The comment is some four years old now, but I still remember him saying it and the significance of his words.
I was speaking to Sir Hugh Orde, who was not yet two years into his reign as Chief Constable, and we were discussing the question of the past and its many unsolved killings.
"We need to close the book," Sir Hugh said. "It's how you close the book in a way that allows victims to come to terms with closing the book and have some sort of satisfaction...That is not a policing issue. That is a far wider issue, but policing will be shackled by it unless people grip that issue."
I remembered his comments because I was so used to hearing police officers and security ministers and other politicians saying that the book would never be closed.
It is going to be — and, for many, justice through jail is not going to be achieved.
The peace process is moving beyond that point.
That is my reading between the Eames/Bradley lines, and the carefully chosen words "that as each day passes securing justice becomes less and less likely".
The book cannot stay open forever.
How do you close it and who makes that decision?
We do not have those answers yet, but this debate is moving onto new ground as the Eames/Bradley Group gets ready to make their report and their recommendations.
None of this will be easy listening for the many victims and survivors. It is one of the hardest truths of our developing peace.
The speech by the co-chairs of the Consultative Group gives us some idea of what they are trying to achieve as they move towards making their report this autumn.
They want not just the IRA and the loyalists to say sorry — but have challenged the State to do the same for those times when it acted outside the law.
The context given in the Eames/Bradley commentary was not one of goodies and baddies, and of a piggy in the middle trying to keep warring tribes apart.
It was more thinking than that — more challenging, more credible in its analysis.
And for all its hard truth, it was worth saying and had to be said.
In that speech in the Titanic Quarter, the book began to close.
Lord Eames has had two long meetings with Gerry Adams on the question of the past, and he still hopes that this dialogue will open a door to the IRA — that that organisation will agree to say something more than its apology to non-combatants.
What will the loyalists say and do? What is the State's contribution to all of this?
They have now been given something to think about £— and maybe the biggest contribution all sides can make is a commitment to never go to the battlefield again, and to settle their arguments in dialogue and negotiation.
There may be some more truth — some further explanation of the various "wars", but there will not be full disclosure.
Eames/Bradley will not put the dirty war on an open stage; will not suggest that the informers are paraded before us.
In the here and now of this place, their speech was an assessment of what is possible and what is not.