But we are not talking about a point as defined by math.

What is the definition of point in Physics?

We are talking about reducing a ball so that it is the smallest it can be and yet still be greater than zero.

You can reduce the radius upto a Planck's distance which is non-zero.

We may be attempting to explore how that definition may need to be changed.

What is your new definition?

We are not talking about the limitations of a mathematical system. We are talking about reducing a ball so that it is the smallest it can be yet still greater than zero.

That is with Planck's radius.

"If we don't have the tools to deal with the situation then I suggest we invent some"

What is your invention?

Isaac Newton developed/evolved calculus for just that reason. The infinitesimal was developed for just that reason. It appears that even these tools are insufficient.

I think calculus is sufficient to deal with infinitesimals.

The paradox can be expressed simply as:

If a ball has a diameter if 1 Planck Unit what is it's volume?

Planck's distance is finite and not infinitesimal. So, where is the paradox?

If a Planck unit has positive dimension than what makes a plank unit the dimension it is?

Planck's units are already well defined. They are always positive and definite.

That is infinitesimal but not possible in Physics.What is less than 1 Planck?

Other than zero...

Zero has both 3 dimensions and zero dimensions simultaneously. It is both immaterial and material simultaneously.

Zero is a number and not an object. How it(zero) can have a dimension? Does the number 1(one) have any dimension?

The proof of this is obvious both in Physics and Math. IMO

What is your proof? It may not be correct.