While warning us so obligingly against the dangers of mixed up definitions,
Jaez seems to have gotten his definitions, erm,
mixed up. While it is true, in the way of all
platitudes, that care need be taken with any attempted definition of human population and identity, it is important to really understand the
terminology and not get bogged down in
fuzzy dissaprobation.
Three concepts are key to the understanding of self-identity: race, ethnicity and nationality.
Race is a largely spurious division of the human species into biologically more and less closely related groups. Apart from some tenuous physical characterisitcs (colour of skin, shape of eyes, etc.), it is highly undefinable and potentially confusing. Just for a brief example, are Etheopian Jews Semitic or Negroid? Race is essentially a hangup from a previous scientific era, kept alive largely by those with a vested interest in separatism. It is used by some to fuel hatred (white supremacists, eg) and by others to create an identity out of a fragmented past (as for the descendants of various African nations who comprise today's African-American population).
Ethnicity is not a biological, but a cultural and geneological phenomenon. This is by no means an academically valid definition, but were I pressed for an answer I would call it the sum total of received knowledge and ideology. If one were to examine all one's inherited personal customs, dress choices, domestic traditions, religious affiliation and family affinities, the distillation of all and more of those characterisitcs would comprise one's ethnic affiliation. Ethnicity is a real, organic human phenomenon, not the fruit of anthropological observation, which is why it is so fluid and difficult to pin down to a definition.
Nationality, at last, is a highly synthetic and relatively modern phenomenon in which regional and historical loyalties are exploited in order to create a larger affinity group (the nation) and provide a basis for a farther-reaching political power. It is the modern substitute to the ancient empire or large kingdom, and democracy as we know it today would be impossible without it. Nationalism is one of the more potentially malignant social forces, in whose name both WWI and II were fought, not to mention countless other conflicts leading up to and including the Israeli-Arab conflict and the wars in former Yugoslavia. It is also, however, and as mentioned above, a prerequisite for the preservation of societies on such a large scale as we are accustomed to having today, with their resulting benefits of highly mobile economies and industrialisation.
Now, then. When one describes themselves as, just for an example, an Indian-America, one is no more limiting oneself to that definition "ethnically" than one is forgetting that one is also human, presumably male or female, of a certain age etc. Personal identity is a complex matter and can take many forms, with different componenst (one's humanity, gender, sexuality, parenthood, nationality, religion etc) ordered according to varying levels of importance.
An Indian American is thus not a person of Indian-American ethnicity, but an American national of Indian ethnicity - a definition which is both coherent and devoid of potential conflict. There very reason that these double-barrelled definitions spring up in places like the US and Australia is because they are so ethnically diverse.