Talking to an audience of around 120 people in the first of the Newman Lectures series, Archbishop Eamon said: "Inspired by a personal encounter with Christ we enter the public square with a conviction that something else is needed. We don't go there simply to win arguments. When we speak, we draw on both reason and faith and an integral vision of the human person that is linked to the common good."
He said the Blessed John Henry Newman, after whom the lectures are named, had a confidence in the harmony of faith and reason which was shared by Pope John Paul II who said: "Faith and reason are like two wings on which the human spirit rises to the contemplation of the truth."
"The media, entertainment, education, the virtual space, business, arts, music sport, all of these areas enter into the public agenda and from all of these emerge messages which shape our understanding of the truth and how we live our lives," said Archbishop Eamon.
"If the church is to effectively enter the public square, then people of faith need to be in all of these areas both as faithful witnesses to the Gospel and also as faithful citizens. Anywhere people meet and share opinions – like the pub, the hairdressers, the dinner party or staff room ' all of these places need to hear the voice of faith.
"We are offering the gift and message of salvation," he said. "The future of humanity rests on those who are capable of handing on reasons for living and hoping."
In Ireland, the context in which the church is entering into the public sphere has shifted dramatically in recent decades, argued Archbishop Eamon. "The church is speaking to a whole new generation. The role of religion and faith in Irish society has been hugely impacted by a wave of secularisation which has swept across Ireland ' evidenced by a steady decline in church attendances and in vocations. It has carried many people away from God and religion altogether. Like other parts of Europe and the Western world, more people in Ireland are now living their lives without reference to God or religious belief.
"We are rapidly moving from a society in which it was virtually impossible not to believe in God to one in which faith is just one possibility among others. Commentary is all about the decline of the church and calls to remove the church's perceived influence in schools, health care and policy making. We need to therefore find new ways of presenting the joy of the Gospel," he said.
The church has also seen great damage to its credibility through the child abuse scandal, acknowledged Archbishop Eamon. "Our witness has been weakened.
"I am convinced that the failures of the past must not be allowed to define us, but we should learn lessons for the present.
"We have to learn new ways to present our message and encourage conversations at a national level. Two-way critical interactions and conversations need to take place between religious traditions and the broader culture.
"Pope Benedict said: "The world of reason and the world of faith need one another. They should not be afraid to enter into a profound and on-going dialogue for the good of our civilisation."
"It is this approach that I would advocate in Ireland, here and beyond," said Archbishop Eamon.
"The state will flourish if it is able to sustain itself as a community of communities. It will struggle if such communities find themselves unwelcome or even forced to retreat from the public square.
"I am completely convinced that the voice of faith can and should remain engaged in the public square. Our faith is not for the privacy of our homes and churches, the Gospel is meant for mission and the cut and thrust of public discourse.
"Our challenge is to present to the world the edifying and inspiring witness of people of faith," he said.
"I am convinced of the importance for all of us to engage and speak out of our faith conviction with those we meet in the public square and do so with compassion and with hope."
The Newman Lecture series is sponsored by the UEA and the Diocese of East Anglia.
You can find out more about the next lectures and watch a streamed video of Archbishop Eamon (in a few days' time) at:
You can hear Dr Andrew Eburne talk about the Newman Lectures on Radio Norfolk by clicking here andstart listening at 2.45.50 hrs
Pictured above is Bishop Alan Hopes (left), UEA Catholic chaplain and event organiser Dr Andrew Eburne and Archbishop Eamon Martin at the UEA in Norwich.