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Analytic philosophy is a broad movement within
Western philosophy Western philosophy refers to the Philosophy, philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre ...
, especially
anglophone The English-speaking world comprises the 88 countries and territories in which English is an official, administrative, or cultural language. In the early 2000s, between one and two billion people spoke English, making it the largest language ...
philosophy, focused on
analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...
as a philosophical method; clarity of
prose Prose is language that follows the natural flow or rhythm of speech, ordinary grammatical structures, or, in writing, typical conventions and formatting. Thus, prose ranges from informal speaking to formal academic writing. Prose differs most n ...
; rigor in arguments; and making use of
formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
, mathematics, and to a lesser degree the
natural sciences Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...
.Mautner, Thomas (editor) (2005) ''The Penguin Dictionary of Philosophy'', entry for "Analytic philosophy", pp. 22–23 It is further characterized by an interest in
language Language is a structured system of communication that consists of grammar and vocabulary. It is the primary means by which humans convey meaning, both in spoken and signed language, signed forms, and may also be conveyed through writing syste ...
,
semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
and meaning, known as the
linguistic turn The linguistic turn was a major development in Western philosophy during the early 20th century, the most important characteristic of which is the focusing of philosophy primarily on the relations between language, language users, and the world. ...
. It has developed several new branches of philosophy and logic, notably
philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...
,
philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...
,
philosophy of science Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, ...
, modern
predicate logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables ove ...
and
mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
. The proliferation of analysis in philosophy began around the turn of the 20th century and has been dominant since the latter half of the 20th century. Central figures in its historical development are
Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philos ...
,
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...
,
G. E. Moore George Edward Moore (4 November 1873 – 24 October 1958) was an English philosopher, who with Bertrand Russell, Ludwig Wittgenstein and earlier Gottlob Frege was among the initiators of analytic philosophy. He and Russell began de-emphasizing ...
, and
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Witt ...
. Other important figures in its history include
Franz Brentano Franz Clemens Honoratus Hermann Josef Brentano (; ; 16 January 1838 – 17 March 1917) was a German philosopher and psychologist. His 1874 '' Psychology from an Empirical Standpoint'', considered his magnum opus, is credited with having reintrod ...
, the
logical positivists Logical positivism, also known as logical empiricism or neo-positivism, was a philosophical movement, in the empiricist tradition, that sought to formulate a scientific philosophy in which philosophical discourse would be, in the perception of ...
(particularly
Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. ...
), the ordinary language philosophers, W. V. O. Quine, and
Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian–British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the ...
. After the decline of logical positivism,
Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American analytic philosophy, analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emer ...
, David Lewis, and others led a revival in
metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
. Analytic philosophy is often contrasted with
continental philosophy Continental philosophy is a group of philosophies prominent in 20th-century continental Europe that derive from a broadly Kantianism, Kantian tradition.Continental philosophers usually identify such conditions with the transcendental subject or ...
, which was coined as a catch-all term for other methods that were prominent in
continental Europe Continental Europe or mainland Europe is the contiguous mainland of Europe, excluding its surrounding islands. It can also be referred to ambiguously as the European continent, – which can conversely mean the whole of Europe – and, by som ...
, most notably
existentialism Existentialism is a family of philosophical views and inquiry that explore the human individual's struggle to lead an authentic life despite the apparent absurdity or incomprehensibility of existence. In examining meaning, purpose, and valu ...
,
phenomenology Phenomenology may refer to: Art * Phenomenology (architecture), based on the experience of building materials and their sensory properties Philosophy * Phenomenology (Peirce), a branch of philosophy according to Charles Sanders Peirce (1839� ...
, and
Hegelianism Georg Wilhelm Friedrich Hegel (27 August 1770 – 14 November 1831) was a 19th-century German idealism, German idealist. His influence extends across a wide range of topics from metaphysical issues in epistemology and ontology, to political phi ...
. There is widespread influence and debate between the analytic and continental traditions; some philosophers see the differences between the two traditions as being based on institutions, relationships, and ideology, rather than anything of significant philosophical substance. The distinction has also been drawn between "analytic" being
academic An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of tertiary education. The name traces back to Plato's school of philosophy, founded approximately 386 BC at Akademia, a sanctuary of Athena, the go ...
or technical philosophy and "continental" being
literary Literature is any collection of written work, but it is also used more narrowly for writings specifically considered to be an art form, especially novels, plays, and poems. It includes both print and digital writing. In recent centuries, ...
philosophy.


Emergence in Germany and Austria

Analytic philosophy was deeply influenced by what is called Austrian realism in the former state of
Austria-Hungary Austria-Hungary, also referred to as the Austro-Hungarian Empire, the Dual Monarchy or the Habsburg Monarchy, was a multi-national constitutional monarchy in Central Europe#Before World War I, Central Europe between 1867 and 1918. A military ...
, so much so that Michael Dummett has remarked that analytic philosophy is better characterized as Anglo-Austrian rather than the usual Anglo-American.
University of Vienna The University of Vienna (, ) is a public university, public research university in Vienna, Austria. Founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365, it is the oldest university in the German-speaking world and among the largest ...
philosopher and psychologist
Franz Brentano Franz Clemens Honoratus Hermann Josef Brentano (; ; 16 January 1838 – 17 March 1917) was a German philosopher and psychologist. His 1874 '' Psychology from an Empirical Standpoint'', considered his magnum opus, is credited with having reintrod ...
—in ''
Psychology from an Empirical Standpoint ''Psychology from an Empirical Standpoint'' () (1874; second edition 1924) is an 1874 book by the Austrian philosopher Franz Brentano, in which the author argues that the goal of psychology should be to establish exact laws. Brentano's best known ...
'' (1874) and through the subsequent influence of the School of Brentano and its members, such as
Edmund Husserl Edmund Gustav Albrecht Husserl (; 8 April 1859 – 27 April 1938) was an Austrian-German philosopher and mathematician who established the school of Phenomenology (philosophy), phenomenology. In his early work, he elaborated critiques of histori ...
and
Alexius Meinong Alexius Meinong von Handschuchsheim (; 17 July 1853 – 27 November 1920) was an Austrian philosopher, a realist known for his unique ontology and theory of objects. He also made contributions to philosophy of mind and theory of value. Lif ...
—gave to analytic philosophy the problem of
intentionality Intentionality is the mental ability to refer to or represent something. Sometimes regarded as the ''mark of the mental'', it is found in mental states like perceptions, beliefs or desires. For example, the perception of a tree has intentionality ...
or of aboutness. For Brentano, all mental events have a real, non-mental intentional object, which the thinking is directed at or "about". Meinong is known for his unique
ontology Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...
of real
nonexistent objects In metaphysics and ontology, nonexistent objects are a concept advanced by Austrian philosopher Alexius Meinong in the 19th and 20th centuries within a " theory of objects". He was interested in intentional states which are directed at nonexiste ...
as a solution to the problem of empty names. The Graz School followed Meinong. The Polish
Lwów–Warsaw school The Lwów–Warsaw School () was an interdisciplinary school of thought, school (mainly philosophy, logic and psychology) founded by Kazimierz Twardowski in 1895 in Lviv, Lwów, Austro-Hungary (now Lviv, Ukraine). Though its members represented a ...
, founded by Kazimierz Twardowski in 1895, grew as an offshoot of the Graz School. It was closely associated with the
Warsaw School of Mathematics Warsaw School of Mathematics is the name given to a group of mathematicians who worked at Warsaw, Poland, in the two decades between the World Wars, especially in the fields of logic, set theory, point-set topology and real analysis. They publish ...
.


Frege

Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philos ...
(1848–1925) was a German
geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
professor at the
University of Jena The University of Jena, officially the Friedrich Schiller University Jena (, abbreviated FSU, shortened form ''Uni Jena''), is a public research university located in Jena, Thuringia, Germany. The university was established in 1558 and is cou ...
who is understood as the father of analytic philosophy. Frege proved influential as a philosopher of mathematics in Germany at the beginning of the 20th century. He advocated
logicism In the philosophy of mathematics, logicism is a programme comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or al ...
, the project of reducing
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
to pure logic.


Logic

As a result of his logicist project, Frege developed
predicate logic First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables ove ...
in his book ''
Begriffsschrift ''Begriffsschrift'' (German for, roughly, "concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept notati ...
'' (English: ''Concept-script'', 1879), which allowed for a much greater range of sentences to be parsed into logical form than was possible using the ancient
Aristotelian logic In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly b ...
. An example of this is the problem of multiple generality.


