here chow elaborates further/in depth on the "natural" condition in the Razborov Rudich proof & finds some evidence for "nearby" functions that potentially could be used to defy the Razborov-Rudich natural proofs barrier:
"By definition, a natural combinatorial property satisfies two conditions, constructivity and largeness. Our main re- sult is that if the largeness condition is weakened slightly, then not only does the Razborov–Rudich proof break down, but such “almost-natural” (and useful) properties provably exist."
http://arxiv.org/pdf/0805.1385v3.pdf
"By definition, a natural combinatorial property satisfies two conditions, constructivity and largeness. Our main re- sult is that if the largeness condition is weakened slightly, then not only does the Razborov–Rudich proof break down, but such “almost-natural” (and useful) properties provably exist."