I love Brian Cox's TV shows, and have now seen him live twice. He seems a softer atheist than the "new atheist" crowd, and when asked last time around about his attitudes towards belief, he was generally tolerant. As long as you engage with science on its own terms, it is ok.
His recent tour promotes his new TV series Human Universe. So far I've enjoyed what I've seen. There are two major premises he makes - we are insignificant, and we are inevitable and hence have meaning (though I've also heard he denies meaning, so what does he mean by meaning).
Insignificance comes from the vastness of our visible universe, the huge number of galaxies and the likelihood there are many planets with life. However, he also claims that our appearance on Earth is so unlikely that intelligent life is rare. We are a freak accident. This revolves round the geology of the Rift valley and aspects of the Earth's orbit (Milankovitch cycles) as they conspire to produce an 800,000 year cycle that helped force our evolution. I've about 5 papers to read on this - and will blog in future.
I toyed with the theme of God's control over weather as described in the bible and human evolution a while back. But paleontologist Simon Conway Morris suggested other factors would have forced the issue at some point, and for example no large bolide was needed (as Cox contends) to do away with the dinosaurs. CO2 is in decline (present human forcing notwithstanding) so that the global climate has cooled and ice ages would have done it anyway (killed off the dinosaur), to make way for mammals. So it may be that Cox is over stating his case about contingency. Conway Morris certainly thinks so.
What makes us inevitable for Cox is the eternal multiverse idea, which falls out of quantum mechanics/inflationary theory, but also a desire to push science further back in time and God out of the picture. Cox assumes that the multiverse must be necessary and eternal, and hence functions like God. This is a philosophical assumption left unexamined, just as is the idea that such a multiverse must produce at least one universe that is biophilic. But why should it be the case that a multiverse should exist that produces an infinite number of universes with at least one that is biophilic (beyond our obvious presence)? What adds fire to the equations of quantum mechanics?
It is of course nonsense to suggest this gives us any sense of meaning, that I must exist because I exist an infinity of times. That makes me insignificantly inevitable. It's turtles all the way down.