A contradiction is a contradiction, the fact that you do not consider contradictions to be invalid is just an aspect of your particular
Dialetheism. The fact is that "the state of mind of the current community of mathematicians" considers both local and non-local points of view, just not your particular Dialetheistic point of view of the definitions of local and non-local.
Thanks for that link, The Man. We're thinking along similar lines, clearly.
There's this bundling of relational operators into "Relation" (and apparently the eqation of this with Non-locality), and the identification of the other parts, constants and variables and what-not, as "Elements" (cf. Locals). This seems somewhat arbitrary, since I could identify any element in an equation as the result of another equation, which itself contains operators and elements. Thus it seems that there is a self-referential definition going on, as though Einstein had suggested E=mc
2+E. Obviously that's physics, not math, but I can't see how it could be acceptable in math either. It just leads to absurdity, I suppose, like (P and ~P).
I can see that perhaps to Doron this seems a power of his system - if 3 is 'researchable' and it is also a result of 2+1, then it is researchable,
because it is a combination of elements and relationship. It's just that I'm not sure if a definition is powerful if I can't find anything that isn't in that set. The power of a definition would seem to be that it discriminates, places set boundaries somewhere. Ah, no, I'm wrong, aren't I? Whatever further equation I find for a number, it involves some operator or other, and that is still unlike a number. Hence relationship seems to keep re-entering any result, which at first I may consider an element, but perhaps elements aren't any part of relations. However, now a new paradoxical problem opens up, which is that Doron's 'Relation' and 'Element' are not distinct species of thing or process. One is intrinsic to the other: relationship is intrinsic to element. The exception, in natural numbers, would be if there were a number that could not be expressed in any equation, thus avoiding introducing relational operators. Since I don't know of any, that seems the weakness - or at least one weakness. The 'researchable realm' of natural numbers ends up just being the natural numbers, and Doron has spent a lot of time in complicated descriptions of nothing at all.
Another idea is this intended integration into mathematics of the mathematician's "cognition". The earlier Relationship\Element (is there a significance of the backslash?) weakness suggests to me someone idly inventing mathematical schemes to approximate the metaphysical hopes in his head - like starting with Mind\Matter. The introduction of the mathematician's mind, in the absense of a clear rationale (apparently) for the R\E maths adds to that impression. Since there has not yet been any clear definition of Element or Relation (or did I miss those)...nor any definition of what the mathematician's "cognition" is supposed to mean, or
how it is part of the maths, I feel as though I'm just being set up to suppose that there is something deeeeeeeeeply significant here.
This with the background of explanatory links to Father - I mean, Doctor - Peat, with his courses at the Pari Centre (2009 courses "Synchronicity: The Bridge Between Matter and Mind", "Art, Science and the Sacred" and "New Science/ New Paradigms") complete the picture that this is meant to be
sacred math. That'll be why we're told:
The contradictory definitions are in the mind of a person that gets anything only by a local point of view (which is the state of mind of the current community of mathematicians).
Roughly translated, this seems to be saying that Doron is cleverer than any critic of his maths, being able to transcend the local POV in which the 'current community' is stuck. It seems to be saying either that in order to get to this erudite spritual maths of relation and element, one needs to be comfortable with 'contrary definitions' (i.e. Doronic Math entails contradicion somehow in it), or that a revelation is possible for one of the lowly mathematicians in which they achieve a new perspective, wherein the contradiction is seen as illusory. (Maybe diagrams of optical illusions will follow, like the old hag-young woman!)
Dear John,
Let us not hijack this thread by personal conversation.

So, er, is consciousness a basic rule of physics?
There is a private message for this.
Ok. I'll ask you privately.