Noumenal entities are beyond the scope of science. That's why it's called metaphysics: it's the stuff beyond the purview of normal physics and sciences. If you try to use maths to prove the existence of the form of the Good (presuming you're into Platonic forms), you're going to have a bad time.
Also: matter has more than three states; time does not necessarily have objective existence, though the causal chain is almost certainly real; and Flatland pretty clearly demonstrated that space may consist of more dimensions than we are capable of perceiving.
If I say there is an invisible elf that resides on my head, and that he commands the weather in North America, you cannot disprove it. It is beyond the scope of science. That does not make it real, or true.
Russell's Teapot.
Science is ultimately using empirical data to demonstrate physical laws. Noumenal entities by definition are outside the scope of empiricism, and thereby not under the purview of science.
That doesn't make the discussion pointless, nor does it mean you should automatically believe in someone telling you about their invisible flour-permeable dragon. It just means that empiricism isn't a useful tool, and by extension, that science can't answer those kinds of questions. Nor should it try to.
There's a corollary, though. Things that are outside of empiricism cannot have any effect upon the world that we inhabit, by definition. If they affected the physical world they could not be outside of empiricism. Although perhaps entertaining to contemplate the infinite possibilities, the existence or non-existence of anything outside of empiricism, having no ability to affect our world, is irrelevant.
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