Was that the paradox of the barber who shaved everyone who didn't shave
themselves.

a) Not a true paradox (more on this later).
b) Yes, it is about shaving beards (root of Barber is Barba - Latin for Beard).

Let's look at Achilles and the Tortoise:

a) Tortoise gets a head start. TRUE
b) Achilles must cover an infinite series of half-the-distance before catching the tortoise. TRUE
c) And if Achilles does reach the position of the Tortoise, it has since moved. TRUE
d) Therefore Achilles will never catch the Tortoise. ????

If the barber (who might well be female) has no beard, she has no need to shave (her beard).
The act of shaving is not necessarily confined to beards.
Barbering is necessarily confined to beards.
As a BARBER, she may shave others' beards and not be in conflict with the paradox as she is still _shaving_ herself, just not a beard.
Logic chopping at its finest, but not a paradox. Conventional: A defined subset containing 0 items cannot be a paradox.

As to Xeno, we have the Crimmins Mack Truck Theory:

Give Mr. Xeno a 100' start on a Mack Truck.
Observe the results.

Reality:

Achilles has no intention of catching the Tortoise, but to go somewhere far ahead of it. He may never reach the far-ahead, but he will pass the Tortoise on his way there.

Similar level of logic-chopping, but none of the premises are falsified in the process. They remain true, but not relevant.

In any case, getting back to the OP, we should all defer to Marvin and wait for his discerning input.

Peter Wieck
Melrose Park, PA