There is a paradox if you use a foundationalist point of view of anti-foundationalism.
But an anti-foundationalist will tell you that his own viewpoint is also relative, so there is no paradox from the point of view of anti-foundationalist.
Hard-objectivist claims that nothing is relative.
Hard anti-objectivist claims that nothing is absolute.
Both claims are based on black\white reasoning.
In
http://www.geocities.com/complementarytheory/UR.pdf I show that no hard approach is researchable, and we are (as conscious complex systems) a significant factor of any research.
I would love to be able to understand all the lovely patterns of numbers in UR.pdf so that I could verify or refute your claim.
I find it hard to imagine that no expert mathematician could not follow your maths and verify or refute your claim.
All I have seen so far is people who are struggling to understand your claim, or who seem to say that it's nonsense.
I am left with my verbal philosophy, my ordinary reason. To my mind, if anti-foundationalist (a-fou from now on) would say that his POV is relative, as you say above, that does not remove the paradox, either in isolation (perhaps) and (more certainly) when trying to make the a-fou 'agree logically' with the fou.
In isolation, the statement "A-fou is a philosophy in which all beliefs are relative"
is not a relative belief, hence it is still self-contradictory. Either a-fou is philosophically
fundamental relativity (I'm making my own terms up now too!...which is presumably something like unconsciousness or void or your own definition of a singularity, something about which nothing can be said at all ever) or it has some form and usefulness - not both. In order for it to do anything, mean anything, relate to other statements or be used by any thinker, it has to be self-consistent, not its own refutation.
This statement is relatively true
is as useless except for philosophy students to go insane thinking about, as
This statement is false
and
This philosophy is that all ideas are relative
is, very unfortunately, unusable, it seems to me.
The problem is not to try to help fou and a-fou to talk the same language, the problem is that a-fou can't talk. To say anything, it needs black-and-white-ness.
The human race has spent millennia on it. The paradox does not get solved, it just moves. Your work seems to me like someone chasing the paradox, trying to get it to fall off the edge of the page, and it seems to be driven by your wish to have spirit, divinity, quantum-mechanical-cosmic-consciousness and the 'meaningful coincidences' of fluttering scarobs (if some of your background information is anything to go by). It seems an endless quest to prove God mathematically.
Yet all the authorities on the matter so far agree that you can only sit in silence and contemplate the One, not form meaningful statements about It. You seem to be trying to name the Tao. (See, again, paradox: "The Tao that can be named is not the real Tao" - so whatever you say it is, it's moved somewhere else.) Hence the long tradition of vows of silence in religion.
Fine if you want to keep trying, and I hope you contribute something to maths, if not perform THE mathematical miricle of all time. I think I've got to a point where I have to choose to stay with black-and-whiteness, only remembering that reality may actually be mysterious (therefore, I give up believing that I can make meaningful statements about the fundamental nature of reality). Like a mathematician, I play with the things I can define, and wonder at the background indefinable-ness, the 'Void'. It's fun to contemplate, but trying to fit it into a formula, I think, causes people to go mad eventually. It's amazing how many of the great mathematicians spent periods of time in mental institutions. They seem to recover in as much as they return to black-and-whiteness. Monks take the other route into Nothingness.
As kindly as I can, I suggest you sharpen your pencil or shave your head. One or the other. I have to retain some humility, however, because, as I have said, I'm not an expert mathematician. There's something called fuzzy logic, and I have no idea what it is. I'm fairly sure it isn't a bridge between science and religion, though, or it would have been on the news.
I should like to apologise for "Go forth and multiply". It was an insult, not a suggested solution to 'how do you get 2?'. "2" doesn't make any sense in anything other than foundationalism. Nothing at all makes sense in anti-foundationalism. It is the complete abandonment of reason.