Number

Neo-Kantianism In late modern philosophy, neo-Kantianism () was a revival of the 18th-century philosophy of Immanuel Kant. The neo-Kantians sought to develop and clarify Kant's theories, particularly his concept of the thing-in-itself and his moral philosophy ...
dominated the late 19th century in German philosophy. Edmund Husserl's 1891 book '' Philosophie der Arithmetik'' argued that the concept of the
cardinal number In mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the cas ...
derived from psychical acts of grouping objects and counting them. In contrast to this "
psychologism Psychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Joh ...
", Frege in '' The Foundations of Arithmetic'' (1884) and ''The Basic Laws of Arithmetic'' (, 1893–1903), argued similarly to
Plato Plato ( ; Greek language, Greek: , ; born  BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...
or
Bolzano Bolzano ( ; ; or ) is the capital city of South Tyrol (officially the province of Bolzano), Northern Italy. With a population of 108,245, Bolzano is also by far the largest city in South Tyrol and the third largest in historical Tyrol. The ...
that mathematics and logic have their own public objects, independent of the private judgments or mental states of individual mathematicians and logicians. Following Frege, the logicists tended to advocate a kind of
mathematical Platonism Mathematical Platonism is the form of realism that suggests that mathematical entities are abstract, have no spatiotemporal or causal properties, and are eternal and unchanging. This is often claimed to be the view most people have of numbers. ...
.


Language

Frege also proved influential in the
philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...
and analytic philosophy's interest in meaning.Jeff Speaks
"Frege's theory of reference"
(2011)
Michael Dummett Sir Michael Anthony Eardley Dummett (; 27 June 1925 – 27 December 2011) was an English academic described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." H ...
traces the
linguistic turn The linguistic turn was a major development in Western philosophy during the early 20th century, the most important characteristic of which is the focusing of philosophy primarily on the relations between language, language users, and the world. ...
to Frege's ''Foundations of Arithmetic'' and his
context principle In the philosophy of language, the context principle is a form of semantic holism holding that a philosopher should "never ... ask for the meaning of a word in isolation, but only in the context of a proposition" (Frege 884/1980x). Analysis The ...
. Frege's paper "
On Sense and Reference In the philosophy of language, the distinction between sense and reference was an idea of the German philosopher and mathematician Gottlob Frege in 1892 (in his paper "On Sense and Reference"; German: "Über Sinn und Bedeutung"), reflecting the ...
" (1892) is seminal, containing Frege's puzzles and providing a mediated reference theory. His paper " The Thought: A Logical Inquiry" (1918) reflects both his anti-idealism or anti-psychologism and his interest in language. In the paper, he argues for a
Platonist Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundam ...
account of
proposition A proposition is a statement that can be either true or false. It is a central concept in the philosophy of language, semantics, logic, and related fields. Propositions are the object s denoted by declarative sentences; for example, "The sky ...
s or thoughts.


Emergence in Great Britain

British philosophy in the 19th century had seen a revival of logic started by Richard Whately, in reaction to the anti-logical tradition of British empiricism. The major figure of this period is English mathematician
George Boole George Boole ( ; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. H ...
. Other figures include William Hamilton,
Augustus De Morgan Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He is best known for De Morgan's laws, relating logical conjunction, disjunction, and negation, and for coining the term "mathematical induction", the ...
,
William Stanley Jevons William Stanley Jevons (; 1 September 1835 – 13 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method i ...
, ''
Alice's Adventures in Wonderland ''Alice's Adventures in Wonderland'' (also known as ''Alice in Wonderland'') is an 1865 English Children's literature, children's novel by Lewis Carroll, a mathematics university don, don at the University of Oxford. It details the story of a ...
'' author
Lewis Carroll Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglicanism, Anglican deacon. His most notable works are ''Alice ...
, Hugh MacColl, and American pragmatist
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...
. However, British philosophy in the late 19th century was dominated by British idealism, a neo-Hegelian movement, as taught by philosophers such as F. H. Bradley (1846–1924) and
T. H. Green Thomas Hill Green (7 April 183626 March 1882), known as T. H. Green, was an English philosopher, political Radicalism (historical), radical and Temperance movement, temperance reformer, and a member of the British idealism movement. Like ...
(1836–1882).


Russell

Analytic philosophy in the narrower sense of 20th and 21st century anglophone philosophy is usually thought to begin with
Cambridge Cambridge ( ) is a List of cities in the United Kingdom, city and non-metropolitan district in the county of Cambridgeshire, England. It is the county town of Cambridgeshire and is located on the River Cam, north of London. As of the 2021 Unit ...
philosophers Bertrand Russell and G. E. Moore's rejection of
Hegelianism Georg Wilhelm Friedrich Hegel (27 August 1770 – 14 November 1831) was a 19th-century German idealism, German idealist. His influence extends across a wide range of topics from metaphysical issues in epistemology and ontology, to political phi ...
for being obscure; or the "revolt against idealism"—see for example Moore's " A Defence of Common Sense". Russell summed up Moore's influence: An important aspect of Hegelianism and British idealism was logical holism—the opinion that there are aspects of the world that can be known only by knowing the whole world. This is closely related to the doctrine of internal relations, the opinion that relations between items are ''internal relations'', that is, essential
properties Property is the ownership of land, resources, improvements or other tangible objects, or intellectual property. Property may also refer to: Philosophy and science * Property (philosophy), in philosophy and logic, an abstraction characterizing an ...
of the nature of those items. Russell and Moore in response promulgated
logical atomism Logical atomism is a philosophical view that originated in the early 20th century with the development of analytic philosophy. It holds that the world consists of ultimate logical "facts" (or "atoms") that cannot be broken down any further, each ...
and the doctrine of ''external relations''—the belief that the world consists of independent facts. Inspired by developments in modern
formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
, the early Russell claimed that the problems of philosophy can be solved by showing the simple constituents of complex notions.
Logical form In logic, the logical form of a statement is a precisely specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unamb ...
would be made clear by
syntax In linguistics, syntax ( ) is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituenc ...
. 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 like Frege, Russell, Moore, and Russell's student
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Witt ...
emphasized creating an ideal language for philosophical analysis, which would be free from the ambiguities of ordinary language that, in their opinion, often made philosophers incorrect.


Paradox

Russell famously discovered the
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictor ...
in Basic Law V which undermined Frege's logicist project. However, like Frege, Russell argued that mathematics is reducible to logical fundamentals, in ''
The Principles of Mathematics ''The Principles of Mathematics'' (''PoM'') is a 1903 book by Bertrand Russell, in which the author presented Russell's paradox, his famous paradox and argued his thesis that mathematics and logic are identical. The book presents a view of ...
'' (1903). He also argued for Meinongianism.


"On Denoting"

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 A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, ...
of
definite description In formal semantics and philosophy of language, a definite description is a denoting phrase in the form of "the X" where X is a noun-phrase or a singular common noun. The definite description is ''proper'' if X applies to a unique individual or ...
s in "
On Denoting "On Denoting" is an essay by Bertrand Russell. It was published in the philosophy journal ''Mind (journal), Mind'' in 1905. In it, Russell introduces and advocates his theory of denoting phrases, according to which definite descriptions and other ...
", published in ''
Mind The mind is that which thinks, feels, perceives, imagines, remembers, and wills. It covers the totality of mental phenomena, including both conscious processes, through which an individual is aware of external and internal circumstances ...
'' in 1905. Russell here argues against Meinongianism. He argues all
name A name is a term used for identification by an external observer. They can identify a class or category of things, or a single thing, either uniquely, or within a given context. The entity identified by a name is called its referent. A person ...
s (aside from demonstratives like ''this'' or ''that'') are disguised definite descriptions, using this to solve ascriptions of nonexistence. This position came to be called descriptivism.


''Principia Mathematica''

Later, his book written with
Alfred North Whitehead Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He created the philosophical school known as process philosophy, which has been applied in a wide variety of disciplines, inclu ...
, ''
Principia Mathematica The ''Principia Mathematica'' (often abbreviated ''PM'') is a three-volume work on the foundations of mathematics written by the mathematician–philosophers Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1 ...
'' (1910–1913), the seminal text of
classical logic Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this c ...
and of the logicist project, encouraged many philosophers to renew their interest in the development of
symbolic logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
. It used a
notation In linguistics and semiotics, a notation system is a system of graphics or symbols, Character_(symbol), characters and abbreviated Expression (language), expressions, used (for example) in Artistic disciplines, artistic and scientific disciplines ...
from Italian logician
Giuseppe Peano Giuseppe Peano (; ; 27 August 1858 – 20 April 1932) was an Italian mathematician and glottologist. The author of over 200 books and papers, he was a founder of mathematical logic and set theory, to which he contributed much Mathematical notati ...
, and it uses a theory of types to avoid the pitfalls of Russell's paradox. Whitehead developed process metaphysics in ''
Process and Reality ''Process and Reality'' is a book by Alfred North Whitehead, in which the author propounds a philosophy of organism, also called process philosophy. The book, published in 1929, is a revision of the Gifford Lectures he gave in 1927–28. Wh ...
''.


