Analytic philosophy is a broad school of thought or style in contemporary Western philosophy, especially anglophone philosophy, with an emphasis on analysis, clear prose, rigorous arguments, formal logic, mathematics, and the natural sciences (with less emphasis on the humanities). It is further characterized by the linguistic turn, or a concern with language and meaning. Analytic philosophy is often contrasted with continental philosophy, a catch-all term for other methods prominent in continental Europe, most notably existentialism, phenomenology, and Hegelianism. The distinction has also been drawn between "analytic" being academic or technical philosophy and "continental" being literary philosophy. The proliferation of analytic philosophy began around the turn of the twentieth century and has been dominant since the second half of the century. Central figures in its history include Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures include Franz Brentano, the logical positivists (especially Rudolf Carnap), and the ordinary language philosophers. Wilfrid Sellars, W. V. O. Quine, Saul Kripke, David Lewis, and others, led a decline of logical positivism and a subsequent revival in metaphysics. Analytic philosophy has also developed several new branches of philosophy and logic, notably philosophy of language, mathematics, and science, and modern predicate and mathematical logic.
History
The history of analytic philosophy (taken in the narrower sense of "20th-/21st-century analytic philosophy") is usually thought to begin with the rejection of British idealism, a neo-Hegelian movement. But important precursors include the work of Gottlob Frege in formal logic and the philosophy of language, as well as the Austrian tradition associated with Bernard Bolzano, Franz Brentano, Alexius Meinong, and the early Edmund Husserl.
Austrian philosophy as a precursor Analytic philosophy was significantly influenced by Austrian realism in the former state of Austria-Hungary, so much so that Michael Dummett has remarked it is better characterized as Anglo-Austrian rather than the usual Anglo-American.
Brentano
In Psychology from an Empirical Standpoint (1874), University of Vienna philosopher and psychologist Franz Brentano gave to philosophy the problem of intentionality, or aboutness. For Brentano, all mental events or acts of consciousness had a real, non-mental intentional object, which the thinking is directed at or "about". Intentionality is "the mark of the mental." Intentionality is to be distinguished from intention or intension.
Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing), or immanent objectivity. Every mental phenomenon includes something as object within itself, although they do not all do so in the same way. In presentation something is presented, in judgement something is affirmed or denied, in love loved, in hate hated, in desire desired and so on. This intentional in-existence is characteristic exclusively of mental phenomena. No physical phenomenon exhibits anything like it. We could, therefore, define mental phenomena by saying that they are those phenomena which contain an object intentionally within themselves.The School of Brentano included Edmund Husserl and Alexius Meinong. Meinong founded the Graz School, and is known for his unique ontology of real, nonexistent objects; a solution to the problem of empty names. This view is known as Meinongianism, or pejoratively as Meinong's jungle. According to Meinong, objects like flying pigs or golden mountains are real and have being, even though they do not exist. The Polish Lwów–Warsaw school, founded by Kazimierz Twardowski, was also influenced by Brentano. Twardowski emphasized "small philosophy", or the detailed, systematic analysis of specific problems. Twardowski was further influenced by the Bohemian logical realist Bernard Bolzano.
Frege
Gottlob Frege was a German geometry professor at the University of Jena, logician, and philosopher who is understood as the father of analytic philosophy. He advocated logicism, the project of reducing arithmetic to pure logic, supporting Leibniz and opposing Kant in the philosophy of mathematics.
Logic Frege developed modern, mathematical and predicate logic with quantifiers in his book Begriffsschrift (English: Concept-script, 1879). Frege unified the two strains of ancient logic: Aristotelian and Stoic; allowing for a much greater range of sentences to be parsed into logical form. An example of this is the problem of multiple generality.
