Watch the latest video at FoxNews.com 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. The Americans and the English know it by -- almost by instinct, but you have got to teach people that. VARNEY: OK. If you catch one of these guys, these cold-blooded, ruthless killers, you catch one, wherever you catch him, however you can catch him... GIULIANI: If they're part of Al Qaeda or if they're part one of these groups that have declared war on the United States, they're like soldiers. They're like -- this would be like the Nazis invading America. VARNEY: You don't give them a lawyer and bring them back to New York City? You don't do that. GIULIANI: I think that -- I think that is extremely dangerous. I think that is extremely irresponsible. I think the -- I think we learned our mistake in 1993, when we treated the World Trade Center bombers as criminal defendants, as if they had bombed a bank or shot a few people in the street. We learned that lesson. And then we got attacked on September 11. September 11, we treated it as if it was an act of war. And look how much safety we got of ourselves for such a long period of time by being tough and by being aggressive and by going on offense. VARNEY: I have to ask you about the man who is likely to become the next mayor of New York City, Bill de Blasio. (LAUGHTER) VARNEY: I don't know why you're laughing, because he wants to raise taxes on the rich again. GIULIANI: Well, I still have hope for my former deputy mayor, Joe Lhota, who -- who would make a fine mayor, is enormously well-qualified. VARNEY: OK. Now, that's a plug for your guy ,OK. GIULIANI: And Joe would keep taxes down. VARNEY: But -- yes, but... GIULIANI: Joe would keep -- Joe would keep what I started and Mayor Bloomberg expanded. VARNEY: Yes. Now, do you... (CROSSTALK) GIULIANI: Keep it going. VARNEY: OK. Come on. Do you... GIULIANI: Twenty darn good years... (LAUGHTER) VARNEY: Well... (LAUGHTER) GIULIANI: Compared -- compared to where I think Mr. de Blasio could take us, which is back to where we were in the late '80s, early '90s. VARNEY: Well, he's going to raise taxes on the rich. GIULIANI: And 1,900 to 2,000 murders a year. VARNEY: What would happen if -- come on. (CROSSTALK) VARNEY: What would happen to New York if you raise taxes on the rich again? GIULIANI: They'd leave. That's what they were doing when I -- when I became mayor, I was given a report that The New York Times heartily endorsed -- someone just wrote about it today, I think in The Post. They gave me a report. They told me, here's how I should fix-- fix the budget deficit. I should raise taxes. You know what I did? I symbolically -- not quite symbolically -- but I took it and I threw it in the trash and I said, if I have to do it once, I will have to do it a hundred times, because I got to get my tax base back. I have got to reduce taxes, and I ended up with a pretty darn good economy, and got reelected in a Democratic city by 18 percent of the vote, because I got the economy moving again. VARNEY: It is incredible that... (CROSSTALK) GIULIANI: This isn't -- this isn't brain surgery. VARNEY: But... GIULIANI: Lower taxes, expand jobs. Raise taxes, lose the people who producer jobs. VARNEY: But if you went under -- if you stood for election today and you had that program, lower taxes, you would you not be elected. GIULIANI: People don't make that connection. I mean, they don't make -- they don't understand it. They don't make the connection. However, you have got to teach them that. You have got to run on that. You have got to explain that. And sometimes being a good executive means doing not necessarily what is popular, but what is right. What is right for New York right now is reducing taxes, so we increase the number of jobs in New York. You reduce things like the sales tax, I can actually show -- I used to have a chart that would show you, you reduce the sales tax, you're going to get X-number more jobs. You reduce the income tax, you're going to get more jobs. We're a very heavily taxed city, and we have multiple -- I eliminated and reduced 22 taxes. When I was running for president, I put that out. They said, it can't be. You couldn't have 22 taxes. VARNEY: Out of time. (LAUGHTER) VARNEY: Would you ever consider running again? (LAUGHTER) GIULIANI: I'm not thinking about that right now. VARNEY: You're not thinking about that right now? GIULIANI: I'm thinking about my trip to Argentina later tonight. VARNEY: Well, good luck with that. (LAUGHTER) VARNEY: Your Honor, thanks very much for joining us. GIULIANI: Take care. VARNEY: Pleasure, sir. GIULIANI: Take care. Content and Programming Copyright 2013 Fox News Network, LLC. ALL RIGHTS RESERVED. Copyright 2013 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.