Early Wittgenstein

Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. From 1929 to 1947, Witt ...
developed a comprehensive system of logical atomism with a picture theory of meaning in his ''
Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and Citation, cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal ...
'' (, 1921) sometimes known as simply the ''Tractatus''. He claimed 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 operator In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, the ...
s. The ''Tractatus'' introduced philosophers to the
truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arg ...
method. Wittgenstein thought he had solved all the problems of philosophy with the ''Tractatus''. The work further ultimately concludes that all of its propositions are meaningless, illustrated with a ladder one must toss away after climbing up it.


Logical positivism

During the late 1920s to 1940s, a group of philosophers known as the
Vienna Circle The Vienna Circle () of logical empiricism was a group of elite philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, chaired by Moritz Sc ...
, and another one known as the
Berlin Circle The Berlin Circle () was a group that maintained logical empiricist views about philosophy. History The "Berlin Circle" had its roots in seminars by Hans Reichenbach between 1926-1928, resulting in the formation of a group that included Reichenb ...
, developed Russell and Wittgenstein's philosophy into a doctrine known as "
logical positivism Logical positivism, also known as logical empiricism or neo-positivism, was a philosophical movement, in the empiricist tradition, that sought to formulate a scientific philosophy in which philosophical discourse would be, in the perception of ...
" (or logical empiricism). The Vienna Circle was led by
Moritz Schlick Friedrich Albert Moritz Schlick (; ; 14 April 1882 – 22 June 1936) was a German philosopher, physicist, and the founding father of logical positivism and the Vienna Circle. He was murdered by a former student, Johann Nelböck, in 1936. Early ...
and included
Rudolf Carnap Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. ...
and
Otto Neurath Otto Karl Wilhelm Neurath (; ; 10 December 1882 – 22 December 1945) was an Austrian-born philosopher of science, sociologist, and political economist. He was also the inventor of the ISOTYPE method of pictorial statistics and an innovator in ...
. The Berlin Circle was led by
Hans Reichenbach Hans Reichenbach (; ; September 26, 1891 – April 9, 1953) was a leading philosopher of science, educator, and proponent of logical empiricism. He was influential in the areas of science, education, and of logical empiricism. He founded the ''G ...
and included
Carl Hempel Carl Gustav "Peter" Hempel (; ; January 8, 1905 – November 9, 1997) was a German writer, philosopher, logician, and epistemologist. He was a major figure in logical empiricism, a 20th-century movement in the philosophy of science. Hempel ...
and mathematician
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...
. 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. This led the logical positivists to reject many traditional problems of philosophy, especially those of
metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
, as meaningless. It had the additional effect of making (ethical and aesthetic) value judgments (as well as religious statements and beliefs) meaningless. Logical positivists therefore typically considered philosophy as having a minimal function. For them, philosophy concerned the clarification of thoughts, rather than having a distinct subject matter of its own. Several logical positivists were Jewish, such as Neurath, Hans Hahn,
Philipp Frank Philipp Frank (; March 20, 1884 – July 21, 1966) was an Austrian-American physicist, mathematician and philosopher of the early-to-mid 20th century. He was a logical positivism, logical positivist, and a member of the Vienna Circle. He was infl ...
, Friedrich Waissmann, and Reichenbach. Others, like Carnap, were gentiles but socialists or pacifists. With the coming to power of
Adolf Hitler Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician who was the dictator of Nazi Germany from 1933 until Death of Adolf Hitler, his suicide in 1945. Adolf Hitler's rise to power, He rose to power as the lea ...
and
Nazism Nazism (), formally named National Socialism (NS; , ), is the far-right totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During Hitler's rise to power, it was fre ...
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. The logical positivists saw their rejection of metaphysics in some ways as a recapitulation of a quote by
David Hume David Hume (; born David Home; – 25 August 1776) was a Scottish philosopher, historian, economist, and essayist who was best known for his highly influential system of empiricism, philosophical scepticism and metaphysical naturalism. Beg ...
:
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.


Ordinary language

After
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, from the late 1940s to the 1950s, analytic philosophy became involved with ordinary-language analysis. This resulted in two main trends.


Later Wittgenstein

One strain of language analysis continued Wittgenstein's later philosophy, from the ''
Philosophical Investigations ''Philosophical Investigations'' () is a work by the philosopher Ludwig Wittgenstein, published posthumously in 1953. ''Philosophical Investigations'' is divided into two parts, consisting of what Wittgenstein calls, in the preface, ''Bemer ...
'' (1953), which differed dramatically from his early work of the ''Tractatus''. The criticisms of
Frank P. Ramsey Frank Plumpton Ramsey (; 22 February 1903 – 19 January 1930) was a British people, British philosopher, mathematician, and economist who made major contributions to all three fields before his death at the age of 26. He was a close friend of ...
on color and logical form in the ''Tractatus'' led to some of Wittgenstein's first doubts with regard to his early philosophy. Philosophers refer to them like two different philosophers: "early Wittgenstein" and "later Wittgenstein". In his later philosophy, Wittgenstein develops the concept of a " language-game" and, rather than his prior picture theory of meaning, advocates a theory of meaning as use. It also contains the private language argument and the notion of
family resemblance Family resemblance () is a philosophical idea made popular by Ludwig Wittgenstein, with the best known exposition given in his posthumously published book '' Philosophical Investigations'' (1953). It argues that things which could be thought to b ...
.


Oxford philosophy

The other trend was known as "
Oxford Oxford () is a City status in the United Kingdom, cathedral city and non-metropolitan district in Oxfordshire, England, of which it is the county town. The city is home to the University of Oxford, the List of oldest universities in continuou ...
philosophy", in contrast to earlier analytic Cambridge philosophers (including the early Wittgenstein) who thought philosophers should avoid the deceptive trappings of natural language by constructing ideal languages. Influenced by Moore's ''Common Sense'' and what they perceived as the later Wittgenstein's quietism, the Oxford philosophers claimed that ordinary language already represents many subtle distinctions not recognized in the formulation of traditional philosophical theories or problems. While schools such as logical positivism emphasize logical terms, which are 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. The most prominent ordinary-language philosophers during the 1950s were P. F. Strawson, J. L. Austin, and
Gilbert Ryle Gilbert Ryle (19 August 1900 – 6 October 1976) was a British philosopher, principally known for his critique of Cartesian dualism, for which he coined the phrase " ghost in the machine". Some of Ryle's ideas in philosophy of mind have been ca ...
. Ordinary-language philosophers often sought to resolve philosophical problems by showing them to be the result of misunderstanding ordinary language. Ryle, in '' The Concept of Mind'' (1949), criticized Cartesian
dualism Dualism most commonly refers to: * Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another * P ...
, arguing in favor of disposing of " Descartes' myth" via recognizing " category errors". Strawson first became well known with his article "On Referring" (1950), a criticism of Russell's theory of descriptions explained in the latter's famous "On Denoting" article. In his book ''Individuals'' (1959), Strawson examines our conceptions of basic
particular In metaphysics, particulars or individuals are usually contrasted with ''universals''. Universals concern features that can be exemplified by various different particulars. Particulars are often seen as concrete, spatiotemporal entities as opposed ...
s. Austin, in the posthumously published ''
How to Do Things with Words John Langshaw Austin (26 March 1911 – 8 February 1960) was an English philosophy of language, philosopher of language and leading proponent of ordinary language philosophy, best known for developing the theory of speech acts. Austin pointe ...
'' (1962), emphasized the theory of
speech act In the philosophy of language and linguistics, a speech act is something expressed by an individual that not only presents information but performs an action as well. For example, the phrase "I would like the mashed potatoes; could you please pas ...
s and 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 Performativity is the concept that language can function as a form of social action and have the effect of change. The concept has multiple applications in diverse fields such as anthropology, Social geography, social and cultural geography, econo ...
. In '' Sense and Sensibilia'' (1962), Austin criticized sense-data theories.


