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If I tell you that science cannot explain why that stone fell to the ground, you will say that I am a lunatic, but if I tell you that science cannot explain the ultimate laws of physics, you will say that perhaps I am right (a read it here, written by one of the panelists). But if science cannot explain part of physical reality, why is it only the ultimate laws of physics? Perhaps physical events that cannot be explained by science are happening all the time. Perhaps some of those events can be called "magic" or "miracles", no?

When you say that science can or cannot explain this or that what you ought to mean is that, at the bare minimum, the proposition that this or that happens can be deduced from some other more general proposition or propositions. So it is not unreasonable to think that there isn't anything science can't explain. Maybe there are infinitely many propositions, and they are all related deductively. Here I am just applying the nomological-deductive model of explanation, but the same point could be made using any other model, in its terms. It also seems to me that your question confuses two senses of "explain", one in which why a stone falls to the ground is explained when we deduce it from a proposition about gravitation, and another one, in which explanation is ultimate and absolute rather than relative to other propositions, and in which we cannot explain why the laws of nature are what they are and why they exist at all. If you stipulate that the second sense of explanation is legitimate, then your problem...

Is the concept of backward causation coherent and is it really taken seriously by philosophers? I doubt whether any scientist would accept the idea and I would like to know what you think.

Is the idea of backwards causation coherent? It seems not, as you could, for example, cause earlier events, such as your own birth, not to have happened. There is also the famous "bilking" (cheating) argument due to Max Black, according to which you can prevent the future cause of something that has already happened from occurring. All the same, philosophers, particularly Michael Dummett, have taken the idea perfectly seriously, and defended it. You write that you doubt that a scientist would take the idea seriously, but plenty of physicists, including Richard Feynman, have indeed used the idea for a variety of purposes, including the remarkable idea of positrons running backwards in time.

I really don't understand what the big deal is with the apparent 'fine tuning' of the constants of the universe, or even if 'fine tuning' is even apparent! The conditions have to be just right for life to emerge, sure, but so what? Conditions have to be just right for many things in the universe to occur, but we don't always suspect an outside agent as responsible for setting them up that way just so they'll happen. Is this the final refuge of the 'god of the gaps' habit the humans tend to fall in to? I also don't get the need for a multiverse theory either. To me it's a bit like saying, because I rolled a six on a die there must be five others each rolling the other possible numbers in order to explain it. Okay, much bigger die....

Right on the money! It is extremely improbable that with say four dice I shall roll four sixes (1/1296 against, if my arithmetic is right, and there are no biases.). But I have done it, with dice that otherwise showed no evidence of being biased. What does this show? Nothing at all! In particular, it does not show the existence of a dice controller who favours me - assuming more sixes are better than fewer. Suppose human life is extremely improbable. What does that show? Alas, again the answer is, absolutely nothing at all. The improbable sometimes happens, although, of course, not very often! We should thank heaven that it did!