I am a citizen of the world.-- Diogenes (4th century BCE)
There are many meanings of the word cosmopolitan. In a philosophical sense, it can refer to the concept of a world citizen (from the Greek, kosmos + politês). The school of thought that supports this idea is sometimes called cosmopolitanism.
From Stanford University's indispensable online Encyclopedia of Philosophy, we learn:
In the eighteenth century, the terms ‘cosmopolitanism’ and ‘world citizenship’ were often used not as labels for determinate philosophical theories, but rather to indicate an attitude of open-mindedness and impartiality. A cosmopolitan was someone who was not subservient to a particular religious or political authority, someone who was not biased by particular loyalties or cultural prejudice.
So, a cosmopolitan can simply be a person who is open-minded, or, more specifically, one who ascribes to a particular geopolitical viewpoint. For example, in the Enlightenment period:
Grotius envisioned a “great society of states” that is bound by a “law of nations” that holds “between all states”.
And taking the idea even further:
The most radical of eighteenth-century political cosmopolitans was no doubt Anarcharsis Cloots (Jean-Baptiste du Val-de-Grace, baron de Cloots, 1755-1794). Cloots advocated the abolition of all existing states and the establishment of a single world state under which all human individuals would be directly subsumed. His arguments drew first of all on the general structure of social contract theory. If it is in the general interest for everyone to submit to the authority of a state that enforces laws that provide security, then this argument applies world-wide and justifies the establishment of a world-wide “republic of united individuals,” not a plurality of states that find themselves in the state of nature vis-à-vis each other. Second, he argues that sovereignty should reside with the people, and that the concept of sovereignty itself, because it involves indivisibility, implies that there can be but one sovereign body in the world, namely, the human race as a whole.
Most other political cosmopolitans did not go as far as Cloots. Immanuel Kant, most famously, advocated a much weaker form of international legal order, namely, that of a ‘league of nations.’ In Perpetual Peace (1795) Kant argues that true and world-wide peace is possible only when states are organized internally according to ‘republican’ principles, when they are organized externally in a voluntary league for the sake of keeping peace, and when they respect the human rights not only of their citizens but also of foreigners. He argues that the league of states should not have coercive military powers because that would violate the internal sovereignty of states, constitute a potential danger to individual freedoms already established within those states (if the federal authority were less respectful of human rights than some of the member states) and reduce the chances that states would actually join.
This "league of states" idea finally was attempted in the early 20th century, first with the League of Nations and then with the United Nations, although in both cases, "essential features of Kant's plan were not implemented, such as the abolition of standing armies."
During the latter half of the 20th century, versions of "economic cosmopolitanism" seemed to gain precedent over political forms, particularly, the "free trade" advocated by eighteenth-century anti-mercantilists like Adam Smith and Dietrich Hermann Hegewisch.
They sought to diminish the role of politics in the economic realm. Their ideal was a world in which tariffs and other restrictions on foreign trade are abolished, a world in which the market, not the government, takes care of the needs of the people. Against mercantilism, they argue that it is more advantageous for everyone involved if a nation imports those goods which are more expensive to produce domestically, and that the assumption that one's own state will profit if other states are unable to export their goods is false. They argue that the situation is quite the contrary: the abolition of protectionism would benefit everyone, because other states would gain from their exports, reach a higher standard of living and then become even better trading partners, because they could then import more, too.
On their view, after trade will have been liberalized world-wide, the importance of national governments will diminish dramatically. As national governments currently focus on the national economy and defense, their future role will be at most auxiliary. In the ideal global market, war is in no one's interest. The freer the global market becomes, the more the role of the states will become negligible.
This is an interesting prediction. Has it come to pass? We can observe that globalized trade has indeed reduced both the incident and the severity of war; it is not clear, however, that the importance of national governments has diminished dramatically. On one hand, the US, Chinese, Indian, and Japanese governments are more important than ever. On the other hand, it could be argued that in Europe, the opening of trade barriers via the EU is inaugurating a period in which "the role of the states will become negligible." We shall see.
Along these same lines, Kwame Anthony Appiah has written a new book titled Cosmopolitanism: Ethics in a World of Strangers, that reviews the historical background of this philosophy and considers its practical application in today's political and social climate. I've read the book and, frankly, I would not give it a hearty recommendation. The subject matter is important, but I found the writing style tedious and pedantic. However, I'm glad to see these issues being raised and discussed.
The wild card in all of this, as usual, is the potentially disruptive impact of exponential general-purpose molecular manufacturing. Whether it will foster cosmopolitanism or not is uncertain. It could be a great boon to humanity, but it also could lead to a decline in interdependence between nations and make warfare again much more likely.