I think you guys are heading in the right direction. I think we’re half done though, because the question we need to answer is: could the gothic arch or the string quartet be developed by a different culture, or is it something absolutely exclusive and un-repeatable? Depending on the answer, we can get the final answer for the stated problem. If it could be repeated by a different culture, the no, it's not a rational element of a western culture, because a completely unrelated train of thought led to same conclusions as those in our culture, and philosophy says that things don't happen twice without a reason (I guess someone said that somewhere
). So there must be something elese, some kind of ideal floating around, that's available for every culture at a certain point. If, however, it is not possible to replicate it in a different culture, then it's a rational element of our culture, exclusive only to us, because we slaved over it for thousands of years and came to this particular conclusion. There's a high level of randomness involved in the process.
You need to go sci-fi on this if you don’t catch my drift. What if a meteor struck Europe four thousand years ago and created a sea in that place. What if Greece never happened. Would someone else come up with these ideas?
So what wouldn’t be a rationale element of the western culture? Roads. Although they were invented by Romans, they were also built by the Chinese, Egyptian and Aztec.