> Philosophy, in its purest form, contains the study of what it is to live a good human life. I don't think this a properly general definition of philosophy (although he says "contains",maybe he is not after generality). I would say philosophy is the science of definitions. This is why it is fundamental.
> I would say philosophy is the science of definitions It depends, I guess. If it matters I for one stand on Socrates's side when it comes to what philosophy is and I find definitions to be just "syntactic sugar", they don't bring anything new to the table. This is also one of the reasons for why I found Aristotle pretty boring, I think he started this trend with categorizing things and defining terms, without trying…
There is no grand view in philosophy either, but millions of tiny conflicts coexisting from which no truth can be gleaned as the philosophers will wriggle out with sophistry. (Just like politicians for that matter.)
It is a good old Wittgesteinian challenge.
Hope so you define concept of free will in axiomatic logic? Should we start with axiom of choice perhaps?