Given a set P of n points in the plane and two points x and y not in P, such that their union is in general position, we say that x and y have the same view of P if the points of P are visible in the same cyclic order from x and y. We show that for every set P of n points in general position in the plane, there are \(\varOmega (n^4)\) points with mutually distinct views of P, confirming a conjecture by Díaz-Báñez, Fabila-Monroy and Pérez-Lantero and a conjecture by Bieri and Schmidt. We also provide an easier alternative proof for point sets in strong general position.