> otherwise it becomes mostly a practice of defining axioms within the realm of thought and manipulating concepts and relations, much like mathematics but without the practicality (in most cases)
That tradition in mathematics comes from analytic philosophy. That's not to say that all philosophy is about defining and manipulating relations (it isn't, and shouldn't be), but that language-games (to borrow Wittgenstein's term) are a subject of valid inquiry.
> It appears to me as if philosophy is in the unfortunate position where on one hand, it is ill equipped to answer the deepest questions and on the other it can't arrive at any important and empirically falsifiable conclusions.
Yeah, it often appears that way. However, we except such a sorry state of affairs in theoretical physics and the workings of the mind -- why should we be any less charitable with philosophy?
> Would be happy to be proved wrong, though.
With emphasis added: wouldn't we all? ;)
Well, personally I don't expect nor accept any non-falsifiable theories from any branch of science. There is a tendency to relax this requirement in some theoretical fields of physics and to say that it suffices if a theory is empirical and unambiguous. Of course one can make the line fuzzy with some of them and say that they are tentatively falsifiable (i.e they can be once humanity will be reach a certain level of progress), but as far as I'm concerned, those type of theories are more suitable as a special branch of mathematics than of physics. Perhaps philosophy can help in categorising these theories ;)
>> Would be happy to be proved wrong, though.
>With emphasis added: wouldn't we all? ;)
Yes, well, I never claimed to be free from the constraints of thought :)
Would be happy to be proved wrong, though.