Number Neo-Kantianism dominated the late nineteenth century in German philosophy. Husserl's book Philosophie der Arithmetik (1891) argued the concept of a cardinal number derived from mental acts of grouping objects and counting them. In contrast to this "psychologism", Frege, in The Foundations of Arithmetic (1884) and The Basic Laws of Arithmetic (German: Grundgesetze der Arithmetik, 1893–1903), argued that mathematics and logic have their own public objects, independent of one's private judgments or mental states. Following Frege, the logicists tended to advocate a kind of mathematical Platonism. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor. Italian mathematician Giuseppe Peano simplified Dedekind's work to systematize mathematics with Peano arithmetic. Frege extended this work in an attempt to reduce arithmetic to logic, developing naive set theory and a set-theoretic definition of natural numbers.
Language Frege also proved influential in the philosophy of language. Dummett traces the linguistic turn to Frege's Foundations of Arithmetic and his context principle. Frege writes "never ... ask for the meaning of a word in isolation, but only in the context of a proposition." As Dummett explains, in order to answer a Kantian question, "How are numbers given to us, granted that we have no idea or intuition of them?", Frege finds the solution in defining "the sense of a proposition in which a number word occurs." Thus a problem, traditionally solved along idealist lines, is instead solved along linguistic ones.
Sense and reference
Frege's paper "On Sense and Reference" (1892) is seminal, containing Frege's puzzles about identity and advancing a mediated reference theory. Frege points out the reference of "the Morning Star" and "the Evening Star" is the same: both refer to the planet Venus. Therefore, substituting one term for the other doesn't change the truth value (salva veritate). However, they differ in what Frege calls cognitive value or the mode of presentation. One has to distinguish between two notions of meaning: the reference of a term and the sense of a term. As Frege points out, "the Morning Star is the Morning Star" is uninformative, but "the Morning Star is the Evening Star" is informative; thus, the two expressions must differ in a way other than reference. A related puzzle is also known as Frege's puzzle, concerning intensional contexts and propositional attitude reports. Consider the statement "The ancients believed the morning star is the evening star." This statement might be false. However, the statement "The ancients believed the morning star is the morning star" is obviously true. Here again, the morning star and the evening star have different meanings, despite having the same reference. In Frege's paper "On Concept and Object" (1892) he distinguishes between a concept which is the reference of a predicate, and an object which is the reference of a proper name.
Thought
The paper "The Thought: A Logical Inquiry" (1918) reflects Frege's anti-idealism. He argues for a Platonist account of propositions or thoughts. Frege claims propositions are intangible, like ideas; yet publicly available, like an object. In addition to the physical, public "first realm" of objects and the private, mental "second realm" of ideas, Frege posits a "third realm" of Platonic propositions, such as the Pythagorean theorem.
Revolt against British idealism British philosophy in the nineteenth century saw a revival of logic started by Richard Whately, in reaction to the anti-logical aspects of British empiricism. The major figure of this period is mathematician George Boole. Other figures include Scottish metaphysician William Hamilton, mathematician and laws namesake Augustus De Morgan, economist William Stanley Jevons, diagram namesake John Venn, Alice's Adventures in Wonderland author Lewis Carroll, Scottish mathematician Hugh MacColl, and American pragmatist Charles Sanders Peirce. However, British philosophy in the late nineteenth century was dominated by British idealism, a neo-Hegelian movement, as taught by philosophers such as F. H. Bradley and T. H. Green. Bradley's work Appearance and Reality (1893) exemplified the school.
Analytic philosophy in the narrower sense of twentieth-century anglophone philosophy is usually thought to begin with Cambridge philosophers Bertrand Russell and G. E. Moore's rejection of Hegelianism for being obscure; or the "revolt against idealism." Russell summed up Moore's common sense influence:
"G. E. Moore...took the lead in rebellion, and I followed, with a sense of emancipation. Bradley had argued that everything common sense believes in is mere appearance; we reverted to the opposite extreme, and that everything is real that common sense, uninfluenced by philosophy or theology, supposes real. With a sense of escaping from prison, we allowed ourselves to think that grass is green, that the sun and stars would exist if no one was aware of them, and also that there is a pluralistic timeless world of Platonic ideas." Russell and Moore contributed to the philosophy of perception with a naïve realism and sense-data theory. In America, George Santayana and the New Realists opposed idealism and its egocentric predicament.
