I ran into an interesting paragraph today. It stated the equation F = ma is used because... it's the fundamental equation in classical mechanics, and it helps to describe a lot of physical phenomena. Essentially, because it is useful. This was described in conjunction with a correlative equation in quantum mechanics that I can't begin to explain, so I'm not typing it out. There was a similar statement made in my Heat and Thermodynamics class that I'm taking: It claimed that Energy was THE fundamental concept of all of physics, and as such, evaded definition. This all brought home to me how much the philosophy of science is seriously influenced by Descartes and all the early modern philosophers: I've personally read that fundamental things escape definition being propagated by Descartes, Locke, and Hume. This shouldn't come up as much of a surprise, seeing as Descartes laid down fundamental work for calculus, and Hume is credited with seriously developing the philosophy behind the scientific method (Taking empiricism to its logical conclusions and inadvertently making a reductio ad absurdum argument for the existence of induction as a separate logical system, in my humble opinion). But this still surprises me.
The process of first principles in logical systems is arational, granted. But the idea that we use concepts in science simply because they are useful for describing the physical world seems, to me, to be a bit off from the idea that we are, indeed, understanding the physical world. I'm fine with stating that science only describes things in useful ways, and that is why we use them, but this description really gives little reason why we would choose one scientific explanation over another, or why even differing disciplines would, indeed, come to the same conclusions. I mean, by this, I could essentially adopt Aristotelian teleology in my description, claim that it's useful for understanding, and stand back satisfied with that use. However, just try and publish a scientific paper today where you ascribe purpose to your explanation, and I sincerely doubt it'll fly. To me, it seems that the "use" approach for validating the logical beginnings of scientific descriptions falls flat. I think the reason for this statement is to cut down the number of assumptions one has to make in making scientific pronouncements (which I would claim is a good thing) -- but unless there is some other validation method, I'm thinking that we are indeed still assuming that our minds are interpreting truth about the physical universe, but we're post hoc attempting to erase the fact that we're making this assumption.
So, sure, they're useful, and that's great. Maybe I'll change my mind when I realize there are other criteria that can be applied to first principles. However, I think it's a far more elegant solution to just admit that we're making something up that sounds like it might be right, then validating it empirically, and assuming all the while that our minds have some connection to the truth of the universe.