Philosophy is the philosophical tradition
which is dominant in the philosophy
departments of universities throughout the English-speaking world today (early 21st Century.)
Though it will theoretically accomodate any point of view, so long as the view is logically consistent and has plausible premises, the Analytic school has mostly produced philosophical theories that are materialist, reductionist and behaviourist in character and which aspire to the status and rigour of mathematics or a hard science.
Indeed, one way of characterising Analytic Philosophy would be as the philosophy taking the view that mathematical standards of truth and inference can and should be applied to natural language.
Analytic philosophers who are feeling particularly insecure about the validity of their discipline will tend to clutter up their papers with lots of logical notation, and quite often even their ordinary sentences will sound like they have been translated back into English from formulae in some exotic calculus.
At its best, it can expose outrageous and unsuspected incongruities and inconsistencies in one's assumptions, it can make the previously incomprehensible seem humdrum, or the humdrum inconceivable. At its worst it can be bombastic, sterile, vacuous and trite.
The term is most used to distinguish the modern Anglo-American trend from so-called Continental1 Philosophy, the tradition of European thinkers such as Kierkegaard, Nietzsche, Sartre, Heidegger and so on. Perhaps the leading contemporary critic of the Analytic school from the Continental tradition is the French philosopher Jacques Derrida who has lately adopted the term phallogocentrism to describe it.
If pressed, I'd say the roots of the Analytic approach are to be found in the works of John Locke and especially David Hume but that it reached its contemporary form as a way of doing philosophy roughly with Bertrand Russell's theory of definite descriptions2, which was strongly influenced by Gottlob Frege's conception of language. Possibly its most noticable practitioner was Ludwig Wittgenstein, whose early ideas were extremely influential for logical positivism and atomic and correspondence theories of truth, and who then, changing his mind, was just as influential for the so-called linguistic turn - the switch of focus towards the examination of the mechanics and minutiae of language.3
The Analytic school has indeed been preoccupied with language and linguistic analysis, especially since the middle of the last century, leading another noted thinker to describe it as 'the description of its own destruction at the hands of linguistic science.'
Since, try as they might, academics cannot sever themselves utterly from the world, criticisms from 'outside' Analytic philosophy are now being given serious consideration by thinkers from within and around the Analytic tradition, some of whom would prefer to see themselves as post-Analytic. The most visible is Richard Rorty who has essayed a pragmatic critique.4
On the Analytic view, the way towards such a post-Analytic perspective is not clear. One would need a supervenient clarity, giving analysis its place in a wider schema. But the very word 'schema' might be thought to imply 'subject to analysis.'
1. One is reminded by the choice of this word of the legendary English newspaper headline: Fog in Channel: Continent Isolated.
2. See Gritchka's writeup on the largest number that can be described in 14 words or less for a nice application of this.
3. Though influential in these matters, it's a fair bet that Wittgenstein would have repudiated both groups of followers.
4. Please click on the hardlink for jderrida's interesting writeup on the critique!