Logical atomism An important aspect of Hegelianism and British idealism was logical holism—the belief that aspects of the world can be known only by knowing the whole world. This is closely related to the doctrine of internal relations, the belief that relations between items are internal relations, or essential properties the items have by nature. Russell and Moore in response promulgated logical atomism and the doctrine of external relations—the belief that the world consists of independent facts.
Russell
In 1901, Russell famously discovered the paradox in Basic Law V (also known as unrestricted comprehension), which undermined Frege's set theory. However, Russell was still a logicist, and in The Principles of Mathematics (1903), he also argued for Meinongianism.
Theory of descriptions During his early career, Russell adopted Frege's predicate logic as his primary philosophical method, thinking it could expose the underlying structure of philosophical problems. This was done most famously in his theory of definite descriptions in "On Denoting", published in Mind in 1905. The essay has been called a "paradigm of philosophy." In this essay, Russell responds to both Meinong and Frege. Russell uses his analysis of descriptions to solve ascriptions of nonexistence, such as with "the present King of France". He argues all proper names (aside from demonstratives like this or that) are disguised definite descriptions; for example, "Walter Scott" can be replaced with "the author of Waverley". This position came to be called descriptivism.
Russell presents his own version of Frege's second puzzle. "If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of Waverley; and in fact Scott was the author of Waverley. Hence we may substitute “Scott” for “the author of Waverley” and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.” The essay also illustrates the concept of scope ambiguity by showing how denying "The present King of France is bald" can mean either "There is no King of France" or "The present King of France is not bald". Russell quips "Hegelians, who love a synthesis, will probably conclude that he wears a wig." For Russell, there was knowledge by description and, from sense-data theory, knowledge by acquaintance.
Principia Mathematica Russell's book written with Alfred North Whitehead, Principia Mathematica (1910–1913), was the seminal text of classical logic and of the logicist project, and encouraged many philosophers to renew their interest in symbolic logic. It used a notation from Peano, and a theory of types to avoid the pitfalls of Russell's paradox. Whitehead developed process metaphysics in Process and Reality (1929).
Ideal language Russell claimed the problems of philosophy can be solved by showing the simple constituents of complex notions. Logical form would be made clear by syntax. For example, the English word is has three distinct meanings, which predicate logic can express as follows:
For the sentence 'the cat is asleep', the is of predication means that "x is P" (denoted as P(x)). For the sentence 'there is a cat', the is of existence means that "there is an x" (∃x). For the sentence 'three is half of six', the is of identity means that "x is the same as y" (x=y). From about 1910 to 1930, analytic philosophers emphasized creating an ideal language for philosophical analysis, which would be free from the ambiguities of ordinary language that, in their opinion, often led philosophers astray.
Early Wittgenstein
Russell's student Ludwig Wittgenstein developed a comprehensive system of logical atomism, with a picture theory of meaning, in his Tractatus Logico-Philosophicus (German: Logisch-Philosophische Abhandlung, 1921), sometimes known as simply the Tractatus. Wittgenstein thought he had solved all the problems of philosophy with the Tractatus. The book starts, "The world is all that is the case." Wittgenstein claims the universe is the totality of actual states of affairs and that these states of affairs can be expressed and mirrored by the language of first-order predicate logic. Thus, a picture of the universe can be constructed by expressing facts in the form of atomic propositions and linking them using logical operators. The Tractatus introduced philosophers to the terms tautology, truth conditions, and to the truth table method. Wittgenstein believed tautologies or logical truths say nothing, but show the logical structure of the world, and has been labeled a mystic who believed in the ineffable by some readers. The Tractatus further ultimately concludes that all of its propositions are meaningless, illustrated with a ladder one must toss away after climbing up it. The book ends, "Whereof one cannot speak, thereof one must be silent."
