Analytic philosophy
Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century.  In the United States the overwhelming majority of university philosophy departments self-identify as "analytic" departments.  (This situation is mirrored in the United Kingdom, Canada, and Australia.)
Given this scope, it is difficult to identify non-trivial philosophical claims that would be common to all analytic philosophy.  The term "analytic philosophy" may mark merely a family resemblance across disparate philosophical views, or historical lines of influence.  Insofar as broad generalizations can be made, analytic philosophy is defined by its emphasis on clarity and argument, often achieved via modern formal logic and analysis of language, and a respect for the natural sciences.
The historical roots of analytic philosophy can be summarily characterised thus:
First, the positivist view that there are no specifically philosophical truths and that the object of philosophy is the logical clarification of thoughts.  This contrasts with the traditional foundationalism, deriving from Aristotle, that views philosophy as a special sort of science, the highest one, which investigates the fundamental reasons and principles of everything.  As a result, analytic philosophers have often considered their inquiries as continuous with, or subordinate to, those of the natural sciences.
Second, the view that the logical clarification of thoughts can only be achieved by analysis of the logical form of philosophical propositions.  The logical form of a proposition is a way of representing it (often using the formal grammar and symbolism of a logical system) to display its similarity with all other propositions of the same type.  However, analytic philosophers disagree widely about the correct logical form of ordinary language.
Third, a rejection of sweeping philosophical systems in favour of close attention to detail.  Among some (but by no means all) analytic philosophers, this rejection of "grand theory" has taken the form of a defence of common sense and ordinary language against the pretensions of metaphysicians.

# History
In the early 20th century, the English philosophers Bertrand Russell and G. E. Moore used close conceptual analysis in a concerted critique of the then-dominant forms of Idealism. Their approach was reinforced by the movement of continental philosophers into English-speaking countries in the first half of the century. Analytic philosophy subsequently took various paths, including a rejection of formal analysis in favour of a close examination of natural language, inquiry into the logical underpinnings of languages and renewed interest in the ethical implications of analytic method.

# The prominence of logic
Gottlob Frege and Edmund Husserl were key figures in early twentieth century philosophy of mathematics. Husserl's Philosophy of Arithmetic, inspired by the teachings of Karl Weierstrass, attempted to show that the concept of the cardinal number, derived from psychical acts of grouping objects and counting them, was the foundation of arithmetic.  Husserl's approach was strongly condemned as psychologism in a review by Frege, who was committed to the view that mathematics and logic have their own validity, independent of the judgments or mental states of individual mathematicians and logicians.  Frege's own work, the Begriffsschrift, developed the concepts of a specific form of modern logic by making use of the notions of the sense and reference. Frege further developed his philosophy of logic and mathematics in The Foundations of Arithmetic and The Basic Laws of Arithmetic where he provides an alternative to psychologistic accounts of the concept of number.
Bertrand Russell and Alfred North Whitehead attempted to show that mathematics is reducible to fundamental logical principles.  Their Principia Mathematica (1910-1913) encouraged many philosophers to take a renewed interest in the development of symbolic logic. This contributed in turn to the evolution of logical positivism, which used formal logical tools to underpin an empiricist account of our knowledge of the world. Philosophers such as Rudolf Carnap and Hans Reichenbach, along with other members of the Vienna Circle, held that the truths of logic and mathematics were tautologies, and that tautologies, together with verifiable empirical claims, constituted the entire universe of meaningful judgments; anything else was, strictly speaking nonsense (including, for example, the claims of ethics, aesthetics and theology). Karl Popper's insistence upon the role of falsification in the philosophy of science was a reaction to the logical positivists.

# Formalism and natural languages
Part of analytic approach is the clarification of philosophical problems by examining the language used to express them. Two major threads weave through this tradition: formalism and natural language.
The former seeks to understand language, and hence philosophical problems, by making use of formal logic. That is, in one way or another it seeks to formalize the way in which philosophical statements are made. This perspective has been taken up in a number of formulations, including Symbolic logic, which assumes the primary importance of sense and reference in the construction of meaning, as well as Kurt Godel's Incompleteness Theorem, Bertrand Russell's theory of definite descriptions,  Karl Popper's theory of falsificationism and Alfred Tarski's Semantic theory of truth.
A second thread seeks to understand philosophical ideas by a close and careful examination of the natural language used to express them  usually with some emphasis on the importance of common sense in dealing with difficult concepts.
These two threads intertwine, sometimes implacably opposed to each other, sometimes virtually identical. Famously, Wittgenstein started out in the formalism camp, but ended up in the natural language camp.

