No, a numerical system is type 4, as there are 8 Planets in the Solar system but If I removed the concept of a Numerical system, the number of Planets is the solar system would be in a new numerical system, like 7e or seque, instead of 8.
If the concept of Numbers ceased then the amount of bodies would cease to be, there would be a trans-finite amount of bodies, the number of planets would become a trans-finite amount, as there are no finite numbers (as the concept of Numbers is gone), so there'd only be an expression of them, which would be algebraic in nature, not numerical.