I presumed it was about the causes of the change of state.
Please correct me if I am wrong.
Not really, no. We can do it as a purely logical or mathematical exercise.
Let's say the state of something ('system' in the broadest sense, we don't care what it is exactly) that changes over time is
St at some time
t. Let's say its environment (anything external that can affect it) at that time is
Et. How consider some small time later
t+d
t at which the system has state
St+dt. We can consider the limit as d
t approaches zero (as in calculus), or take it to be the Planck time or some representation of how fast the system can possibly change or react.
Now, we don't care what
S is or what rules apply to it, we don't care if it's a physical system or operates under entirely different rules that we just made up or under rules that we have no idea about. In any case, we can ask a simple question, namely, given
St and
Et is there always only one possible
St+dt?
This is a question that will always have a yes/no answer (whether we know the answer or not) for any system that changes its state over time, regardless of the complexity or of the rules that it operates under.
If the answer is yes, then we have a deterministic system, if it is no, then there must be some randomness in how the system is changing.
Note that there are no assumptions or observations of the physical world needed. All we assumed was something (anything) that sits in some environment (which again could be anything, or nothing for that matter) and changes over time.
In fact, it's so general, we could even replace time with any other variable and see if our something varies deterministically with that.