Earlier quoted context omitted.
> 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…
Axiomatized mathematics and logic too complicated, compared to undefined meanings in philosophy? 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? Shou…
I agree that those two can be "simplified" to something that people who haven't a PhD in mathematics can talk and write about, but once we go to more advanced stuff things become really, really hard to describe in layman's terms, and as such they are not interesting from a philosophical point of view.
I mean, things like a double integral or an Abelian group are indeed useful from an efficiency point of view, meaning that a technical society like ours needed them in order to build most of the stuff that surrounds us (bridges that don't fall at the first major earthquake, computers, rockets that have taken us to space) but they are completely and utterly useless at answering questions that have bugged us for thousands of years: why is it bad to randomly kill someone? Why is it bad to kill someone even if that potentially means a better economical prospect for me and my family? Why is it bad to kill at all? Why shouldn't we kill ourselves right here and now, thus avoiding future psychic and physical pains like illness or the disappearance of closed ones? These are all fundamental questions related to our very nature to which philosophy has offered some answers which have been satisfactory to some people, in any case, the rate of success has been much higher for philosophy compared to maths or physics when trying to find a satisfactory answer.
> Should we start with axiom of choice perhaps?
What does that say?