I am curious. Do you think language shows how a culture thinks? I think what I mean is is some of the properties of their culture and way of thinking and who they were inherit in their language? If so, how is this displayed with Ancient Greek? How do you think who the Ancient Greeks were is revealed through their language and ways of expressing themselves?
sure. people have linked the greek tendency to think in binaries to the profusion of “men-de” constructions in greek literature. isocrates, for example, probably thought exclusively in binaries, and this shows up in his speeches. it’s tiresome for us to hear “on the one hand this, on the other hand that” over and over again, but it seems that there was a widespread expectation and appreciation for that in greek audiences, since the best greek prose stylists do it.
the fact that virtually no sentence in greek prose stands in isolation, but instead features some causal or temporal connective, might also point to an appreciation of “flow,” for lack of a better word.
I think this a really good example. It seems that one of the main thrusts of Greek thought was that clear thinking involved putting everything in its proper place and defining its relations with everything else and this is reflected in how they expressed themselves. Although, I’d say that that “they” refers to a cultural elite of sorts whose polished works have come down to us. More popular Greek works (like the New Testament) often show a more “choppy” style (although this has sometimes been seen as a non-Greek influence, but it’s probably just how most average people speak).
Maybe a good place to look for these kinds of things would be to look at the grammatical changes that occured in Greek, although I’m not entirely convinced a language’s grammar does reflect anything of what a culture thinks; I think stylistic choices like the one’s aso mentioned are best for understanding what a certain group thought. But maybe the development of the article (eventually used even with proper names) suggests an appreciation for being as specific as possible? Does the perfect going from a present tense to an English-like perfect to an aorist before dissappearing (almost) completely say anything? Probably not, considering the time scales involved, plus the fact that Greek later developed a new perfect.
It’s an interesting, thought-provoking question though 
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I don’t know about grammar, but Greek vocabulary is drenched in Greek culture, with all the nuances and imperfect capacity to be translated.
Could you expand on that?
I have vague memories of one of my college profs saying that even something as fundamental as which direction in which people write affects the way they think. He compared hebrew (right to left) to greek (left to right) and talked about the differences in thought between the two cultures. In this case it had to do with left-brain right-brain stuff. I’m not sure where one could find more info about this.
It seems to me, though, that if the medium is the message, then there must be many ways in which the language reflects the culture, and vv.
Which part of their language? I think it’s reasonable to say that the vocabulary of a a language may reflect the material and social culture, without of course going into the “Eskimos have 40 words for snow” nonsense.
But relating any other feature of the language to the culture quickly because less reliable. Think about the divergent cultures around the world that use English or Spanish as their primary language. I’d also take the greatest care assigning meaning to the forms of the classical Greek that come down to us. They are almost all highly refined literary productions, not probably very like the way the the average Joe spoke.
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Which part of their language?
Well, I guess I was planning to leave that up to whoever responded. And the responses have been interesting so far.
I think that this is a really interesting discussion and agree with what everybody has said.
From my perspective, I feel that language definitely influences culture. People use language to think in and therefore differences in the way a language describes and interprets the world will lead to cultural differences, as that is the framework within which the members of the speech community are interpreting the world around them.
Most languages interpret time quite differently which has resulted in the very different tense systems languages possess.