A logician’s wife tells him: “Run to the store and pick up a loaf of bread. If they have eggs, get a dozen.” The logician comes home with 12 loaves of bread.
The goal of analytic philosophy to analyze statements, and to use logic to make their meanings unambiguous and their consequences clear. So, what's not to like?
Continental philosophy, in contrast, is often written in dense prose that is extremely difficult to parse. For example, here is a quote from Jacques Derrida:
"A determination or an effect within a system which is no longer that of a presence but of a différance, a system that no longer tolerates the opposition of activity and passivity, nor that of cause and effect, or of indetermination and determination, etc., such that in designating consciousness as an effect or a determination, one continues - for strategic reasons that can be more or less lucidly deliberated and systematically calculated - to operate according to the lexicon of that which one is de-limiting."
Who can honestly say that they can clearly understand such sentences? And if this statement is meaningful, who would say that this is the best presentation of its claim?
Advocates of continental philosophy have generally responded to their critics by saying that the continental style expresses ideas that are beyond the realm of analysis, and that their textual criticism leads us to radically discount the value of any single way (e.g., the analytic approach) of looking at the world.
At this meeting, I will argue that:
1) Logic and analysis clarifies meaning, and solves real problems. It serves as the philosophical analogue of scientific control. To claim that a treatise only has meaning when we don't treat it analytically is like saying that a corporation is only profitable when we don't check its bookkeeping, or that space aliens visit us only when the cameras stop rolling.
2) Logic is general and universal. If analytic epistemology is universal, then public claims about humanity become scientific matters, i.e., they become psychology, anthropology, etc. Concepts and language can be mapped, and cultural differences can be bridged and translated. Attempts to waffle one's way through human affairs (politics, history, feminism, human nature, etc.) with philosophy is just bad science.
I'll argue that philosophy is supposed to make sense, and we ought to have high standards of clarity and intelligibility. If we ignore analytic methods, we're bound to fall into a sort of anti-intellectual philosophical cargo cult that worships words at the expense of their meanings.
Rudolf Carnap's paper The Elimination of Metaphysics Through Logical Analysis of Language hits the spot.
Alternatively, Wikipedia has articles on analytic philosophy, continental philosophy, and Jacques Derrida.
*The image is from the Uncyclopedia article on Analytic Tradition