Could the laws governing the fundamental forces of nature be inferred mathematically from some basic and simple assumptions?

Question

The fundamental forces of nature include Gravity, Electromagnetism, and so on. The laws governing these basic forces of nature are typically conclusions based on repeated scientific experiments and observations over many years and which have become accepted universally within the scientific communities. Mathematically and based on the principle of general covariance, the laws governing the fundamental forces are usually expressed in terms of tensor fields.

Now the question is: "why do the fundamental forces acting on the universe (which cause all the movements and interactions) manifest in the way, shape, and form they do?", and  "could the laws governing the fundamental forces of nature be inferred (uniquely) from some basic and simple assumptions?"

Answer 1

I don't think anybody knows how the laws of nature can be inferred *uniquely* from a set of basic assumptions, since that would correspond to knowing the TOE, wouldn't it? However, a usual procedure in QFT is to write down a "reasonably simple" Lagrangean functional which respects all the "basic and simple" symmetries which we assume to be universally valid, but at the same time is rich enough to contain the physics we want to describe (i.e., contains all the abelian&nonabelian, bosonic&fermionic fundamental fields necessary to produce the desired particle content). One is then left with a set of model parameters (like coupling constants, mixing angles, bare masses in the Standard Model). One almost never tries to guess the equations of nature in terms of equations of motion for the tensor (or spinor) fields from the start, since that would usually be much more difficult to do in a covariant way. So, the simple starting point that you are looking for might be the Lagrangean of your field theory.

Hope this helped.  

Answer 2

The answer is "No."

First of all, the nature is not mathematics and is not described with mathematics. It is we who try to describe it with mathematics for our practical purposes. And we, human beings, cannot distinguish fine differences in similar events/things, so we consider different things as the same. Now counting becomes possible.  We can count apples despite their differences. You see, we oversimplify things to be countable; otherwise we get all things different and no math is applicable.

The answer might be "Yes" if you oversimplify things.