Is there a constant $\delta >0$ such that, for all large $n$, if $G$ is a graph on $n$ vertices which is not Ramsey for $K_3$ (i.e. there exists a 2-colouring of the edges of $G$ with no monochromatic triangle) then $G$ contains an independent set of size $\gg n^{1/3+\delta }$?