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The Problems of Philosophy
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Second, it's pretty hard to ask whether Wittgenstein was right. Anyone who arrived at his conclusion should also be cured of the corresponding illness. Thus, they should no longer care and are unlikely to answer. On the other hand, if he's right, the people still suffering under the illness or delusion will simply insist that he is wrong.
Finally, isn't it possible that he was right as applied to some problems, but perhaps not to all philosophical problems. Once upon a time, the nature of a "force" was a philosophical question. Answering the question satisfactorily removed it from the realm of philosophy. It's conceivable, I suppose, that similar resolutions might be in the wings with respect to other problems, but a genius like Newton doesn't even come along once in a century, so it's impossible to guess when this will occur, or what the revelation might look like.

"...are the problems of philosophy articulations of real tensions in our experience that we somehow -must- resolve in order to fulfil our humanity?"(which I would answer in the affirmative) - this unresolvability essentially creates the possibility of an infinity of resolutions. For example: that I am scientific means that for me the Newtonian conception of force is generally satisfactory; however, someone decidedly nonscientific might conceptualize it as the will of a supreme being; moreover, there might exist an anti-Newtonian scientist for whom force still retains its problematic character. In any case it is obvious that there cannot exist a single all-encompassing concept of force which would ease the associated tension for everyone. In other words, even if the problem must be resolved, the manner in which it is to be resolved is not etched in stone anywhere.
Which brings me to the third reason that philosophical unresolvability is inherently a positive thing: it serves as an inexhaustible source of inspiration to anyone compelled to discover resolutions. So I am not sure whether Wittgenstein was right or wrong, since to me it seems that inspiration could just as easily arise from confusion and mental cramps as it could from experiential tensions. After all, is not a mental cramp caused by confusions in my thinking a real tension in my experience?
Even if the latter distinction is more than merely semantic, I certainly believe that Wittgenstein did not annul all philosophical problems. Alternately, I believe that philosophical problems will always exist, and serve a much greater purpose than simply the entertainment of philosophers: specifically in that nothing we encounter - whether presented to us by nature, scientists, or sages - is so certain as to be truly unquestionable. It is essentially in this way I think that 'the problems of philosophy' are pervasive and continually stimulate not only the development of existing fields of knowledge and inquiry, but also the creation of them.
The problems of philosophy all begin with mixing religion and philosophy.
Was Wittgenstein right? Are what seem to us to be "philosophical problems" really just something akin to mental cramps caused by confusions in our thinking that can be dispelled through conceptual elucidation? Is the task of philosophy to "shew the fly the way out of the fly bottle"?
Or are the problems of philosophy articulations of real tensions in our experience that we somehow -must- resolve in order to fulfil our humanity?
And why do the same problems recur? Why is the fly attracted to the same sources of light? Mind/Body, Freedom/Necessity, God/Nature, is there some logical absoluteness about the problems these distinctions have bred time and again over the centuries? And if not, then why do these exert such an enormous pull over all of us, walling up our thought and experience in the same structures with each new generation?
Is it possible to so entirely redefine the fundamental experiences of our lives so as to breed concepts and distinctions that would not solve, but eliminate the traditional problems, giving rise to an entirely new landscape of philosophical problems? Or are these current formulations logically justified as supreme and binding to human reason?