I think that Antoine made a rather good point. I don't see anywhere in there where he suggested that only songs written in native Irish should be considered "Irish Songs." That was a leap of illogic that someone else made later.

It is this sort of thing that muddies up the historical record. I can't tell you how many times I have seen "Amazing Grace" listed as "Celtic." (It is of course a an American song set to the Virginian tune "Loving Lambs.")

For the record: "Water Is Wide" is also American, set to the tune "Waly,Waly." It is one of my favorite songs.
I am kind of partial to "Biddy Mulligan" too.

Mulligan