Greek philosophers held a deep interest in politics. what did this reflect about greek society?

This reflects the advances of Greek society. They realised that in order to evolve as society and improve, they needed better rules, system and leader able to apply those changes. Also, liberty and freedom was understood by the Greeks us a essence of life, the difference between animals and humans.

So, a greater society was a free society, and that could only be achieved through a improved system.