Logical positivism
During the late 1920s to 1940s, two groups of philosophers known as the Vienna Circle and the Berlin Circle developed Russell and Wittgenstein's philosophy into a doctrine known as "logical positivism" (or "logical empiricism"). The Vienna Circle (previously the Ernst Mach Society) was led by Moritz Schlick and included Rudolf Carnap and Otto Neurath. The Berlin Circle was led by Hans Reichenbach and included Carl Hempel and mathematician David Hilbert. There was also the Dutch signific circle, which included L. E. J. Brouwer, founder of intuitionistic logic. Logical positivists used formal logical methods to develop an empiricist account of knowledge. They adopted the verification principle, according to which every meaningful statement is either analytic or synthetic. The truths of logic and mathematics were tautologies, and those of science were verifiable empirical claims. These two constituted the entire universe of meaningful judgments; anything else was nonsense. Thus the principle rejected statements of metaphysics, theology, ethics, and aesthetics as cognitively meaningless. The logical positivists saw their verificationism as a recapitulation of a quote by David Hume, the closing lines from An Enquiry Concerning Human Understanding (1748):
If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion. This led the logical positivists to reject many traditional problems of philosophy. They typically considered philosophy to have a minimal function, concerning the clarification of thoughts, rather than having a distinct subject matter of its own. Epistemology was still discussed. Schlick was a foundationalist, believing knowledge was like a pyramid, built on prior layers of knowledge except for the first layer. Neurath was an anti-foundationalist, coherentist who famously gave the analogy of reconstructing a ship while on the open sea. Friedrich Waismann introduced the concept of open texture to describe the universal possibility of vagueness in empirical statements. Waismann never finished a book titled Logik, Sprache, Philosophie intended to present the ideas of logical positivism to a wider audience. Carnap and Reichenbach started the journal Erkenntnis. Carnap advocated solving problems by "semantic ascent", talking about language instead of its objects. Carnap also distinguished between trivial internal questions and meaningless external questions. He is best known for works like Der logische Aufbau der Welt (translated as The Logical Structure of the World, 1967) and The Elimination of Metaphysics Through Logical Analysis of Language (1959). Several logical positivists were Jewish, such as Neurath, Waismann, Hans Hahn, and Reichenbach. Others, like Carnap, were gentiles but socialists or pacifists. With the coming to power of Adolf Hitler and Nazism in 1933, many members of the Vienna and Berlin Circles fled to Britain and the United States, which helped to reinforce the dominance of logical positivism and analytic philosophy in anglophone countries. In 1936, Schlick was murdered in Vienna by his former student, Hans Nelböck. The same year, A. J. Ayer's work Language, Truth and Logic introduced the English speaking world to logical positivism.
Ordinary language After World War II, analytic philosophy became interested in ordinary language philosophy, in contrast to ideal language philosophy. Rather than rely on logical constructions, philosophers emphasized the use of natural language. There were two strains of ordinary language philosophy: the later Wittgenstein and Oxford philosophies.
Later Wittgenstein Wittgenstein's later philosophy, from the posthumous Philosophical Investigations (1953), differed dramatically from his early work of the Tractatus. Philosophers refer to them like two different philosophers: "early Wittgenstein" and "later Wittgenstein". One notion found in both early and later Wittgenstein is that "Philosophy is a battle against the bewitchment of our intelligence by means of language." Philosophers had been misusing language and asking meaningless questions, and it was Wittgenstein's job "to show the fly the way out of the fly bottle."
Ramsey The criticisms of Frank Ramsey on the "color-exclusion problem" led to some of Wittgenstein's first doubts with regard to his early philosophy. Wittgenstein in the Tractatus thought the only necessity is logical necessity; yet that no point in space can have two different colors at the same time seems a necessary truth but not a logical one. Wittgenstein responded to Ramsey in "Some Remarks on Logical Form" (1929), the only academic paper he ever published. Ramsey died of jaundice the next year at the age of 26.