Spread


Australia and New Zealand

The school known as Australian realism began when John Anderson accepted the Challis Chair of Philosophy at the
University of Sydney The University of Sydney (USYD) is a public university, public research university in Sydney, Australia. Founded in 1850, it is the oldest university in both Australia and Oceania. One of Australia's six sandstone universities, it was one of the ...
in 1927. His elder brother was William Anderson, Professor of Philosophy at Auckland University College from 1921 to his death in 1955, who was described as "the most dominant figure in New Zealand philosophy." J. N. Findlay was a student of
Ernst Mally Ernst Mally (; ; 11 October 1879 – 8 March 1944) was an Austrian analytic philosopher, initially affiliated with Alexius Meinong's Graz School of object theory. Mally was one of the founders of deontic logic and is mainly known for his co ...
of the Austrian realists and taught at the
University of Otago The University of Otago () is a public university, public research university, research collegiate university based in Dunedin, Otago, New Zealand. Founded in 1869, Otago is New Zealand's oldest university and one of the oldest universities in ...
.


Finland

The Finnish Georg Henrik von Wright succeeded Wittgenstein at Cambridge in 1948.


Contemporary developments


Metaphysics

One difference with respect to early analytic philosophy was the revival of metaphysical theorizing during the second half of the 20th century, and metaphysics remains a fertile topic of research. Although many discussions are continuations of old ones from previous decades and centuries, the debates remains active.Van Inwagen, Peter, and Dean Zimmerman (eds.) (1998), ''Metaphysics: The Big Questions.''


Decline of logical positivism

The rise of metaphysics mirrored the decline of logical positivism, first challenged by the later Wittgenstein.


= Sellars

=
Wilfred Sellars Wilfrid Stalker Sellars (; May 20, 1912 – July 2, 1989) was an American philosopher and prominent developer of Critical realism (philosophy of perception), critical realism who "revolutionized both the content and the method of philosophy in t ...
'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. In his "Philosophy and the Scientific Image of Man" (1962), Sellars distinguishes between the "manifest image" and the "scientific image" of the world. Sellars's goal of a
synoptic philosophy Synoptic philosophy comes from the Greek word συνοπτικός ''synoptikos'' ("seeing everything together") and together with the word philosophy, means the love of wisdom emerging from a coherent understanding of everything together.Christian ...
that unites the everyday and scientific views of reality is the foundation and archetype of what is sometimes called the Pittsburgh School, whose members include Robert Brandom,
John McDowell John Henry McDowell (born 7 March 1942) is a South African philosopher, formerly a fellow of University College, Oxford, and now university professor at the University of Pittsburgh. Although he has written on metaphysics, epistemology, anci ...
, and John Haugeland.


= Quine

= Also among the developments that resulted in the decline of logical positivism and the revival of metaphysical theorizing was
Harvard Harvard University is a private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher lear ...
philosopher W. V. O. Quine's attack on the
analytic–synthetic distinction The analytic–synthetic distinction is a semantic distinction used primarily in philosophy to distinguish between propositions (in particular, statements that are affirmative subject– predicate judgments) that are of two types: analytic propos ...
in "
Two Dogmas of Empiricism "Two Dogmas of Empiricism" is a canonical essay by analytic philosopher Willard Van Orman Quine published in 1951. According to University of Sydney professor of philosophy Peter Godfrey-Smith, this "paper ssometimes regarded as the most impor ...
", published in 1951 in ''
The Philosophical Review ''The Philosophical Review'' is a quarterly journal of philosophy edited by the faculty of the Sage School of Philosophy at Cornell University. Since September 2006, it is published by Duke University Press. Overview The journal publishes origin ...
'' and republished in Quine's book ''From A Logical Point of View'' (1953), a paper "sometimes regarded as the most important in all of twentieth-century philosophy". Reprinted in his 1953 ''From a Logical Point of View''. Harvard University Press. ''From a Logical Point of View'' also contains Quine's essay " On What There Is" (1948), which elucidates Russell's theory of descriptions and contains Quine's famous dictum of
ontological commitment Ontology is the philosophical study of being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of reality and every ...
, "To be is to be the value of a variable". He also dubbed the problem of nonexistence
Plato's beard In metaphysics, Plato's beard is a paradoxical argument dubbed by Willard Van Orman Quine in his 1948 paper "On What There Is". The phrase came to be identified as the philosophy of understanding something based on what does not exist. Doctrine ...
. Quine sought to naturalize philosophy and saw philosophy as continuous with science, but instead of logical positivism advocated a kind of semantic holism and
ontological relativity Ontology is the philosophical study of existence, being. It is traditionally understood as the subdiscipline of metaphysics focused on the most general features of reality. As one of the most fundamental concepts, being encompasses all of realit ...
, 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. In his magnum opus ''
Word and Object ''Word and Object'', philosopher Willard Van Orman Quine's most famous work, expands on ideas in ''From a Logical Point of View'' (1953) and reformulates earlier arguments like his attack on the analytic–synthetic distinction from " Two Dogmas ...
'' (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 inscrutability or indeterminacy of reference (also referential inscrutability) is a thesis by 20th century analytic philosophy, analytic philosopher Willard Van Orman Quine in his book ''Word and Object''. The main claim of this theory is t ...
.


= Kripke

= Important also for the revival of metaphysics was the further development of
modal logic Modal logic is a kind of logic used to represent statements about Modality (natural language), necessity and possibility. In philosophy and related fields it is used as a tool for understanding concepts such as knowledge, obligation, and causality ...
, first introduced by pragmatist C. I. Lewis, especially the work of
Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American analytic philosophy, analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emer ...
and his '' 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."Soames, Scott. 2005. ''Philosophical Analysis in the Twentieth Century: Volume 2: The Age of Meaning''.
Princeton University Press Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial ...
. Cited in Byrne, Alex and Hall, Ned. 2004. 'Necessary Truths'. ''Boston Review'' October/November 2004.
Kripke was influential in arguing that flaws in common theories of descriptions and proper names are indicative of larger misunderstandings of the
metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
of necessity and possibility. Kripke also argued that
necessity Necessary or necessity may refer to: Concept of necessity * Need ** An action somebody may feel they must do ** An important task or essential thing to do at a particular time or by a particular moment * Necessary and sufficient condition, in l ...
is a metaphysical notion distinct from the
epistemic Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowledg ...
notion of ''
a priori ('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, Justification (epistemology), justification, or argument by their reliance on experience. knowledge is independent from any ...
'', and that there are necessary truths that are known ''
a posteriori ('from the earlier') and ('from the later') are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on experience. knowledge is independent from any experience. Examples include ...
'', such as that water is H2O. Zimmerman, Dean W., "Prologue" in ''Oxford Studies in Metaphysics, Volume 1'' (Oxford University Press, 2004), p. xix. Kripke is widely regarded as having revived theories of
essence Essence () has various meanings and uses for different thinkers and in different contexts. It is used in philosophy and theology as a designation for the property (philosophy), property or set of properties or attributes that make an entity the ...
and identity as respectable topics of philosophical discussion. Kripke and
Hilary Putnam Hilary Whitehall Putnam (; July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, computer scientist, and figure in analytic philosophy in the second half of the 20th century. He contributed to the studies of philosophy of ...
argued for realism about
natural kind In the philosophy of science and some other branches of philosophy, a "natural kind" is an intellectual grouping, or categorizing of things, that is reflective of the actual world and not just human interests. Some treat it as a classification ide ...
s. Kripke holds that it is essential that water is H2O, or for
gold Gold is a chemical element; it has chemical symbol Au (from Latin ) and atomic number 79. In its pure form, it is a brightness, bright, slightly orange-yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal ...
to be
atomic number The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of pro ...
79. Putnam's Twin Earth thought experiment can be used to illustrate the same point with water.


= David Lewis

= American philosopher David Lewis defended a number of elaborate metaphysical theories. In works such as ''
On the Plurality of Worlds ''On the Plurality of Worlds'' (1986) is a book by the philosopher David Lewis that defends the thesis of modal realism. "The thesis states that the world we are part of is but one of a plurality of worlds," as he writes in the preface, "and ...
'' (1986) and ''Counterfactuals'' (1973) he argued for
modal realism Modal realism is the view propounded by the philosopher David Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It states that possible worlds exist, possible worlds are ...
and counterpart theorythe belief in real, concrete
possible world A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their met ...
s. According to Lewis, "actual" is merely an indexical label we give a world when we are in it. Lewis also defended what he called Humean
supervenience In philosophy, supervenience refers to a relation between sets of properties or sets of facts. X is said to ''supervene'' on Y if and only if some difference in Y is necessary for any difference in X to be possible. Examples of supervenience, i ...
, a counterfactual theory of causation, and contributed to
abstract object In philosophy and the arts, a fundamental distinction exists between abstract and concrete entities. While there is no universally accepted definition, common examples illustrate the difference: numbers, sets, and ideas are typically classif ...
theory. He became closely associated with Australia, whose philosophical community he visited almost annually for more than 30 years.


