Dawkins has a point: science works. I would throw logic in there as well, given that the same question gets applied to it. I've seen theists - in an attempt to either "level the playing field" or discredit science - try to argue that "faith" in science commits the begging the question fallacy. How can I justify the scientific method without appealing to the scientific method and thus committing circular reasoning? Concerning logic, how can we justify the reliability and necessity of logic without appealing to logic and thus (again) arguing in circles?
Because it works.
Science is an extension of logic. Aristotle, known as the "father of the sciences," developed or rather discovered and quantified the laws of logic, and consequently applied it to the study of our world. Science is utilized logic for the purpose of understanding reality. How can I trust science? Because it works.
Stephen Law (sitting next to Richard Dawkins in the video) rebuts that "it's the inductive argument." Well, yeah, it is. So what? Sure, there might come a day in which the sun turns pink and starts singing "Die Young" by Ke$ha, penguins suddenly acquire the ability to escape our atmosphere and survive in space, and all the scientific discoveries and achievements of the human race are rendered nonsense. Yeah... No, that's not gonna happen. But it might, right? At least it could. We can't prove that it won't. "All we've got" is this little inductive argument. Come on. Even the Ken Hammiest of believers wouldn't make that kind of argument against science, right?
Let us, for the sake of argument, agree with the theists who argue that we have "faith" in science. Fine. Let's use that word.
(If I may digress, when they try to attach the word "faith" to the secular community, it's another attempt to either "level the playing field" or discredit the views of skeptics. I find it interesting that the attempt to take down the secular community is an attempt to make it look more like the religious community. Like when a theist argues that "atheism is a religion" or that "it takes just as much faith to be an atheist." They aren't lauding atheism, they're trying to knock it down to religion's level. Interesting, n'est-ce pas? #EndDigression)
Let's say we have "faith in science." Let me borrow WLC's phrase and say that, if we have faith, it is most certainly a "reasonable faith." And while modern science is still relatively new, we have so much already to attest to its integrity and veracity. As Dawkins notes in the video, "planes fly, cars drive, computers compute." We have seen the application of the scientific method beget so many advancements and achievements. We've certainly come a long way since the horse-drawn carriage and trepanation. I'm sure Aristotle would be amazed at how far we've come, even if he wouldn't be all that surprised.
To put this another way, try to achieve what science has achieved without use of the scientific method. How far would you get in achieving flight or in successfully performing a heart transplant if left to guesswork or faith? Even the strongest dissenters of science utilize the scientific method every day. That's why they don't repeat the mistake of putting their hands on hot stoves. That's why they don't try to walk on air as they leave for work through the upstairs window, but use the door instead. Reminds me of what Tim Minchin wrote in his poem "Storm":
Chatter is initially bright and light hearted
But it's not long before Storm gets started:
"You can't know anything
Knowledge is merely opinion"
She opines, over her Cabernet Sauvignon
... I resist the urge to ask Storm
Whether knowledge is so loose-weave
Of a morning
When deciding whether to leave
Her apartment by the front door
Or a window on the second floor.
So, yeah. Science. It works, bitches.
[Actually, this photo was taken under water in Antarctica. The penguins are swimming, not flying, and that's not another planet, it's an air hole in the ice with light trickling through.]