Dr. Alexander began his presentation by asserting that the history of Christian and Muslim relations is one of both conflict and cooperation. A major component of the conflict between the two religions is what Alexander referred to as "competing universalism." Both religions claim their truths are universal truths, and as a result, both religions are often seen as predatory religions that are fixated on dominating the other.
However, Dr. Alexander asserted that perhaps the problem is not competing truth claims, but "triumphalism" or a triumphalist attitude. Alexander defined triumphalism as "a praxis of asserting the authenticity...of ones own religious tradition or identity... [by] exercising the will to dominate and subjugate religious others." In order to follow commands from the Christian New Testament and the Qur'an to spread their respective faiths, adherents of both Christianity and Islam have resorted to military conquest and subjugation of outsiders. For a believer who holds a triumphalist attitude, a victory over a people group is considered a victory for the faith.
At present we are seeing a new phenomenon that Dr. Alexander refers to as "inverse triumphalism." In response to perceived encroachments by the other faith tradition, religious leaders have started taking a defensive triumphalist stance that is best described in the words of Dr. Alexander as "my triumphalism is because of your triumphalism." In recent years this can be exemplified by the actions of Terry Jones of Florida who gained global attention for his plans to burn the Qur'an, as well as Osama Bin Laden and Al-Qaeda who felt an invasion of the West as a threat to their values and responded violently. In comparison to traditional triumphalism, Dr. Alexander argues that this newer form may be a more dangerous occurrence since there is no end to the reciprocity.
Dr. Alexander goes on to explain that, although triumphalism may be a natural growth of religious traditions with competing universal truth claims, nothing undermines religion more than the use of it to claim cultural superiority or to justify forceful domination. However, in the absence of triumphalism between Christianity and Islam, Dr. Alexander argues that both faiths can not only learn to respect one another, but also make one better. Dr. Alexander used the athletic sisters Venus and Serena Williams as an example of this phenomenon. Although these rival sisters try to outplay the other, they do not wish to completely dominate the other, but rather bring out the best in one another. When adherents of both faiths begin to respect one another for their views without attempting to dominate the other, both religions will benefit and truly achieve their highest potential."