the most basic postulates may be very wrong. Along the correct path there are always infinite combinations of partially correct paths. So we must be in one such path and there are always room for more perfectness.
That way we can never reach the perfect construction of logic, (as it implies from the fact that there is perhaps no perfect logic). Nature seems to me very much in denail with precision in the micro level. This might well be the case with mathematics, which in today's world we still hope and know it as a perfect knowledge.
But this does not mean total chaos or uncertainty. The direction towards correctness is probably correct, or at least it's reachable in theory. But the exact path or the point of destination can not be known or found with any single consistent set of mathematical theories. Nature prefers superposition of many related theories resulting into a fuzzy world of choice and micro randmoness, over a consistent single set of logics. It's all about intermixing and overlapping. The basic rules are forever hidden because of their interactions. We perhaps, can not unwind these rules into the basic constitutes, but only approximate one by losing the remaining ones proportionately.
I will be surprised if any of the infinities is not related with some sort of spherical construction from the geometric perspective.
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