A: But why are the dynamics of the electromagnetic field derived from Maxwell's Lagrangian rather than some other equation? And why does the path integral method work at all?

B: What do you mean by "why"?

A: Hey, wait a minute, I'm asking the questions here! Um ... I mean ... I want an explanation of what makes the world that way.

B: Really, you do? You didn't like the last three explanations I gave you. What was wrong with them?

A: They didn't go deep enough. They explained things in the world in terms of deeper and deeper levels, but there was always something left to explain.

B: What would it feel like to have a deep-enough explanation? What are some things for which you think you do have a deep-enough explanation?

A: I don't know. Arithmetic, maybe? I don't feel the need to have a deeper explanation of 1 + 1 = 2, I'm happy saying that it just does equal two, and if you set it up to be different you'd just be talking about some operation other than addition on the naturals.

B: I wonder why arithmetic feels adequately explained to you, but electromagnetism doesn't? What would it feel like if arithmetic were as problematic to you as electromagnetism is?

A: ... I'd be asking why 1 + 1 = 2, I suppose. I wouldn't know the answers to questions that are intuitively obvious; or I wouldn't trust my intuition about them.

B: So you have intuitions about natural numbers, but not about electromagnetic fields?

A: I guess not.

B: Any ideas why not?

A: Well, nobody does! Arithmetic really is obvious — even birds can count, and they really aren't very bright.

B: Crows and parrots are. But you're right, it doesn't take advanced symbolic reasoning to count. Lots of animals do it instinctively, and presumably we do too. We have instincts that tell us that $$ and $$ put together would look like $$$$, and not like $$$$$ or $$$. It's difficult to imagine what it would even mean to question that.

A: So what are you saying? I don't look for explanations of arithmetic because ... my instincts don't allow me to?

B: Or, truths of arithmetic have been coded into your instincts by evolution, but truths of Maxwell's equations aren't.

A: But dude! How the fuck do you know they're truths? You're assuming just what I wanted to challenge in the first place! Stop petting the prince!

B: So now what you're after is "by what mechanism do we know that they're true" rather than "what mechanism makes the world operate that way"? You're satisfied with epistemology rather than metaphysics?

A: Well, it would be a start ...