is the universe an axiomatic system? I am curious to know the philosophical point of view on this?
To qualify the universe as an axiomatic system, we would have to 1. be certain that laws exist in our universe 2. that the universe is logical. Now, in my opinion, the second is the more worthy of philosophical inquiry. Reinterpreted, it requires us to establish that conclusions reached by means of standard logic from the said laws, assuming they exist, are necessarily true statements in our universe.
That said, standard logic is not arbitrary but rather conceived to agree with what we observe of the universe. Therefore the question "is the universe logical" is equivalent to the question "do things that are reached by induction form truths?" and we know that it can neither be answered in affirmative nor the negative.
We are then led to the following question: is there a logic to our universe? I'm not going to try to answer that question because I don't think any answer I would produce would present points that I haven't already raised.
Also, if the universe is a logical system, is it complete? That question raises the classic question "does free will exist?" as if the universe is indeed a complete logical system, free will cannot exist.
Before attempting to answer I wonder what you mean. The question is unclear to me. I assume that you mean that either it is, or it's not?
Suppose it is
Suppose it's not
then what conclusions would you draw from each case and what difference does it make?
If you are thinking of a scientific method consisting of constructing/finding axiom systems, so that all our knowledge of the world would follow by deductions then I do not think that is a good idea. To me that is an out of faishon and static view of science, that somehow smells like seeing knowledge as uncovering universal truth, and the axioms of the universe are those fundamental truths, from which all that can be said follows deductively.
Often the models of science, when matured and tested good, are reworked into axiomatic systems, in which you have theorems etc. That is very handy, but I don't think that reflects the deepest nature of science if you consider the axioms universal truths.
However if you consider the axioms to be dynamical, then the overall picture of making deductions from an inductively guessed set of axioms, is after all just a particular way of making inductions. This type of axiomatisation makes more sense to me. Then the axioms really somehow serve the purpose of "probable laws", inferred presumably from experiments. Wether we choose to call them postulated axioms, or inferred laws of nature - I see no major difference beyond the words.
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