> "Now, imagine two identical particles and nothing else (Fig. 1A). Existence is a measure of relationships. (...) Except for their position, the particles are identical; therefore the distance between them is their only relationship. However, distance has a problem in this system. There is only one distance: the distance between the two particles. (...) Similar to the situation in the one-particle system, the distance between the two particles does not exist as there are no other distances to compare it to. There is no distance between the two particles, there are not two particles. The particles cannot exist."

I think this reasoning is flawed. The distance between the two particles is not only the relationship between the particles. The particles itself define a relationship with respect to the distance. Not only does the distance define the particles, the particles define the distance. What you are effectively trying to postulate is that sets of two items cannot exist. The premise that there are two particles implies that there exists some kind of distance, otherwise there would be only one particle.