The Grey Man
το φως εν τη σκοτια φαινει
"Why" and "how" are two completely different spheres of inquiry. "Why" addresses purpose, meaning, reasoning, agency; its very nature is subjective. "How" addresses process, function, mechanics. Whereas the steps and processes of "how" can be measured, it's impossible to measure "why," though lots of "sciencey" people do seem to insert reasoning into processes, like "peahens choose to mate with males who have brightly colored tails because their tails are an indicator of fitness." No way in hell do they actually know why the females make that choice. "Why" is also definitely misused in place of "how," like in "Why is the sky blue?"
Do you have specific examples of where I'm conflating "Why?" and "How?"
I'm not sure what you want me to do? Break epistemology with the existential equivalent of Kim Kardashian's ass? If you want me to make a "how" argument, the best I have atm is what's apparently a rule of math (I'm not a mathematician) that dictates that an n-dimensional space must be contained within an n+1-dimensional space, contained within (n+1)+1, etc., which is inconceivable to anything within the n-dimensional space. This extrapolates to nothing existing without being contained within something inconceivable, which seems to meet the criteria of the "undetermined transcendent reality" required for a belief in ietsism, to me. I mentioned it here via Sagan. It also seems to answer "If the universe is expanding, what is it expanding into?"
I haven't read much of this thread, but since you've invoked me, I'll comment on the difference between 'why' and 'how' and on ietsism.
A 'why' is the explanation of a phenomenon from a final cause, a 'how' its explanation from an efficient cause. The final cause of a phenomenon is always some intended outcome, a temporal consequence which follows from it if certain conditions are met, whereas its efficient cause is its cause sensu stricto, its immediate temporal precedent from which it follows inexorably. You are right in saying that 'why' is subjective in that the intended outcome must be intended by some one, who is none other than the subject of the objectification of that outcome in some temporally preceding phenomenon, which is attractive or, to borrow a psychology term, has incentive salience to him. To complete the duality, the cause of a phenomenon sensu stricto does not necessarily have incentive salience, nor even any particular motivational property: in this sense, 'how' is objective. To conclude, the 'why' of a thing is its subjective motive, its 'how' its objective cause. Materialists think to assimilate the former into the latter in accordance with their overall metaphysical programme of perversely denying the subject and recognizing only objects, which should be no less an object of ridicule than its physical cognate in the fool who emerges triumphantly from the wilderness to declare that he has found only a multiplicity of trees and no forest.
Concerning ietsism, I'm unfamiliar with the doctrine, but it based on your broad description of it as the belief in an "undetermined transcendent reality", it appears to be an adaptation of Kant's transcendental idealism. If by 'transcendent' you mean 'not immanent', then this transcendent reality would be equivalent to the Kantian thing in itself, which is completely unknowable. All analogies, including your dimensional analogy, are inadequate for describing what it might be because it need not share any of the properties of our immanent intuitive knowledge, including time and space as conditions of possibility for other properties.
I will have more to say about subject-object duality and the thing in itself in my next thread (when I get around to posting it), to which I hope you'll redirect any responses to my previous posts, should you still feel bound to make them.