Rudy Giuliani on 9/11 Memorial Museum dedication

Former NYC mayor reflects on 'Your World'

This is a rush transcript from "Your World," May 15, 2014. This copy may not be in its final form and may be updated.

(BEGIN VIDEO CLIP)

RUDY GIULIANI, R-FORMER MAYOR OF NEW YORK: We will never understand why one person escaped and another didn't, how random it all seems and how powerless it makes us all feel.

But what this museum does is allow us to see is that we absolutely can effect each other's lives by what we do at a time of crisis.

(END VIDEO CLIP)

NEIL CAVUTO, HOST: Pretty powerful, pretty emotional ceremony today to mark the opening of the 9/11 Museum.

To America's mayor, Rudy Giuliani. You were very moving, Mayor, very moving.

You have seen the museum. You know it's there. And we were talking about all the kids who have born since who don't quite feel that. How do you tell them?

GIULIANI: Well, I think the museum will help. It's a very powerful experience.

Neil, I have been there, of course, while it was being developed at various times. I'm an honorary chairman, honorary member of the board. But then I went to see it yesterday for two hours just to kind of get a sense of the completed museum.

I was deeply moved. And for me to be deeply moved after all these years and after all I have been through -- I lived through this experience 1,000 times in explaining it to people or testifying about it or writing about it.

But it was almost like going through it all over again. And to see -- for me, the two most powerful things were to see the things that were left behind by the people, because many of those things I used to help identify people, because people weren't identified by and large in the way we normally would do it.

They identified with belt buckles or shoes. I saw some of the things that I identified at the morgue.

CAVUTO: And there are still many that are not accounted for. Right?

(CROSSTALK)

CAVUTO: There are lot of families who are upset.

GIULIANI: When I saw the first one, it just took me back 13 years to be standing there at the temporary morgue and saying I think this may be someone's body part. So, that really got to me.

And then the second one, strangely enough, was seeing the television footage of the cloud over Manhattan, because I lived in that cloud for about 40 minutes in trying to get out of it and getting my people out of it. And it reminded me of a nuclear cloud when I was going through it.

And now when I see the pictures of it, including from the satellite, unbelievably powerful, those breezes and clouds. And now I know why so many people got injured. So, those were the difficult -- those were the difficult things, and then of course just seeing all my friends up on the wall was difficult.

CAVUTO: You know, there are a lot of folks -- you and I certainly particularly can remember the day like it was yesterday. But a lot of people don't, and I have two sons myself who were born after that. So, how do you keep that alive to them? How do you -- what do you do?

GIULIANI: I think this museum will help do that.

I remember having a similar experience way back in 1985, first time I went to Yad Vashem in Jerusalem. Of course, I knew all about the Holocaust. I had even handled a Nazi war criminal case. In fact, I was in the middle of handling it. I thought myself something of an expert on that.

But then to go through Yad Vashem and see what happened to the Jewish people and what the Nazis did, it -- you walk out and you're just completely exhausted. And then when you see all the numbers, and it makes you, to the extent you can, understand the Holocaust.

I believe this museum can do the same thing. It makes you understand the devastation of what happened there and also the resiliency of the people. There's an upside to this museum.

Half of it brings you down and half of it brings you up, when you think of the remarkable heroism and the people that I introduced today who I went to see $15 minutes after they were rescued at St. Vincent's Hospital and at Bellevue. These men were saved by a miracle.

They fell all these stories, they got caught in an alcove. The building fell on them.

CAVUTO: Right.

GIULIANI: The building fell on them. But they were just in like a perfect storm, perfect, perfect situation. They were in -- right in the middle of an area that was protected and they were all saved.

So you get stories like that. And when you say to me, children born after, I think of Terry Hatton's daughter Terri who is married to my administrative -- that was married to my administrative assistance, and she was born after Terry passed.

And Terry never knew about her.

CAVUTO: Amazing.

GIULIANI: But this is the way you teach each of them. This is part of their history and it's part of their present. And they have got to know about it.

CAVUTO: Thank you, Mayor, for then and now.

GIULIANI: And thank you, Neil.

CAVUTO: We will have more after this.

Content and Programming Copyright 2014 Fox News Network, LLC. ALL RIGHTS RESERVED. Copyright 2014 CQ-Roll Call, Inc. All materials herein are protected by United States copyright law and may not be reproduced, distributed, transmitted, displayed, published or broadcast without the prior written permission of CQ-Roll Call. You may not alter or remove any trademark, copyright or other notice from copies of the content.