# Formalism

## Logical atomism
Analytic philosophy has its origins in Gottlob Freges development of predicate logic. This permitted a much wider range of sentences to be parsed into logical form. Bertrand Russell adopted it as his primary philosophical tool; a tool he thought could expose the underlying structure of philosophical problems.  For example, the English word is can be parsed in three distinct ways:
- in 'the cat is asleep: the is of predication says that 'x is P': P(x)
- in 'there is a cat: the is of existence says that there is an x: (x)
- in 'three is half of six': the is of identity says that x is the same as y: x=y
Russell sought to resolve various philosophical issues by applying such clear and clean distinctions, most famously in the case of the Present King of France.

## The Tractatus
As a young Austrian soldier, Ludwig Wittgenstein expanded and developed Russell's logical atomism into a comprehensive system in a brief book, the Tractatus Logico-Philosophicus. The argument therein suggests that the world is the existence of certain states of affairs and these states of affairs can be expressed in the language of first-order predicate logic. So a picture of the world can be built up by expressing atomic facts in atomic propositions, and linking them using logical operators.
One of the central movements within analytic philosophy is linked closely to the following statement from the Tractatus:
This attitude is one of the reasons for the close relationship between philosophy of language and analytic philosophy. Language, on this view is the principalor perhaps the onlytool of the philosopher. For Wittgenstein, and many other analytic philosophers, philosophy consists in clarifying how language can be used.  The hope is that when language is used clearly, philosophical problems are found to dissolve. This view has come to be known as quietism.
Wittgenstein thought he had set out the 'final solution' to all philosophical problems, and so went off to become a school teacher.  However, he later revisited the inadequacy of logical atomism, and further expanded the philosophy of language by what became his posthumous book Philosophical Investigations.

## Natural language semantics
Davidson. Oxford in 1970s. Strawson, Dummett, McDowell, Evans.

# Natural language

## Reaction against idealism
G. E. Moore, Common Sense philosophy. This philosophy is a rejection of British Post-Hegel Idealism.

## Ordinary language philosophy
Main article: Ordinary language philosophy
Oxford School. Associated with such philosophers as Austin, Ryle, Searle, and, as well, the later teachings of Wittgenstein.
Rather than viewing philosophical problems with respect to logic, ordinary language philosophy sets forth the notion of consideration with respect to the ordinary usage of the linguistic terms germane to such problems. While schools such as logical positivism focus on logical terms, supposed to be universal and separate from contingent factors (such as culture, language, historical conditions), ordinary language philosophy emphasizes the use of language by ordinary people. It may be argued, then, that ordinary language philosophy is of a more sociological grounding, as it essentially focuses on the use of language within social contexts.
Ordinary language philosophy was often used to disperse philosophical problems, by exposing them as results of fundamental misunderstandings regarding the ordinary usage of the pertinent linguistic terms. Indeed, this is apparent in Ryle (who attempted to dispose of "Descartes' myth"), as well as Wittgenstein, among others.

# Logical positivism and logical empiricism
Vienna Circle, Carnap, Verificationism. Analytic-synthetic distinction. Rejection of Metaphysics, Ethics, Aesthetics. "Emotivism."
Immigration of logicians and scientists from Europe in the 1930s. Philosophy of science. Quine, who attempted to dispose of the supposed Two Dogmas of Empiricism, and especially the analytic-synthetic distinction. Behaviorism.
See the separate article on Logical Positivism for further information.

# Philosophy of mind and cognitive science
Paul and Patricia Churchland, Dennett. See philosophy of mind or cognitive science for further information.

