[4] From 1977 to 1982, and between 1987 and 1993, Murphy represented the National University constituency as an independent member of Seanad Éireann.

[7][8] Originally advocating for Irish reunification in the 1960s, and protesting the introduction of internment of Republican prisoners in 1971 as well as the Emergency Powers Act of 1976, by the 1980s Murphy's position had switched to the view that "the national question" around Northern Ireland was little more than a border dispute.

In 1982, Murphy delivered a speech at Béal na mBláth to mark the 60th anniversary of Michael Collins’ death, and declared Irish reunification "was not worth the shedding of a single drop of blood".

[9] In the 1990s Murphy condemned John Hume, for being willing to make overtures to Gerry Adams in seeking to end the Troubles peacefully.

[8] An atheist and a secularist, Murphy criticised the role of the Catholic Church's clergy in Irish politics, and opposed their influence on the 1979 Family Planning Act (relating to the sale of contraceptives in Ireland) and the 1986 Divorce referendum.