Sraffa's gesture Norman Malcolm also famously credits Piero Sraffa for providing Wittgenstein with the conceptual break from his earlier philosophy, by means of a rude gesture:Wittgenstein was insisting that a proposition and what it describes must have the same 'logical form', the same 'logical multiplicity'. Sraffa made a gesture, familiar to Neapolitans as meaning something like disgust or contempt, of brushing the underneath of his chin with an outward sweep of the fingertips of one hand. And he asked: 'What is the logical form of that?' Prior to the publication of the Philosophical Investigations, philosophers like John Wisdom and Rush Rhees were some of the few sources of information about Wittgenstein's later philosophy. Wisdom's 1936 essay "Philosophical Perplexity" was described by J. O. Urmson as the first article "which throughout embodied the new philosophical outlook, it is something of a landmark in the history of philosophy." Another work of Wisdom's was Other Minds (1952) which discusses the problem of other minds. The later Wittgenstein develops a therapeutic approach. He introduces the concept of a "language-game" as a "form of life". By "language-game", he meant a language simpler than an entire language. Wittgenstein argued that a word or sentence has meaning only as a result of the "rule" of the "game" being played. Depending on the context, for example, the utterance "Water!" could be an order, the answer to a question, or some other form of communication. Rather than his prior picture theory of meaning, the later Wittgenstein advocates a theory of meaning as use, according to which words are defined by how they are used within the language-game.
The notion of family resemblance thinks things thought to be connected by one essential, common feature may in fact be connected by a series of overlapping similarities, where no one feature is common to all of them. Games, which Wittgenstein used as an example to explain the notion, have become the classic example of a group that is related by family resemblance. Philosophical Investigations also contains the private language argument. Another point Wittgenstein makes against the possibility of a private language involves the beetle-in-a-box thought experiment. He asks the reader to imagine that each person has a box, inside which is something that everyone intends to refer to with the word beetle. Further, suppose that no one can look inside another's box. Under such a situation, Wittgenstein says the word beetle is meaningless. He also famously uses the duck-rabbit, an ambiguous image, as a means of describing two different ways of seeing: "seeing that" versus "seeing as".
Oxford philosophy The other trend of ordinary language philosophy was known as "Oxford philosophy", in contrast to the earlier analytic Cambridge philosophers. Influenced by Moore's common sense and the later Wittgenstein's quietism, the Oxford philosophers claimed ordinary language already represented many subtle distinctions not recognized in traditional philosophy. The most prominent Oxford philosophers were Gilbert Ryle, Peter Strawson, and John L. Austin.
Ryle Ryle, in The Concept of Mind (1949), criticized Cartesian dualism, arguing in favor of disposing of "Descartes' myth" of the ghost in the machine by recognizing "category errors". Ryle sees Descartes' error as similar to saying one sees the campus, buildings, faculty, students, and so on, but still goes on to ask "Where is the university?"
Strawson Strawson first became well known with his article "On Referring" (1950), a criticism of Russell's theory of descriptions. On Strawson's account, the use of a description presupposes the existence of the object fitting the description. In his book Individuals (1959), Strawson examines our conceptions of basic particulars.
Austin Austin, in the posthumously published How to Do Things with Words (1962), articulated the theory of speech acts and emphasized the ability of words to do things (e.g. "I promise") and not just say things. This influenced several fields to undertake what is called a performative turn. In Sense and Sensibilia (1962), Austin criticized sense-data theories.
Spread to other countries
Australia and New Zealand Samuel Alexander's realism influenced Australian philosophy. The school known as Australian realism began when John Anderson accepted the Challis Chair of Philosophy at the University of Sydney in 1927. American philosopher David Lewis later became closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years. In New Zealand, South African J. N. Findlay, a student of Austrian realist Ernst Mally, taught at the University of Otago. Karl Popper lectured at the Canterbury University College in Christchurch.
Sweden and Finland In Sweden, Axel Hägerström broke away from Christopher Jacob Boström's idealism, founding the Uppsala School of Philosophy. The Finnish philosopher Eino Kaila is considered to have founded Finnish analytic philosophy. Kaila's student Georg Henrik von Wright succeeded Wittgenstein at Cambridge in 1948.