Universals

In response to the
problem Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business an ...
of universals, Australian
David Malet Armstrong David Malet Armstrong (8 July 1926 – 13 May 2014), often D. M. Armstrong, was an Australian philosopher. He is well known for his work on metaphysics and the philosophy of mind, and for his defence of a factualist ontology, a function ...
defended a kind of
moderate realism Moderate realism (also called immanent realism) is a position in the debate on the metaphysics of universals which holds that there is no realm in which universals exist (in opposition to Platonic realism, which asserts the existence of abstrac ...
. Quine and Lewis defended
nominalism In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are two main versions of nominalism. One denies the existence of universals—that which can be inst ...
.


Mereology

Polish philosopher Stanisław Leśniewski coined the term
mereology Mereology (; from Greek μέρος 'part' (root: μερε-, ''mere-'') and the suffix ''-logy'', 'study, discussion, science') is the philosophical study of part-whole relationships, also called ''parthood relationships''. As a branch of metaphys ...
, which is the formal study of parts and wholes, a subject that arguably goes back to the time of the
pre-Socratics Pre-Socratic philosophy, also known as early Greek philosophy, is ancient Greek philosophy before Socrates. Pre-Socratic philosophers were mostly interested in cosmology, the beginning and the substance of the universe, but the inquiries of the ...
. David Lewis believed in
perdurantism Perdurantism or perdurance theory is a philosophical theory of persistence and identity.Temporal parts
and introduced the term ' gunk'. Peter Van Inwagen believes in mereological nihilism, except for living beings, a view called
organicism Organicism is the philosophical position that states that the universe and its various parts (including human societies) ought to be considered alive and naturally ordered, much like a living organism.Gilbert, S. F., and S. Sarkar. 2000. "Emb ...
.


Free will and determinism

Peter van Inwagen's 1983
monograph A monograph is generally a long-form work on one (usually scholarly) subject, or one aspect of a subject, typically created by a single author or artist (or, sometimes, by two or more authors). Traditionally it is in written form and published a ...
''An Essay on Free Will'' played an important role in rehabilitating
libertarianism Libertarianism (from ; or from ) is a political philosophy that holds freedom, personal sovereignty, and liberty as primary values. Many libertarians believe that the concept of freedom is in accord with the Non-Aggression Principle, according t ...
with respect to
free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...
, in mainstream analytical philosophy. In the book, he introduces the consequence argument and the term
incompatibilism Incompatibilism is the view that the thesis of determinism is logically incompatible with the classical thesis of free will. The term was coined in the 1960s, most likely by philosopher Keith Lehrer. The term ''compatibilism'' was coined (also by ...
about free will and
determinism Determinism is the Metaphysics, metaphysical view that all events within the universe (or multiverse) can occur only in one possible way. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes ov ...
, to stand in contrast to
compatibilism Compatibilism is the belief that free will and determinism are mutually compatible and that it is possible to believe in both without being logically inconsistent. As Steven Weinberg puts it: "I would say that free will is nothing but our consc ...
—the view that free will is compatible with determinism. Charlie Broad had previously made similar arguments.


Personal identity

Since
John Locke John Locke (; 29 August 1632 (Old Style and New Style dates, O.S.) – 28 October 1704 (Old Style and New Style dates, O.S.)) was an English philosopher and physician, widely regarded as one of the most influential of the Enlightenment thi ...
, philosophers have been concerned with the problem of
personal identity Personal identity is the unique numerical identity of a person over time. Discussions regarding personal identity typically aim to determine the necessary and sufficient conditions under which a person at one time and a person at another time ...
.
Derek Parfit Derek Antony Parfit (; 11 December 1942 – 2 January 2017) was a British philosopher who specialised in personal identity, rationality, and ethics. He is widely considered one of the most important and influential moral philosophers of the lat ...
in ''
Reasons and Persons ''Reasons and Persons'' is a 1984 book by the philosopher Derek Parfit, in which the author discusses ethics, rationality and personal identity. It is divided into four parts, dedicated to self-defeating theories, rationality and time, personal ...
'' (1984) defends a kind of
bundle theory Bundle or Bundling may refer to: * Bundling (packaging), the process of using straps to bundle up items Biology * Bundle of His, a collection of heart muscle cells specialized for electrical conduction * Bundle of Kent, an extra conduction pa ...
, while David Lewis again defends perdurantism.
Bernard Williams Sir Bernard Arthur Owen Williams (21 September 1929 – 10 June 2003) was an English Ethics, moral philosopher. His publications include ''Problems of the Self'' (1973), ''Ethics and the Limits of Philosophy'' (1985), ''Shame and Necessit ...
in ''The Self and the Future'' (1970) argues that personal identity is bodily identity rather than mental continuity.


Principle of sufficient reason

Since
Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...
philosophers have discussed the
principle of sufficient reason The principle of sufficient reason states that everything must have a Reason (argument), reason or a cause. The principle was articulated and made prominent by Gottfried Wilhelm Leibniz, with many antecedents, and was further used and developed by ...
or PSR. Van Inwagen criticizes the PSR. Alexander Pruss defends it.


Philosophy of time

Analytic
philosophy of time Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, value, mind, and language. It is a rational and critical inquiry that reflects on ...
traces its roots to the British idealist J. M. E. McTaggart's article " The Unreality of Time" (1908). In it, McTaggart distinguishes between the dynamic, A-, or tensed, 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). Eternalism holds that past, present, and future are equally real. In contrast, Presentism holds that only entities in the present exist. The theory of special relativity seems to advocate a B-theory of time. David Lewis's perdurantism, or
four-dimensionalism In philosophy, four-dimensionalism (also known as the doctrine of temporal parts) is the ontological position that an object's persistence through time is like its extension through space. Thus, an object that exists in time has temporal parts ...
, requires a B-theory of time. A. N. Prior, who invented tense logic, advocated the A-theory of time.


Logical pluralism

Many-valued and non-classical logics have been popular since the Polish logician
Jan Lukasiewicz Jan, JaN or JAN may refer to: Acronyms * Jackson, Mississippi (Amtrak station), US, Amtrak station code JAN * Jackson-Evers International Airport, Mississippi, US, IATA code * Jabhat al-Nusra (JaN), a Syrian militant group * Japanese Article Nu ...
.
Graham Priest Graham Priest (born 1948) is a philosopher and logician who is distinguished professor of philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne, where he was Boyce Gibson Professor of Philosophy an ...
is a dialetheist, seeing it as the most natural solution to problems such as the
liar paradox In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the trut ...
. JC Beall, together with
Greg Restall Greg Restall (born 11 January 1969) is an Australian philosopher and Professor of Philosophy at the University of St Andrews. He is a fellow of the Australian Academy of the Humanities. Restall is known for his research on logic and theories ...
, is a pioneer of a widely-discussed version of logical pluralism.


Epistemology


Justification


= Gettier

= Owing largely to
Edmund Gettier Edmund Lee Gettier III (; October 31, 1927 – March 23, 2021) was an American philosopher at the University of Massachusetts Amherst. He is best known for his article written in 1963: "Is Justified True Belief Knowledge?", which has generated ...
's 1963 paper "Is Justified True Belief Knowledge?", and the so-called Gettier problem, epistemology has enjoyed a resurgence as a topic of analytic philosophy during the last 50 years. A large portion of current epistemological research is intended to resolve the problems that Gettier's examples presented to the traditional "justified true belief" model of knowledge, found as early as Plato's dialogue '' Theaetetus''. These include developing
theories of justification Justification (also called epistemic justification) is a property of beliefs that fulfill certain norms about what a person should believe. Epistemology, Epistemologists often identify justification as a component of knowledge distinguishing it f ...
to deal with Gettier's examples, or giving alternatives to the justified-true-belief model.


= Theories

= Chisholm defended
foundationalism Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises.Simon Blackburn, ''The Oxford Dict ...
. Quine defended
coherentism In philosophical epistemology, there are two types of coherentism: the coherence theory of truth, and the coherence theory of justification (also known as epistemic coherentism). Coherent truth is divided between an anthropological approach, w ...
, a "web of belief". Quine proposed
naturalized epistemology Naturalized epistemology (a term coined by W. V. O. Quine) is a collection of philosophic views about the theory of knowledge that emphasize the role of natural scientific methods. This shared emphasis on scientific methods of studying knowledg ...
.


