Can the Variational Principle Explain the Laws of Nature for Classic Fields?

[Phymath]

I'm trying to understand why you can get away with using the variational principle on classic fields at all. The variational principle says minimize some value of a function the action. This idea is for point particles and is also motivated by the fact that Newton's laws can be derived via the action principle also be used to prove the validity of the Euler-Lagrange function, and also vice versa Newtons laws can be used to derive the Euler-Lagrange equation for classic particles. So how is it at all possible that variation of a field in a local area gives the correct formulation of the laws of nature, is there any reason this works and any motivations that this should work?

Is this just a law of nature that can not be derived similar to Newtons laws being simply stated and unprovable without experimentation. Any book suggestions would also be useful

 

[olgranpappy]

a posteriori justification aint so bad

 

[Andy Resnick]

I took the variational principle to simply mean the universe, and everything in it, is as lazy as possible. This is in agreement with my personal experience since I am as lazy as possible as well.