Differences in how Catholics and Protestants in Northern Ireland used the English language lay at the heart of past failures in political negotiations there, Mrs McAleese told the audience.
In what was afterwards the most talked-about point she made, the President said the Belfast Agreement was made possible because each side finally came to understand how the other used words.
She made her comments in response to Mr Padraig O'Malley, of the University of Massachusetts, author of seminal works on modern political discourse in Northern Ireland. He said that in some of his research he had found that "part of the problem in Northern Ireland was that both communities, the nationalist community and the unionist community, used the same language, the English language, in two very, very different ways".
Mrs McAleese said she had written about this and experienced this herself. "I remember John Dunlop, the former Moderator of the Presbyterian Church, explaining to us that within the Presbyterian or Protestant mindset a word has to have a definitive meaning. So they would go into a negotiation with a bottom line. Not an opening bid position, just a bottom line, because a word had to mean `X'.
"On the Catholic side - not to use the word `Jesuitry' in a pejorative way - but you are quite right, there is a soft centre to language, and an ease around the edges of words that we would use to try to create a space for consensus and compromise. So you would have one side going in with an opening bid position, and the first thing they meet is the bottom line from the other side, which invariably leads to breakdown.
"One side then has the view: `You always come in, you have no compromise in your heart at all, no intention of compromising', and on the other side you have the Protestants saying: `You always come in with weasely words, we don't know what your words mean, they're like mercury, we can't nail them down, they keep going all over the place'.
"So you had always these dialogues in which people presumed the other side was daft, or downright silly or downright meanspirited. But it is actually about cultural mindsets."
People in the North were educated and taught to have these different attitudes to language, so what was needed was for each side to know and understand each other. "We have to now, so when we sit down next and hear the bottom line we are able to say not: `Oh God, there they go again with the same old thing, breakdown before we even start', but rather to say: `Hang on a moment, we understand this process, we understand where this is coming from'.
"One of the strengths of the Good Friday agreement is that factored into it is an intuitive understanding of that thing which we did not intuitively know before.
"I think the Good Friday agreement is a manifestly wonderful example of being able to manage the process by using those very psychological insights. Having been able to construct this extraordinary agreement against all the odds, having finessed all those problems, we have now shown we can do it."