Not really. Furthermore, how do you figure logic and Platos’s forms AREN’T informed by culture? Everything we do is informed by the culture we grew up in, to some extent or another. Plato developed his philosophy as a consequence to the time, place, and society he grew up in. Also, logic isn’t a single road that leads to the same place for every circumstance. The values, norms, taboos, etc. of a society can and will dictate many outcomes to a single question, and those answers can be perfectly “logical” in those contexts.