Finally took the trouble to look up "solipsism: the theory that only the self exists or can be proved to exist". It astounds me that anyone could think that they could prove anything beyond that. I have no idea what sort of proof they might have in mind.
I think we need to define your concept of "exists". (I notice that ontology is the study of existence.) I can't discuss that issue unless I know exactly what you mean.
>>> They usually see the material world as being caused from Platonist concepts. Mathematical concepts are thus considered as a 'meta-rule' to the Universe (i.e., a rule that exists above or primary to the thing governed by the rule).
Here I do not understand your use of the word "caused". How can existence alone cause anything?
>>>I used 'law' and 'constraint' interchangeably in this instance. In other words, if something cannot self-contradict itself then this is a constraint (or law). If the platonic view is wrong, then I don't see how such a constraint can have a legitimate reason other than "that's just the way it is". >If there is a 'reason' for self-consistency>, then it would seem that this 'reason' exists as a platonic rule (i.e., a meta-rule to the universe). For example, a non-legitimate reason would be the universe causes its own self-consistency, but that is circular making it an irrational explanation - which is not a reason but rather a mysterious description.