On Hume's Problem of Induction and the Original Topic
Hume's problem of induction, which with regards to science effectively rules out the principle of the uniformity of nature and restricts how general a theory can be, itself has problems. I'd like to point out a situation in which the problem of induction fails:
Einstein postulated in his general theory of relativity that space-time behaves like a differentiable manifold. This was a reasonable assumption, but an assumption nonetheless and deserved to be tested. Well, it has been, and since general relativity has been verified to ridiculous extents, it has been confirmed that, at least over all observed regions of space and time, space-time has the properties of a differentiable manifold. Thus, the regions that behave like a differentiable manifold should obey the rules of differential geometry. In differential geometry, geometric equations inherit a property called covariance - a geometric equation (such as something that relates a vector to some other vector) expressible in a covariant form in one coordinate system in a region on a differentiable manifold will have the same algebraic form in any other coordinate system and at any other point on the manifold.
Let's bring this over to the laws of physics. If we can express a law in a covariant way, then, since space-time acts as a differentiable manifold, the law should be good over all space and all time.
But wait! What if there is some strange and sudden discontinuity in space-time and it no longer behaves as a differentiable manifold? Well if that happens, then it's no longer the same space-time we've come to know and love. So to this end, how much sense to it make to say "at this point in time, time is no longer time" or "at this point in space, space is no longer space?" None. To refer to a point in time, we need a time coordinate; to say at that coordinate time is no longer time means that we can't refer to that coordinate since it can't be a time coordinate.
I feel like this gives plenty of motivation to accept the principle of uniformity of nature and ought to make one question Hume's problem of induction. Furthermore, it shows how through the immutable power of mathematics, a theory can be confirmed, not just facets of it. With regards to experimental falsification, if a facet of a theory is confirmed, certain mathematical requirements may demand that many other facets of the theory be correct (if a vibrating string is discovered to obey the wave equation over some region, then the endpoints of the region that obeys the equation MUST have one of the two boundary conditions admitted by the equation, otherwise the region CAN'T be described by the equation).
Now, on to the original problem with the friend.
So, "what if gravity is just God's will?" I like your response: that's just giving gravity another name. No matter what the "metaphysical" cause is, it still happens, it's still mathematically modeled, it's still covariant, and it's therefore still a good physical law. I know some physicists who say that if there is a god, then it's nothing more than nature. This gets into another topic which I wish to avoid, but my point is if your friend is going to argue such a thing, then it has no physical consequence...I would imagine an all powerful being should get bored by moving stuff all the time, though. :)
I read someone's earlier post discussing that crackpot reformed physicst, Thomas Kuhn (I refer to him as such simply because his book is misleading. One can hardly say that the science of the middle ages, Ptolemy, and the Greeks compares to the method used today - namely now we require evidence). I believe Kuhn's point that there was a paradigm shift between Newton and Einstein and that the explanations and equations for gravity between them differ was brought up. I want to say, if I may, that this is bull****. :) The correspondance principle isn't applied to just quantum mechanics, it's a generally good principle. The same variables in Newton's equations DO appear in Einstein's! Mass isn't a relativistically important quantity, so it was generalized to energy density. The energy density isn't covariant, so it was generalized to the stress-energy tensor. You can see in the non-relativistic limit that the energy density becomes mass density and the spatial components of the stress-energy tensor vanish. Taking the weak-field limit and describing space as flat space with a slight perturbation produces Poisson's equation for Newtonian gravity, an embodiment of Newton's laws. True, Newton's space was flat, but in the weak field limit, space is generally treated as flat with the gravitational potential (the perturbation to flat space) kept the same as Newton's. There was no change, and Newtonian equations and modes of thought are STILL valid in the appropriate limit.
I would then like to say that GOOD theories aren't replaced, they're generalized. The generalizations always reproduce the special theory in the appropriate limits and circumstances.