China Chinese philosopher Zhang Shenfu first introduced Russell's ideas to China, and later translated the Tractatus. In 1920, Russell visited China at the invitation of Liang Qichao. This begins the first phase of analytic philosophy in China. Tscha Hung then introduced logical positivism to China with The Philosophy of the Vienna Circle (1945). During the second phase, scholars such as Jin Yuelin and Hong Qian spread analytic philosophy, until Communist political pressure sidelined research. After the reform and opening up of the 1970s, analytic philosophy in China is now in its third phase, and is an active and growing area of study.
Metaphysics During the second half of the twentieth century, analytic philosophy saw the demise of logical positivism and a revival of metaphysical theorizing.
Sellars Kant scholar Wilfrid Sellars, the son of Roy Wood Sellars, "revolutionized both the content and the method of philosophy in the United States". Sellars's criticism of the "Myth of the Given", in Empiricism and the Philosophy of Mind (1956), challenged logical positivism by arguing against sense-data theories and knowledge by acquaintance. In his "Philosophy and the Scientific Image of Man" (1962), Sellars's critical realism distinguishes between the "manifest image" and the "scientific image" of the world. Sellars's goal of a synoptic philosophy uniting the everyday and scientific views of reality is the basis of what is sometimes called the Pittsburgh School, whose members include Robert Brandom, John McDowell, and John Haugeland.
Quine
Harvard philosopher W. V. O. Quine shaped much of subsequent philosophy and is recognized as "one of the most influential philosophers of the twentieth century". He is regularly cited as the greatest philosopher of the second half of the twentieth century, or the next great philosopher after Wittgenstein. Quine was a student of Carnap. He was an empiricist who sought to naturalize philosophy and saw philosophy as continuous with science, distinguished only by philosophy being the most general science. However, Quine doubted usual theories of meaning, and, instead of logical positivism, advocated a kind of semantic holism and ontological relativity, which explained that every term in any statement has its meaning contingent on a vast network of knowledge and belief, the speaker's conception of the entire world.
Word and Object In his magnum opus Word and Object (1960), Quine introduces the idea of radical translation, an introduction to his theory of the indeterminacy of translation, and specifically to prove the inscrutability of reference. The gavagai thought experiment tells about a linguist, who tries to find out what the expression gavagai means when uttered by a speaker of a yet-unknown native language upon seeing a rabbit. At first glance, it seems that gavagai simply translates with rabbit. Quine points out there is no way to tell that the speaker did not mean, for instance, "undetached rabbit-part" (such as its ear) as well as several other scenarios.
On What There Is Quine's essay on ontology, "On What There Is" (1948) elucidates Russell's theory of descriptions. Quine uses Pegasus instead of "the present King of France" and dubs the problem of nonexistence Plato's beard. The essay contains Quine's famous dictum of ontological commitment, "To be is to be the value of a variable". One is committed to the entities his theory posits by use of the existential quantifier, like "There are some so-and-sos". Other parts of speech do not commit one to entities and so for Quine are syncategorematic.
Two Dogmas of Empiricism Also among the developments that resulted in the decline of logical positivism and the revival of metaphysics was Quine's attack on the analytic–synthetic distinction in "Two Dogmas of Empiricism" (1951), published in The Philosophical Review, a paper "sometimes regarded as the most important in all of twentieth-century philosophy". The paper made Quine the most dominant philosopher in America before Kripke.
Kripke
Saul Kripke is widely regarded as having revived theories of essence and identity as respectable topics of philosophical discussion. He was influential in arguing that flaws in common theories of descriptions and proper names are indicative of larger misunderstandings of the metaphysics of modality, or of necessity and possibility. Modal logic was developed by pragmatist C. I. Lewis to deal with the paradoxes of material implication. Carnap also contributed to modal logic with works like Meaning and Necessity (1947). Ruth Barcan Marcus introduced the now standard "box" operator for necessity and "diamond" operator for possibility in her treatment of the Barcan formula. Kripke provided a semantics for modal logic; he and Barcan both argued identity is a necessary relation.
