Do you think Western culture is a continuation of Classical culture?

I think it is a mistake to think of civilizations as singular, self-containing organisms with set life-spans. Rather, they are more like colonies of organisms which exist independently of the colonies that they form, and which function as specialized organs within that colony with indefinite lifes, and can transfer from one colony to another, serving different roles therein. In this sense, it is correct to say that modern western culture does retain many of the organisms from classical Mediterranean civilizations, while other have long since left or even perished. It can also be said that the Modern West has adopted and even spawned many other organisms which now form essential functions as part of the colony (the American and various germanic-derived organisms being the most obvious cases of this).

IMO During the Renaissance, yes, but from Age of Enlightenment to date, no.