# Ethics in analytic philosophy
As a side-effect of the focus on logic and language in the early years of analytic philosophy, the tradition initially had little to say on the subject of ethics. The attitude was widespread among early analytics that these subjects were unsystematic, and merely expressed personal attitudes about which philosophy could have little or nothing to say. Wittgenstein, in the Tractatus, remarks that values cannot be a part of the world, and if they are anything at all they must be beyond or outside the world somehow, and that hence language, which describes the world, can say nothing about them. One interpretation of these remarks found expression in the doctrine of the logical positivists that statements about value  including all ethical and aesthetic judgments  are, like metaphysical claims, literally meaningless and therefore non-cognitive; that is, not able to be either true or false. Social and political philosophy, aesthetics, and various more specialized subjects like philosophy of history thus moved to the fringes of English-language philosophy for some time.
By the 1950s debates had begun to arise over whether  and if so, how  ethical statements really were non-cognitive. Charles Stevenson argued for expressivism, R. M. Hare advocated a view called universal prescriptivism. Phillipa Foot contributed several essays attacking all these positions, and the collapse of logical positivism as a cohesive research programme led to a renewed interest in ethics. Perhaps most influential in this area was Elizabeth Anscombe, whose landmark monograph "Intention" was called by Donald Davidson "the most important treatment of action since Aristotle", and is widely regarded as a masterpiece of moral psychology. A favorite student and close friend of Ludwig Wittgenstein, her 1958 article "Modern Moral Philosophy" introduced the term "consequentialism" into the philosophical lexicon, declared the "is-ought" impasse to be a dead end, and led to a revival in virtue ethics.

# Analytic philosophy of religion
As with the study of ethics, early analytic philosophy avoided the study of philosophy of religion, dismissing the subject as part of metaphysics and meaningless. The collapse of logical positivism renewed interest in philosophy of religion, prompting philosophers such as William Alston, John Mackie, Alvin Plantinga, Robert Merrihew Adams, and Antony Flew to not only introduce new problems, but to re-open classical ones, such as the nature of miracles and the arguments for and against the existence of God.
Plantinga, Mackie and Flew debated the logical validity of the free will defense as a way to solve the problem of evil. Alston, grappling with the consequences of analytic philosophy of language, worked on the nature of religious language. Adams worked on the relationship of faith and morality.
Analytic philosophy of religion has also been preoccupied with Ludwig Wittgenstein and his interpretation of Sren Kierkegaard's philosophy of religion. Using first-hand remarks (which would later be published in Philosophical Investigations, Culture and Value, and other works), philosophers such as Peter Winch and Norman Malcolm developed a fideist interpretation of Wittgenstein. Responding to this interpretation, Kai Nielsen and D.Z. Phillips became two of the most prominent philosophers on Wittgenstein's philosophy of religion.

# Political philosophy
Current analytic political philosophy owes much to John Rawls, who, in a series of papers from the 1950s onward (most notably "Two Concepts of Rules" and "Justice as Fairness") and his 1971 book A Theory of Justice, produced a sophisticated and closely argued defence of a liberal welfare state.  This was followed in short order by Rawls's colleague Robert Nozick's book Anarchy, State, and Utopia, a defence of free-market libertarianism.

## Analytical Marxism
Another interesting development in the area of political philosophy has been the emergence of a school known as Analytical Marxism.  Members of this school seek to apply the techniques of analytic philosophy, along with tools of modern social science such as rational choice theory to the elucidation of the theories of Karl Marx and his successors.  The best known member of this school, is Oxford University philosopher G.A. Cohen, whose 1978 work, Karl Marx's Theory of History: A Defence is generally taken as representing the genesis of this school.  In that book, Cohen attempted to apply the tools of logical and linguistic analysis to the elucidation and defense of Marx's materialist conception of history.  Other prominent Analytical Marxists include the economist John Roemer, the social scientist Jon Elster, and the sociologist Erik Olin Wright. All these people have attempted to build upon Cohen's work by bringing to bear modern social science methods, such as rational choice theory, to supplement Cohen's use of analytic philosophical techniques in the interpretation of Marxian  theory.
Cohen himself would later engage directly with Rawlsian political philosophy in attempt to advance a socialist theory of justice that stands in contrast to both traditional Marxism and the theories advanced by Rawls and Nozick. In particular, he points to Marx's principle of from each according to his ability, to each according to his need.

## Communitarianism
Communitarians such as Alasdair MacIntyre, Charles Taylor, Michael Walzer and Michael Sandel advance a critique of Liberalism that uses analytic techniques to isolate the key assumptions of Liberal individualists, such as Rawls, and then challenges these assumptions. In particular, Communitarians challenge the Liberal assumption that the individual can be viewed as fully autonomous from the community in which he lives and is brought up. Instead, they push for a conception of the individual that emphasizes the role that the community plays in shaping his or her values, thought processes and opinions.