Naming and Necessity Especially important was Kripke's book Naming and Necessity (1980). According to one author, Naming and Necessity "played a large role in the implicit, but widespread, rejection of the view—so popular among ordinary language philosophers—that philosophy is nothing more than the analysis of language." Kripke argued proper names are rigid designators, or designate the same thing in all possible worlds, unlike descriptions. For example, an election may have turned out differently, so the description "winner of the 1968 US presidential election" might have designated Hubert Humphrey instead of Richard Nixon. However, the name "Richard Nixon" designates the man Richard Nixon, regardless of the election results. Kant stated in the Critique of Pure Reason (1781) that necessity is the criterion for a priori knowledge. Kripke argued that necessity is a metaphysical notion distinct from the epistemic notion of a priori, and that there are necessary truths that are known a posteriori, such as that water is H2O, or gold is atomic number 79. Kripke and Quine's colleague Hilary Putnam argued for realism about natural kinds. Putnam's Twin Earth thought experiment is used to argue water is a natural kind.
David Lewis
David Lewis defended a number of elaborate metaphysical theories. In works such as On the Plurality of Worlds (1986) and Counterfactuals (1973), Lewis argued for modal realism and counterpart theory – the belief in real, concrete possible worlds, and argued against any "ersatz" conception of possibility. According to Lewis, "actual" is merely an indexical label we give a world when we are in it. Lewis applied Quine's dictum of ontological commitment to the statement "There are other ways things could have been;" committing Lewis (by his lights) to the real existence of other ways things could have been. He also defended what he called Humean supervenience, and a counterfactual theory of causation, another view of Hume's.
Truth Frege questioned standard theories of truth, and sometimes advocated a deflationary, redundancy theory of truth, i. e. that the predicate "is true" does not express anything above and beyond the statement to which it is attributed. Frank Ramsey also advocated a redundancy theory.
Alfred Tarski put forward an influential semantic theory of truth, that truth is a property of sentences. Tarski's semantic methods culminated in model theory, as opposed to proof theory. In Truth-Makers (1984), Kevin Mulligan, Peter Simons, and Barry Smith introduced the truth-maker idea as a contribution to the correspondence theory of truth. A truth-maker is contrasted with a truth-bearer. A truth-bearer's truth is grounded by the truth-maker.
Universals In response to the problem of universals, Australian David Armstrong defended a kind of moderate realism. David Lewis and Anthony Quinton defended nominalism.
Mereology Polish philosopher Stanisław Leśniewski, along with Nelson Goodman, established mereology, the formal study of parts and wholes. Mereology was originally a variant of nominalism arguing one should dispense with set theory, but the now broader subject of parts and wholes arguably goes back to the time of the pre-Socratics. David Lewis introduced the term 'atomless gunk' for something not made up of simples, which instead divides forever into smaller and smaller parts. Peter Van Inwagen believes in mereological nihilism, except for living beings, a view called organicism. According to mereological nihilism, there are no (say) chairs, just fundamental particles arranged chair-wise.
Personal identity Since John Locke's An Essay Concerning Human Understanding (1690), philosophers have been concerned with the problem of personal identity. Locke thought psychological continuity or memory made one the same person over time. Bernard Williams in The Self and the Future (1970) takes the opposite view, and argues that personal identity is bodily identity rather than mental continuity. Derek Parfit in Reasons and Persons (1984) defends a kind of bundle theory of personal identity. Parfit issues several thought experiments including teleportation, and cases of fission, where one person splits into two, say surviving with half of their brain, while the other half is put into a new body. David Lewis defends perdurantism, where people are four-dimensional, so a person at any one time is only a part or slice of the whole person.
Free will and determinism Peter van Inwagen's monograph An Essay on Free Will (1983) played an important role in rehabilitating libertarianism, with respect to free will, in mainstream analytic philosophy. He introduces the consequence argument and the term incompatibilism about free will and determinism, to stand in contrast to compatibilism—the view that free will is compatible with determinism. Charlie Broad had previously made similar arguments.
