Politicians and philosophers,
early forms of democratic government and public discourse were pioneered by the ancient Greeks, laying the groundwork for much of modern society.
A) early forms of democratic government and public discourse were pioneered by the ancient Greeks, laying the groundwork for much of modern society -> Are we saying, "Politicians and philosophers were early forms of democratic government and public discourse.." This is absurd. Incorrect.
B) laying the groundwork for much of modern society, early forms of democratic government and public discourse were pioneered by the ancient Greeks -> Oh No! Let's read two options 1) Early forms of democratic government and public discourse..., laying the ground work 2) laying the groundwork..., early forms of democratic government and public discourse.. Option 1 is better, it has sequence of events. Incorrect.
C) the ancient Greeks pioneered early forms of democratic government and public discourse, laying the groundwork for much of modern society -> Now, We have modifier for "Politicians and philosophers", the ancient Greeks. It is correct. Let's read further. We can see events are in order too. Event 1) pioneered early forms of democratic government and public discourse and event 2) laying the groundwork for much of modern society. Let's keep it.
D) there were pioneered, laying the groundwork for much of modern society, early forms of democratic government and public discourse by the ancient Greeks -> Again, we can see events are out of order. Incorrect.
E) were the ancient Greeks who, laying the groundwork for much of modern society, pioneered early forms of democratic government and public discourse -> We don't have the correct modifier for "Politicians and philosophers". Incorrect.
So, I think C.