"Must be open to the inclusion"? I would interpret that to mean "may include", no? So, the set of just the prime numbers may include all the composites (among other things).
How is this "nothing is what you say it is" concept useful?
Here's where Doron would qualify with "deeper" or some such.
A set may be "Locally" complete. But "Non-Locally" incomplete.
It's "Non-Locally" speaking that the myriad is both within and without.
He's also used the analogy of a square. 2D it's an enclosed space, but 3D it's open.
So take your set of prime numbers.
For Doron, merely Locally speaking this is a restriction of thought.
Going "deeper" or "higher" the creativity of mind is free.
Where mental freedom is seen in the ability to create and manipulate new defined catagories, Doron instead seeks creative flexibility in transcending defintions, or in a complex matrix where all the possible in and outs are spread open to view.We are able to manipulate the fabric of this mathematical universe exactly because we are also beyond it.
Where those cellphone towers that look like trees are included in the Tree/Forest matrix that encompasses beyond definitions, or includes the flux of definition.
Even Sylvia's there! (She's one of my fictional characters.)
The upshot of it, as you have seen, is not so much a "nothing is what you say it is" concept, but a
"anything is what I say it is" concept.
Doron doesn't object to bankers who dealing in finite sums restrict bank accounts in what he most recently called the "Asymmetric observation."
But when it comes to the non-finite, or when it comes to TM's Universal Consciousness, that's where he thinks Mathmatics must move beyond manipulating defined classes and analysis to a kind of intuition of open possibilities.
It's similar in intent to Nicholas of Cusa's "Coincidence of Opposites."
Though Doron's take involves a different view regarding Infinity.
As Doron sees it, traditional, "local only" mathematics, cannot address the paradoxes of the quantum realm or included consciousness.
He believes the answers are in his un-math kind of math.
But we're not getting from him applications of this "Organic Mathematics" because we're expecting the sort of local-only manipulations conventional math does.
Complexity isn't restricted to formulas and dirivations.
The use of Organic Mathmatics is esoteric.
However for Doron it does have some impact on the field of Mathmatics,
Much of the underpinning of modern Mathematics is philosophically untenable for him, so his major mathematical application of Organic mathematics is to critique and excise anything that makes an absolute completion, as the concept of Mathematical Infinity does.
Such a concept, to his thinking, is a tyranical jailor who locks minds into local-only thinking.
So, there's the use of it, as far as I've been able to learn.