
TL;DR: Given the Cartesian dualism that is underlying scientific methodology, reducing the physical sphere into the mental, i.e. Idealism, is effectively better capable of explaining why the two spheres (physical/mental) should converge and how they relate to each other. Hence, there is a "natural" tendency underlying all scientific endeavour to lead towards idealistic metaphysics.
Note: This is a rather rough sketch of the whole argument, but the parts that are important for the question are included.
Personal comment: The same problem occurs between data and theory in science, and lead up to Quine et al.
At some point one needs a motivation to do science, and a belief that there is something underlying scientific reality. Everyone needs an underlying faith, and faith that does not directly interfere with science is always going to be metaphysical (in the broader sense that not just philosophies, but religions are also metaphysical).
Science itself requires a faith in the meaningfulness of reproducible results. And it provides no basis for this faith. The idea of rules of nature is, at its core, metaphysical. There is no reason within science itself for why the rules should not just change. So there is nothing wrong with pursuing motivation for this metaphysical necessity.
The reason to do metaphysics is that physics, and science more broadly, is a philosophical construct built on nothing in particular other than a social process. Since Logical Positivism ultimately failed to prove metaphysics is redundant and can be grounded entirely within objective reality, we can ignore this baselessness, which may be the best approach for most of us, or we can do metaphysics.
Metaphysics with no ideal content is just an elaborate denial that there is a basis. If we simply say all reality is based in physical reality and physical reality is based in itself, we have not given an explanation, we have ruled one out. Upon what basis should one rule out the possibility of an underlying explanation that might shape your role in the world? On the basis that it is not useful? How would you know unless you found it?
If you do not have a metaphysics, and you are doing science, you have a faith that cannot be explained or at least cannot be articulated. How is that better?