Internalism and externalism

The debate between
internalism and externalism Internalism and externalism are two opposite ways of integrating and explaining various subjects in several areas of philosophy. These include human motivation, knowledge, justification, meaning, and truth. The distinction arises in many areas of d ...
still exists in analytic philosophy.
Alvin Goldman Alvin Ira Goldman (October 1, 1938 – August 4, 2024) was an American philosopher who was emeritus Board of Governors Professor of Philosophy and Cognitive Science at Rutgers University in New Jersey and a leading figure in epistemology. Educat ...
is an externalist known for developing a popular form of externalism called
reliabilism Reliabilism, a category of theories in the philosophical discipline of epistemology, has been advanced as a theory both of justification and of knowledge. Process reliabilism has been used as an argument against philosophical skepticism, such as ...
. Most externalists reject the KK thesis, which has been disputed since the introduction of the epistemic logic by
Jaakko Hintikka Kaarlo Jaakko Juhani Hintikka (; ; 12 January 1929 – 12 August 2015) was a Finnish philosopher and logician. Hintikka is regarded as the founder of formal epistemic logic and of game semantics for logic. Life and career Hintikka was born in ...
in 1962.


Problem of the Criterion

While a problem since antiquity, American philosopher
Roderick Chisholm Roderick Milton Chisholm ( ; November 27, 1916 – January 19, 1999) was an American philosopher known for his work on epistemology, metaphysics, free will, value theory, deontology, deontic logic and the philosophy of perception. Richard and ...
, in his ''Theory of Knowledge'', details the
problem of the criterion In the field of epistemology, the problem of the criterion is an issue regarding the starting point of knowledge. This is a separate and more fundamental issue than the regress argument found in discussions on justification of knowledge. In W ...
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? An answer to either set of questions will allow us to devise a means of answering the other. Answering the former question-set first is called '' particularism'', whereas answering the latter set first is called ''
methodism Methodism, also called the Methodist movement, is a Protestant Christianity, Christian Christian tradition, tradition whose origins, doctrine and practice derive from the life and teachings of John Wesley. George Whitefield and John's brother ...
''. A third solution is ''
skepticism Skepticism ( US) or scepticism ( UK) is a questioning attitude or doubt toward knowledge claims that are seen as mere belief or dogma. For example, if a person is skeptical about claims made by their government about an ongoing war then the p ...
'', or doubting there is such a thing as knowledge.


Truth

Frege questioned standard theories of
truth Truth or verity is the Property (philosophy), property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth, 2005 In everyday language, it is typically ascribed to things that aim to represent reality or otherwise cor ...
, and sometimes advocated a
redundancy theory of truth According to the redundancy theory of truth (also known as the disquotational theory of truth), asserting that a statement is true is completely equivalent to asserting the statement itself. For example, asserting the sentence Snow is white' is tru ...
. Frank Ramsey also advocated a redundancy theory.
Alfred Tarski Alfred Tarski (; ; born Alfred Teitelbaum;School of Mathematics and Statistics, University of St Andrews ''School of Mathematics and Statistics, University of St Andrews''. January 14, 1901 – October 26, 1983) was a Polish-American logician ...
put forward a
semantic theory of truth A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences. Origin The semantic conception of truth, which is related in different ways to both the correspondence and deflat ...
. Feferman & Feferman, p. 1 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 In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that worl ...
. A truth-maker is contrasted with a
truth-bearer A truth-bearer is an entity that is said to be either true or false and nothing else. The thesis that some things are true while others are false has led to different theories about the nature of these entities. Since there is divergence of ...
.


Closure

Epistemic closure is the claim that knowledge is closed under
entailment Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid l ...
; in other words epistemic closure is a
property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, re ...
or the
principle A principle may relate to a fundamental truth or proposition that serves as the foundation for a system of beliefs or behavior or a chain of reasoning. They provide a guide for behavior or evaluation. A principle can make values explicit, so t ...
that if a subject S knows p, and S knows that p entails q, then S can thereby come to know q. Most
epistemological Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowled ...
theories involve a closure principle, and many skeptical arguments assume a closure principle. In ''Proof of An External World'', G. E. Moore uses closure in his famous anti-skeptical " here is one hand" argument. Shortly before his death, Wittgenstein wrote ''
On Certainty ''On Certainty'' (, original spelling ) is a philosophical book composed from notes written by Ludwig Wittgenstein over four separate periods in the eighteen months before his death on 29 April 1951. He left his initial notes at the home of Eli ...
'' in response to Moore. While the principle of epistemic closure is generally regarded as intuitive, philosophers, such as
Fred Dretske Frederick Irwin "Fred" Dretske (; December 9, 1932 – July 24, 2013) was an American philosopher noted for his contributions to epistemology and the philosophy of mind. Life and career Born to Frederick and Hattie Dretske, Dretske first planned ...
with relevant alternatives theory and Robert Nozick in '' Philosophical Explanations'', have argued against it.


Induction

In his book '' Fact, Fiction, and Forecast'',
Nelson Goodman Henry Nelson Goodman (7 August 1906 – 25 November 1998) was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics. Life and career Goodman was born in Somerville, Ma ...
introduced the " new riddle of induction", so-called by analogy with Hume's classical
problem of induction The problem of induction is a philosophical problem that questions the rationality of predictions about unobserved things based on previous observations. These inferences from the observed to the unobserved are known as "inductive inferences" ...
. Goodman's famous example was to introduce the predicates grue and bleen. "Grue" applies to all things before a certain time ''t'', just in case they are green, but also just in case they are blue after time ''t''; and "bleen" applies to all things before a certain time ''t'', just in the case they are blue, but also just in case they are green after time ''t''.


Other topics

Other, related topics of contemporary research include debates over basic knowledge, the nature of
evidence Evidence for a proposition is what supports the proposition. It is usually understood as an indication that the proposition is truth, true. The exact definition and role of evidence vary across different fields. In epistemology, evidence is what J ...
, the value of knowledge, epistemic luck, virtue epistemology, the role of intuitions in justification, and treating knowledge as a primitive concept.


Ethics

Due to the commitments to
empiricism In philosophy, empiricism is an epistemological view which holds that true knowledge or justification comes only or primarily from sensory experience and empirical evidence. It is one of several competing views within epistemology, along ...
and
symbolic logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
in the early analytic period, early analytic philosophers often thought that inquiry in the ethical domain could not be made rigorous enough to merit any attention. It was only with the emergence of ordinary-language philosophers that ethics started to become an acceptable area of inquiry for analytic philosophers. Philosophers working within the analytic tradition have gradually come to distinguish three major types of moral philosophy. *
Meta-ethics In metaphilosophy and ethics, metaethics is the study of the nature, scope, ground, and meaning of moral judgment, ethical belief, or values. It is one of the three branches of ethics generally studied by philosophers, the others being normativ ...
, which investigates moral terms and concepts; *
Normative ethics Normative ethics is the study of ethics, ethical behaviour and is the branch of Philosophy, philosophical ethics that investigates questions regarding how one ought to act, in a Morality, moral sense. Normative ethics is distinct from metaethics i ...
, which examines and produces normative ethical judgments; *
Applied ethics Applied ethics is the practical aspect of morality, moral considerations. It is ethics with respect to real-world actions and their moral considerations in private and public life, the professions, health, technology, law, and leadership. For ex ...
, which investigates how existing normative principles should be applied to difficult or borderline cases, often cases created by new technology or new scientific knowledge.


Meta-ethics

As well as Hume's famous is/ought distinction, twentieth-century meta-ethics has two original strains.


= ''Principia Ethica''

= The first is
G. E. Moore George Edward Moore (4 November 1873 – 24 October 1958) was an English philosopher, who with Bertrand Russell, Ludwig Wittgenstein and earlier Gottlob Frege was among the initiators of analytic philosophy. He and Russell began de-emphasizing ...
's investigation into the nature of ethical terms (e.g., good) in his ''Principia Ethica'' (1903), which advances a kind of
moral realism Moral realism (also ethical realism) is the position that ethical sentences express propositions that refer to objective features of the world (that is, features independent of subjective opinion), some of which may be true to the extent that t ...
called ethical non-naturalism and is known for the open question argument and identifying the naturalistic fallacy, a major topic of investigation for analytical philosophers. According to Moore, " Goodness is a simple, undefinable, non-natural
property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, re ...
." Contemporary philosophers, such as Russ Shafer-Landau in '' Moral Realism: A Defence'', defend ethical non-naturalism.


