Yes, I think we are kind of chasing a ghost in trying to seek something out there which we would finally catch and nail as "ultimate knowledge". May be, it does not exist not even due to possible infinite "multilayering" in depth of processes in nature, but due to blurring of those processes as we dig in depth (I think, this or something like this is what B.L.Nelson tried to say a few times). In this case in search for a new way to describe, say, topology of beyond-Plank space-time, or statistics of virtual pair dymamics, or properties of "false vacuum" or whatever is "blurring" we may do one of the following: a) use known math, b) invent logical "extension" of known math (fractional/imaginary dimensions, virtual numbers, fractal time, etc.) c) try to built new math based on "blurry logic" (like assumption of existence and non-existence "at the same time"- well, where actually "time" is poorly defined, or may not exist in "classical sense", etc.).

In this case, as always, all "old" mathematics and logic will continue to prosper, correctly describing "classical physics" outside of, say Plank values, but inside (where we can not extend space and time "classically" thus have to "extend" their definition some new way) we will use "new branch of math". This way, as always happened before, math/logic "in general" will be enriched by new objects and methods (rather than "found to be completely incorrect" as some may insist).

I think, this is another point Nelson try to communicate about and should be credited for.

Opinions?