I've mentioned my qualms with philosophical intuitions several times in the past here. (here, here, here, and here among other places) My basic qualm is that a lot of philosophers use intuitions to establish what something must be, yet their intuitions are really just kinds of judgments, as Williamson points out. Further a lot of these judgments are unconscious and taken for granted. They don't even conduct experimental analysis to determine what our intuitions even are. This is armchair philosophy at its worse. (For some reason I always tend to think of Husserl sitting alone in his office trying to do phenomenological reductions of various things when I think of armchair philosophy)
It's not that I think intuitions are bad. Far from it. They are a great way to start thinking about issues. Further, if we are attempting to answer questions, then the meaning of the terms in our questions has to be discerned before we can answer them. I think that quite often intuitions provide the content for questions. Therefore even if some philosopher's intuition might be unusual, if it allows them to attempt to answer the question formed out of that intuition, then its not that bad a thing. Perhaps it isn't the question someone else would ask, but so what? Change of perspectives aren't that bad a thing for philosophers.
Where I think some philosophers go wrong is to get too dogmatic about certain intuitions or to treat intuitions as something beyond language - a kind of privileged access to some truth. Now then I get very nervous, if only because peoples intuitions are so often wrong in the sciences. If you've been trained in the sciences, chances are you have a very skeptical attitude towards intuitions. To a scientist an intuition is just the instinctive judgment of your prejudices. A good education ought be about reforming ones intuitions based upon our encounters with the way the world really is. Indeed even philosophers are quite willing to place whole sets of intuitions into categories like "folk psychology." Why they then persist in appealing to intuitions escapes me, beyond a kind of hubris that they are being careful in their thinking.
Why do I bring up this rant? (Or perhaps why do I once again repeat my rant?) Well Chris over at Mixing Memory has a great post regarding philosophical intuitions. Indeed he even has a great Nietzsche quote that I'll quote here if only so I can easily find it again.
Collectively they take up a position as if they had discovered and reached their real opinions through the self-development of a cool, pure, god-like disinterested dialectic (in contrast to the mystics of all ranks, who are more honestly stupid with their talk of "inspiration"—), while basically they defend with reasons sought out after the fact an assumed principle, an idea, an "inspiration," for the most part some heart-felt wish which has been abstracted and sifted. (Nietzsche, On the Prejudices of the Philosophers)
Now as Chris points out Nietzsche was engaging in a bit of his typical hyperbole. Still there is running through a lot of philosophy at least from Descartes on, this sense that philosophers can engage in a kind of "reduction" to get at some truth within our intuitions or at least mind. Few philosophers would be as unskeptical of this reduction as Descartes. But, as I mentioned, Husserl is an excellent example of someone doing just this. I personally think that the positivists are quite guilty here as well, even if they are in their later periods a tad more careful. But I think this trend still can be found in contemporary philosophy. Read Chris' post. It's quite good. I think there is a hubris among philosophers that they can get at these issues independent of a careful psychology. (Which is not to say one ought embrace a kind of psychologism - the very thing that Husserl was reacting against as were other philosophers such as Peirce)
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