We call American civilization Western Civilization because we've inherited political values, philosophy, and cultural traditions from the Greeks and the Romans for two primary reasons: one, Rome spread Christianity as well as its own culture traditions to its empires and, two, the Renaissance rekindled interest in ancient Greek and Roman art, architecture, literature, plays, philosophy, athletic competition, and political idealogies. Rome occupied England before the Anglo-Saxon invasion, and Augustine sent the Romans to convert the pagans of England to Christianity; therefore, we have inherited a mix of cultures we now know as "Western Civilization."
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