= Emotivism

= The second is founded on logical positivism and its attitude that unverifiable statements are meaningless. As a result, they avoided normative ethics and instead began
meta-ethical In metaphilosophy and ethics, metaethics is the study of the nature, scope, ground, and meaning of moral judgment, ethical belief, or Value_(ethics), values. It is one of the three branches of ethics generally studied by philosophers, the others ...
investigations into the nature of moral terms, statements, and judgments. The logical positivists opined that statements about value—including all ethical and aesthetic judgments—are non-cognitive; that is, they cannot be objectively verified or falsified. Instead, the logical positivists adopted an emotivist theory, which was that value judgments expressed the attitude of the speaker. It is also known as the boo/hurrah theory. For example, in this view, saying, "Murder is wrong", is equivalent to saying, "Boo to murder", or saying the word "murder" with a particular tone of disapproval. While analytic philosophers generally accepted non-cognitivism, emotivism had many deficiencies. It evolved into more sophisticated non-cognitivist theories, such as the
expressivism In meta-ethics, expressivism is a theory about the meaning of moral language. According to expressivism, sentences that employ moral terms – for example, "It is wrong to torture an innocent human being" – are not descriptive or fact-stating; ...
of Charles Stevenson, and the
universal prescriptivism Universal is the adjective for universe. Universal may also refer to: Companies * NBCUniversal, a media and entertainment company that is a subsidiary of Comcast ** Universal Animation Studios, an American Animation studio, and a subsidiary of ...
of R. M. Hare, which was based on J. L. Austin's philosophy of
speech acts Speech is the use of the human voice as a medium for language. Spoken language combines vowel and consonant sounds to form units of meaning like words, which belong to a language's lexicon. There are many different intentional speech acts, suc ...
.


= Critics

= As non-cognitivism, the is/ought distinction, and the naturalistic fallacy were questioned, analytic philosophers showed a renewed interest in the traditional questions of moral philosophy. Philippa Foot defended
naturalist Natural history is a domain of inquiry involving organisms, including animals, fungi, and plants, in their natural environment, leaning more towards observational than experimental methods of study. A person who studies natural history is cal ...
moral realism and contributed several essays attacking other theories. Foot introduced the famous "
trolley problem The trolley problem is a series of thought experiments in ethics, psychology, and artificial intelligence involving stylized ethical dilemmas of whether to sacrifice one person to save a larger number. The series usually begins with a Scenario ...
" into the ethical discourse.Philippa Foot,
The Problem of Abortion and the Doctrine of the Double Effect
in ''Virtues and Vices'' (Oxford: Basil Blackwell, 1978) (originally in the ''Oxford Review'', No. 5, 1967).
Perhaps the most influential critic was
Elizabeth Anscombe Gertrude Elizabeth Margaret Anscombe (; 18 March 1919 – 5 January 2001), usually cited as G. E. M. Anscombe or Elizabeth Anscombe, was a British analytic philosopher. She wrote on the philosophy of mind, philosophy of action, philosophi ...
, whose monograph ''Intention'' was called by Donald Davidson "the most important treatment of action since Aristotle". A favorite student and friend of Ludwig Wittgenstein, her 1958 article "
Modern Moral Philosophy "Modern Moral Philosophy" is an article on moral philosophy by G. E. M. Anscombe, originally published in the journal ''Philosophy'', vol. 33, no. 124 (January 1958). The article has influenced the emergence of contemporary virtue ethics, especi ...
" declared the "is-ought" impasse to be unproductive. J.O. Urmson's article "On Grading" also called the is/ought distinction into question. Australian J. L. Mackie, in ''Ethics: Inventing Right And Wrong'', defended anti-realist
error theory Moral nihilism (also called ethical nihilism) is the meta-ethics, metaethical view that nothing is morally right or morally wrong and that morality does not exist. Moral nihilism is distinct from moral relativism, which allows for actions to ...
.
Bernard Williams Sir Bernard Arthur Owen Williams (21 September 1929 – 10 June 2003) was an English Ethics, moral philosopher. His publications include ''Problems of the Self'' (1973), ''Ethics and the Limits of Philosophy'' (1985), ''Shame and Necessit ...
also influenced ethics by advocating a kind of
moral relativism Moral relativism or ethical relativism (often reformulated as relativist ethics or relativist morality) is used to describe several Philosophy, philosophical positions concerned with the differences in Morality, moral judgments across different p ...
and rejecting all other theories.


Normative ethics

The first half of the 20th century was marked by skepticism toward, and neglect of, normative ethics. However, contemporary normative ethics is dominated by three schools:
consequentialism In moral philosophy, consequentialism is a class of normative, teleological ethical theories that holds that the consequences of one's conduct are the ultimate basis for judgement about the rightness or wrongness of that conduct. Thus, from a ...
,
virtue ethics Virtue ethics (also aretaic ethics, from Greek []) is a philosophical approach that treats virtue and moral character, character as the primary subjects of ethics, in contrast to other ethical systems that put consequences of voluntary acts, pri ...
, and
deontology In moral philosophy, deontological ethics or deontology (from Greek language, Greek: and ) is the normative ethics, normative ethical theory that the morality of an action should be based on whether that action itself is right or wrong under a ...
.


= Consequentialism, or Utilitarianism

= During the early 20th century,
utilitarianism In ethical philosophy, utilitarianism is a family of normative ethical theories that prescribe actions that maximize happiness and well-being for the affected individuals. In other words, utilitarian ideas encourage actions that lead to the ...
was the only non-skeptical type of ethics to remain popular among analytic philosophers. However, as the influence of logical positivism declined mid-century, analytic philosophers had a renewed interest in ethics. ''Utilitarianism: For and Against'' was written with
J. J. C. Smart John Jamieson Carswell Smart (16 September 1920 – 6 October 2012) was a British-Australian philosopher who was appointed as an Emeritus Professor by the Australian National University. He worked in the fields of metaphysics, philosophy of sci ...
arguing for and Bernard Williams arguing against.


= Virtue ethics

= Anscombe, Foot, and
Alasdair Macintyre Alasdair Chalmers MacIntyre (12 January 1929 – 21 May 2025) was a Scottish-American philosopher who contributed to moral and political philosophy as well as history of philosophy and theology. MacIntyre's '' After Virtue'' (1981) is one of ...
's ''After Virtue'' sparked a revival of
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
's virtue ethical approach. This increased interest in virtue ethics has been dubbed the " aretaic turn" mimicking the linguistic turn.


= Deontology

=
John Rawls John Bordley Rawls (; February 21, 1921 – November 24, 2002) was an American moral philosophy, moral, legal philosophy, legal and Political philosophy, political philosopher in the Modern liberalism in the United States, modern liberal tradit ...
's 1971 ''
A Theory of Justice ''A Theory of Justice'' is a 1971 work of political philosophy and ethics by the philosopher John Rawls (1921–2002) in which the author attempts to provide a moral theory alternative to utilitarianism and that addresses the problem of distribu ...
'' restored interest in
Kantian Kantianism () is the philosophy of Immanuel Kant, a German philosopher born in Königsberg, Prussia (now Kaliningrad, Russia). The term ''Kantianism'' or ''Kantian'' is sometimes also used to describe contemporary positions in philosophy of mi ...
ethical philosophy.


Applied ethics

Since around 1970, a significant feature of analytic philosophy has been the emergence of
applied ethics Applied ethics is the practical aspect of morality, moral considerations. It is ethics with respect to real-world actions and their moral considerations in private and public life, the professions, health, technology, law, and leadership. For ex ...
—an interest in the application of moral principles to specific practical issues. The philosophers following this orientation view ethics as involving humanistic values, which involve practical implications and applications in the way people interact and lead their lives socially. Topics of special interest for applied ethics include
environmental ethics In environmental philosophy, environmental ethics is an established field of practical philosophy "which reconstructs the essential types of argumentation that can be made for protecting natural entities and the sustainable use of natural resourc ...
,
animal rights Animal rights is the philosophy according to which many or all Animal consciousness, sentient animals have Moral patienthood, moral worth independent of their Utilitarianism, utility to humans, and that their most basic interests—such as ...
, and the many challenges created by advancing
medical science Medicine is the science and practice of caring for patients, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pra ...
. In education, applied ethics addressed themes such as punishment in schools, equality of educational opportunity, and education for democracy.


