Erdős's weak Dirac conjecture

Let $\mathcal{P}\subset \mathbb{P}^{2}_{\mathbb{C}}$ be a finite set of mutually distinct $n$ points, and let $\mathcal{L}(\mathcal{P})$ be the set of lines determined by pairs of points of $\mathcal{P}$. Erdős's weak Dirac conjecture. Every set $\mathcal{P}$ of $n$ non-collinear points in the plane (presumably over the real numbers) contains a point which is incident to at least

$$\left\lceil \frac{n}{c} \right\rceil$$

lines from $\mathcal{L}(\mathcal{P})$ for a certain constant $c>0$. This is a classical incidence-geometric conjecture asserting the existence of a point incident to linearly many determined lines; the source does not provide evidence of a resolution.