As an analyst, I've always been struck unsatisfied by the overall Western approach to constructing philosophical arguments by following each statement to its logical extreme. I guess, more precisely, what leaves me ambivalent and skeptical is how cluttered and shoddy a thinking is used in coming up with an original premise.
Like, for eg, Russell's paradox: the barber shaves only the men who do not shave themselves; who, then, shaves him? To me, this is more indicative of a tendecy to confuse linguistic anomalies for structural integrity, not to mention its unvoiced assumption of a singular possibility of interpretation. What if the barber has severe trichotillomania (the psycholgical urge to pull out one's hair)? The linguistic ambiguity is thus resolvable withhout generating a paradox (also, using such a slogan for a barber shop as tongue in cheek is permissible); another way of resolving the apparent antinomy in mathematical terms is to define the barber as a "function" among other permissible operations on a set. In other words, it is an economic transaction between men who do not shave themselves and the barber, which is permissible, and without necessarily negating the personal hygiene needs of the barber - ie, the barber, by necessity, transcends a given set by virtue of his function role and the function's larger generality outside of the set).
In terms of philosophical analysis to logical extremes (a la, Hume, Kant, etc.), a similar problem occurs where there is profound confusion over linguistic ambiguities and structural antinomies. Hume started out a strong believer in and advocate for applying rigorous Newtonian principles in the examination of humanity and human being but all he found was nothingness. In short, he come to conclude that if all human knowledge is based on, and derivative of, empirical facts, but inductive reconstruction cannot be justified by logic, then all knowledge is suspect.
The problem here is even worst than trying to resolve mathematical antinomies because the metaphysical arguments are not based on an axiomatically-derived overall theory to inform their constructs. What I mean here is that there is a lack of that creative and predictive power of succinct statements of principle to build up arguments that is afforded axiomatic mathematics.
The dichotomy between idealism and materialism is assumed without any thought given to how the two extremes might be related, how they may relate, to generate novelty from the logical structure itself. The great Kant goes slightly further by basing all of consciousness of being on the primitive, elemental notions of space and time. But he falls short in suggesting that there is no plausible division between our awareness of existence and the outer world. It was before his time, but quantum physical principles that allow chemistry and life to happen can also be used to explain that sensation is facilitated by photon, phonon and molecular interactions within our corporeal bodies by way of a cerebral structure which, in turn, facilitates and gives order to and acts upon these interactions. It is a seamless, continuous cybernetic reality between us and the world.
The use of external sensing devices (empiricism par excellence), such as in particle physics, is a complement of and intimately linked to an interpretative apparatus we call a "theory", else empiricism would be sterile and pointless collections of data. Somewhere along the line, volitional consciousness and awareness becomes a necessary logical element of the system, reason is born and decisions are made. Upon looking at the disparate, raw sets of sense data and lexemes without a theory/grammar (linguistic or mathematical) to inform one's interpretations and reconstructions of them, as like Hume, only meaninglessness and chaos is to be seen.
It is the playing with these logical elements within a rule-based system (our consciousness, and its theories) that creates meaning and novelty but because the process itself can generate anomalies, decision-making for allowable and unallowable (appropriate) outcomes and reactions becomes a necessity. How and why it is thus we act and behave becomes a more productive enterprise.
Kantian notions of space and time, by the way, is cognate with IQ conceptions of "sila", that which allows existence to happen.