I think the fact that there wasn't a universal "state" religion, and people had to choose what to believe (the Hellenes had just thrown off their primitive matrilineal society of Moon-goddess worship, superceding it with patrilineal Zeus-worship), coupled with a curious aristocratic branch of society (all of the Greek philosophers were idle rich, otherwise they would be mending shoes, rather than talking about the cobblers' place in society ), led to people investigating more and coming up with some basic philosophical methods ... after all, theology and natural history (life sciences) and philosophy were all one and the same, and closely linked to astrology (which the Greeks borrowed directly from the Babylonians), which eventually led to astronomy. It wouldn't be centuries until the Mohammadans (the Eastern inheritors of the Greek sciences) turned their efforts to alchemy, leading to chemistry. The Greek city-states were finished, replaced by larger civilizations like the Macedonians.
Certainly existing religio-political conditions affected (and continue to effect) philosophical (and all) thought.
Mr Russell sums up the state of investigations by reminding readers that although it may have kick-started the thirst for understanding: