• With: Rudy Giuliani

    This is a rush transcript from "Your World," October 18, 2013. This copy may not be in its final form and may be updated.

    STUART VARNEY, GUEST HOST: A chilling new video of the deadly Kenya mall attack, it is too graphic for us to air all of it, the security cameras capturing panicked shoppers running for their lives, and the terrorist ruthlessly gunning down their victims.

    To America's mayor, Rudy Giuliani.

    Looking at the new face of terror, are we?

    RUDY GIULIANI, R-FORMER MAYOR OF NEW YORK: Yes. We're looking at an escalation of the kind of horror and the kind of bizarre things that they do.

    VARNEY: We did not show it, Your Honor.

    GIULIANI: I know you didn't.

    VARNEY: But...

    (CROSSTALK)

    GIULIANI: I have seen -- I have seen -- those graphics are...

    (CROSSTALK)

    VARNEY: It's awful. They just...

    GIULIANI: Well, it is awful.

    (CROSSTALK)

    VARNEY: They just -- they have got them pinned down and they fire right at them.

    (CROSSTALK)

    VARNEY: It was the most cold-blooded thing I have ever seen, looking them in the eye and doing it.

    GIULIANI: Well, you get an idea of how these groups have gotten more and more vicious as they try to outdo the prior attack. I mean, what's the whole purpose of terrorism? To shock us. Right?

    VARNEY: Yes.

    GIULIANI: So I guess their thinking is, they do one thing. They get -- we get to a certain shock level. They got to exceed it in order to shock us even more.

    VARNEY: It terrorizes -- literally terrorizes.

    GIULIANI: And the whole purpose of it...

    VARNEY: They want you to submit.

    GIULIANI: That's right.

    VARNEY: They want you to be so terrified that you submit...

    GIULIANI: Right.

    VARNEY: ... to whatever demand that they're making.

    GIULIANI: Exactly right. And...

    (CROSSTALK)

    VARNEY: So, how do you fight it?

    GIULIANI: Well, you have to fight it in a couple ways.

    First of all, you have got to try to root them out, find them. You have got to try to prevent as many as possible, which we have done a pretty darn good job of. I think maybe there are a couple other things we could be doing now that we're not doing, but we have done a pretty good job of doing that.

    And then you have to have a resiliency to it, too. You have to realize that these things don't happen every day. They don't happen in the kind of frequency that domestic crime happens, and don't over -- don't overreact to it. That's hard to tell people. But you have got to train them to do that.

    I have often told the people in New York their resiliency was one of the reasons why we didn't get attacked again, because the terrorists realized, man, they hit us really hard...

    VARNEY: Yes.

    GIULIANI: ... but they didn't ruin the city.

    VARNEY: Yes.

    GIULIANI: And I just told the governor of Massachusetts the same thing in Boston.

    They came back the very next day. That's important. Same thing in London. And I was in London in '05 when London -- when London they got hit. Next day, everybody back at work. I believe that reduces -- that resiliency is a defense to terrorism. And you have got to teach people that.