Miller has said that tragedy springs from the individual's quest for a proper place in the world and from his or her readiness "to lay down...life, if need be, to secure [a] sense of personal dignity." Does this apply to all, or only American tragedies? Should America teach us there is no "proper place" or that we can define our own, thus avoiding tragedy altogether?

Arthur Miller's statement on the tragic consequences of not finding one's place in the world is a universal sentiment that is relevant even outside of the American tragedy. While Miller's work explores the relationship between people and places frequently, this theme can be seen in British and continental European plays as well. For example, Othello and Macbeth by William Shakespeare feature characters that exhibit self-destructive behaviors due to delusional ideas about their place in the world and the concept of equating attaining power with making your mark on the world.
Outside of literature, Miller's sentiment can be seen in everyday life, whether on a micro scale like individual perspectives on the self's relation to society, or on a macro level such as authoritarianism and genocide. America itself is a concept, or social construct, based on Enlightenment-era ideas about democracy and liberty. But these values, many of which were written in the U.S. Constitution, were not always applied in the real world. For instance, the white colonial populace fought for their freedom against the British Empire and believed in grand ideas about liberty, and yet slavery in the United States continued for centuries after the revolution.
This begs the question: Is the right to a place in the world only limited to a certain demographic? What about the African slaves who were literally displaced from their homes and had their identities taken away? The struggle of African slaves and African Americans is a true example of finding one's place in the world. The fact that African Americans and other minorities were able to create their own hyphenated cultures (e.g. African-American, Asian-American, Mexican-American, et al.) in a new environment illustrates that "place" is just as much as an idea as it is a geographical location.