Principle of sufficient reason Since Leibniz philosophers have discussed the principle of sufficient reason, or PSR. Van Inwagen criticizes the PSR, while Alexander Pruss defends it.
Philosophy of time Analytic philosophy of time traces its roots to British idealist John McTaggart's article "The Unreality of Time" (1908). McTaggart distinguishes between the dynamic or tensed A-theory of time (past, present, future), in which time flows; and the static or tenseless B-theory of time (earlier than, simultaneous with, later than). Arthur Prior, who invented tense logic, advocated the A-theory of time. Along with David Lewis's perdurantism, the theory of special relativity seems to advocate a B-theory of time. Eternalism holds that past, present, and future are equally real. In contrast, presentism holds that only entities in the present exist. The moving spotlight theory is a kind of hybrid view where all moments exist, but only one moment is present. Growing block, advocated by Charlie Broad, holds that only the past and present exist, but the future does not (yet) exist (there is also the reverse, a shrinking block).
Logical pluralism Many-valued and non-classical logics have been popular since the Polish logician Jan Łukasiewicz. Graham Priest is a dialetheist, denying the law of non-contradiction, seeing it as the most natural solution to problems such as the liar paradox. JC Beall, together with Greg Restall, is a pioneer of a widely discussed version of logical pluralism, the view that there is more than one correct logic.
Epistemology
Owing largely to Edmund Gettier's paper "Is Justified True Belief Knowledge?" (1963) and the so-called Gettier problem, epistemology has since enjoyed a resurgence as a topic of analytic philosophy. Using epistemic luck, Gettier provided counterexamples to the "justified true belief" (JTB) definition of knowledge, found as early as Plato's dialogue Theaetetus. Philosophers give alternatives to the JTB account or develop theories of justification to deal with Gettier's examples. For example, Timothy Williamson argues in Knowledge and Its Limits (2000) that knowledge is sui generis and indefinable.
Theories of justification American philosopher Roderick Chisholm defended foundationalism. Michael Huemer defends a type of foundationalism called phenomenal conservatism. Quine defended coherentism, a "web of belief", and thought all beliefs are open to revision; some are just held stronger than others, and so hold come what may. Ernest Sosa proposed virtue epistemology in "The Raft and the Pyramid" (1980). Alvin Goldman developed a causal theory of knowledge. The debate between internalism and externalism still exists in analytic philosophy. Huemer is an internalist. Goldman is an externalist known for developing a popular form of externalism called reliabilism. Most externalists reject the KK thesis, which has been disputed since the introduction of epistemic logic by Jaakko Hintikka in 1962. Fallibilists also often reject the KK thesis.
Problem of the criterion Discussed since antiquity, Chisholm, in his Theory of Knowledge (1966), details the problem of the criterion with two sets of questions:
What do we know? or What is the extent of our knowledge? How do we know? or What is the criterion for deciding whether we have knowledge in any particular case? Answering the former question first is called particularism, whereas answering the latter first is called methodism. A third solution is skepticism, or doubting there is such a thing as knowledge.
Closure Epistemic closure is the claim that knowledge is closed under entailment; in other words, epistemic closure is a property or the principle that if a subject S {\displaystyle S} knows p {\displaystyle p} , and S {\displaystyle S} knows that p {\displaystyle p} entails q {\displaystyle q} , then S {\displaystyle S} can thereby come to know q {\displaystyle q} . Most epistemological theories involve a closure principle, as do many skeptical arguments (e. g. the dream argument). In Proof of An External World (1939), G. E. Moore uses closure in his famous anti-skeptical "here is one hand" argument. Shortly before his death, Wittgenstein wrote the posthumously published On Certainty (1969) in response to Moore. While the closure principle is generally regarded as intuitive, philosophers, such as Fred Dretske with relevant alternatives theory and Robert Nozick's truth tracking theory of knowledge in Philosophical Explanations (1981), have argued against it. Others argue it is true but only given a specific contex