Political philosophy


Liberalism

Isaiah Berlin Sir Isaiah Berlin (6 June 1909 – 5 November 1997) was a Russian-British social and political theorist, philosopher, and historian of ideas. Although he became increasingly averse to writing for publication, his improvised lectures and talks ...
had a lasting influence on both analytic political philosophy and liberalism with his lecture "
Two Concepts of Liberty "Two Concepts of Liberty" was the inaugural lecture delivered by the liberal philosopher Isaiah Berlin before the University of Oxford on 31 October 1958. It was subsequently published as a 57-page pamphlet by Oxford at the Clarendon Press. It a ...
". Berlin defined 'negative liberty' as absence of coercion or interference in private actions. 'Positive liberty' Berlin maintained, could be thought of as self-mastery, which asks not what we are free from, but what we are free to do. Current analytic political philosophy owes much to
John Rawls John Bordley Rawls (; February 21, 1921 – November 24, 2002) was an American moral philosophy, moral, legal philosophy, legal and Political philosophy, political philosopher in the Modern liberalism in the United States, modern liberal tradit ...
, 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 ''A Theory of Justice'' is a 1971 work of political philosophy and ethics by the philosopher John Rawls (1921–2002) in which the author attempts to provide a moral theory alternative to utilitarianism and that addresses the problem of distribu ...
'', produced a sophisticated defense of a generally liberal
egalitarian Egalitarianism (; also equalitarianism) is a school of thought within political philosophy that builds on the concept of social equality, prioritizing it for all people. Egalitarian doctrines are generally characterized by the idea that all h ...
account of distributive justice. Rawls introduced the term the
veil of ignorance The original position is a hypothetical position from which members of society would consider which principles they would select for the basic structure of their society if they had no knowledge ahead of time regarding the position which they w ...
. This was followed soon by Rawls's colleague
Robert Nozick Robert Nozick (; November 16, 1938 – January 23, 2002) was an American philosopher. He held the Joseph Pellegrino Harvard University Professor, University Professorship at Harvard University,Anarchy, State, and Utopia ''Anarchy, State, and Utopia'' is a 1974 book by the American political philosopher Robert Nozick. It won the 1975 US National Book Award in category Philosophy and Religion, has been translated into 11 languages, and was named one of the "100 m ...
'', a defense of
free-market In economics, a free market is an economic system in which the prices of goods and services are determined by supply and demand expressed by sellers and buyers. Such markets, as modeled, operate without the intervention of government or any ot ...
libertarianism Libertarianism (from ; or from ) is a political philosophy that holds freedom, personal sovereignty, and liberty as primary values. Many libertarians believe that the concept of freedom is in accord with the Non-Aggression Principle, according t ...
. Consequentialist libertarianism also derives from the analytic tradition . During recent decades there have also been several critics of liberalism, including the
feminist Feminism is a range of socio-political movements and ideology, ideologies that aim to define and establish the political, economic, personal, and social gender equality, equality of the sexes. Feminism holds the position that modern soci ...
critiques by Catharine MacKinnon and
Andrea Dworkin Andrea Rita Dworkin (September 26, 1946 – April 9, 2005) was an American radical feminist writer and activist best known for her analysis of pornography. Her feminist writings, beginning in 1974, span 30 years. They are found in a dozen sol ...
, the multiculturalist critiques by Amy Gutmann and Charles Taylor, and the
communitarian Communitarianism is a philosophy that emphasizes the connection between the individual and the community. Its overriding philosophy is based on the belief that a person's social identity and personality are largely molded by community relation ...
critiques by
Michael Sandel Michael Joseph Sandel (; born March 5, 1953) is an American political philosopher and the Anne T. and Robert M. Bass Professor of Government at Harvard University, where his course ''Justice'' was the university's first course to be made fre ...
and
Alasdair MacIntyre Alasdair Chalmers MacIntyre (12 January 1929 – 21 May 2025) was a Scottish-American philosopher who contributed to moral and political philosophy as well as history of philosophy and theology. MacIntyre's '' After Virtue'' (1981) is one of ...
(although neither of them endorses the term).


Analytical Marxism

Another development of political philosophy was the emergence of the school of
analytical Marxism Analytical Marxism is an academic school of Marxist theory which emerged in the late 1970s, largely prompted by G. A. Cohen's '' Karl Marx's Theory of History: A Defence'' (1978). In this book, Cohen drew on the Anglo–American tradition of an ...
. Members of this school seek to apply techniques of analytic philosophy and modern social science to clarify the theories of
Karl Marx Karl Marx (; 5 May 1818 – 14 March 1883) was a German philosopher, political theorist, economist, journalist, and revolutionary socialist. He is best-known for the 1848 pamphlet '' The Communist Manifesto'' (written with Friedrich Engels) ...
and his successors. The best-known member of this school is
G. A. Cohen Gerald Allan Cohen ( ; 14 April 1941 – 5 August 2009) was a Canadian political philosophy, political philosopher who held the positions of Quain Professor, Quain Professor of Jurisprudence, University College London and Chichele Professor of ...
, whose 1978 book, '' Karl Marx's Theory of History: A Defence'', is generally considered to represent the genesis of this school. In that book, Cohen used logical and linguistic analysis to clarify and defend Marx's materialist conception of history. Other prominent analytical Marxists include the economist John Roemer, the social scientist
Jon Elster Jon Elster (; born 22 February 1940) is a Norwegian philosopher and political theorist who holds the Robert K. Merton professorship of Social Science at Columbia University and since 2005 professor of social science at the Collège de France. ...
, and the sociologist
Erik Olin Wright Erik Olin Wright (February 9, 1947 – January 23, 2019) was an American analytical Marxist sociologist at the University of Wisconsin–Madison, specializing in social stratification and in egalitarian alternative futures to capitalism. He ...
. The work of these later philosophers has furthered Cohen's work by bringing to bear modern social science methods, such as
rational choice theory Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behav ...
, 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 to advance a
socialist Socialism is an economic ideology, economic and political philosophy encompassing diverse Economic system, economic and social systems characterised by social ownership of the means of production, as opposed to private ownership. It describes ...
theory of justice that contrasts with both traditional Marxism and the theories advanced by Rawls and Nozick. In particular, he indicates Marx's principle of
from each according to his ability, to each according to his need "From each according to his ability, to each according to his needs" () is a slogan popularised by Karl Marx in his 1875 '' Critique of the Gotha Programme''. The principle refers to free access to and distribution of goods, capital and services. ...
. Although not an analytic philosopher,
Jürgen Habermas Jürgen Habermas ( , ; ; born 18 June 1929) is a German philosopher and social theorist in the tradition of critical theory and pragmatism. His work addresses communicative rationality and the public sphere. Associated with the Frankfurt S ...
is another influential—if controversial—author in contemporary analytic political philosophy, whose social theory is a blend of social science, Marxism,
neo-Kantianism In late modern philosophy, neo-Kantianism () was a revival of the 18th-century philosophy of Immanuel Kant. The neo-Kantians sought to develop and clarify Kant's theories, particularly his concept of the thing-in-itself and his moral philosophy ...
, and American
pragmatism Pragmatism is a philosophical tradition that views language and thought as tools for prediction, problem solving, and action, rather than describing, representing, or mirroring reality. Pragmatists contend that most philosophical topics� ...
.


Communitarianism

Communitarian Communitarianism is a philosophy that emphasizes the connection between the individual and the community. Its overriding philosophy is based on the belief that a person's social identity and personality are largely molded by community relation ...
s such as
Alasdair MacIntyre Alasdair Chalmers MacIntyre (12 January 1929 – 21 May 2025) was a Scottish-American philosopher who contributed to moral and political philosophy as well as history of philosophy and theology. MacIntyre's '' After Virtue'' (1981) is one of ...
, Charles Taylor,
Michael Walzer Michael Laban Walzer (born March 3, 1935) is an American Political theory, political theorist and public intellectual. A professor emeritus at the Institute for Advanced Study (IAS) in Princeton, New Jersey, he is editor emeritus of the left-win ...
, and
Michael Sandel Michael Joseph Sandel (; born March 5, 1953) is an American political philosopher and the Anne T. and Robert M. Bass Professor of Government at Harvard University, where his course ''Justice'' was the university's first course to be made fre ...
advance a critique of liberalism that uses analytic techniques to isolate the main assumptions of liberal individualists, such as Rawls, and then challenges these assumptions. In particular, communitarians challenge the liberal assumption that the individual can be considered as fully autonomous from the community in which he is brought up and lives. Instead, they argue for a conception of the individual that emphasizes the role that the community plays in forming his or her values, thought processes, and opinions. While in the analytic tradition, its major exponents often also engage at length with figures generally considered continental, notably
G. W. F. Hegel Georg Wilhelm Friedrich Hegel (27 August 1770 – 14 November 1831) was a 19th-century German idealism, German idealist. His influence extends across a wide range of topics from metaphysical issues in epistemology and ontology, to political phi ...
and
Friedrich Nietzsche Friedrich Wilhelm Nietzsche (15 October 1844 – 25 August 1900) was a German philosopher. He began his career as a classical philology, classical philologist, turning to philosophy early in his academic career. In 1869, aged 24, Nietzsche bec ...
.


Aesthetics

As a result of logical positivism, as well as what seemed like rejections of the traditional aesthetic notions of beauty and sublimity from
post-modern Postmodernism encompasses a variety of artistic, cultural, and philosophical movements that claim to mark a break from modernism Modernism was an early 20th-century movement in literature, visual arts, and music that emphasized experi ...
thinkers, analytic philosophers were slow to consider art and aesthetic judgment. Susanne Langer and
Nelson Goodman Henry Nelson Goodman (7 August 1906 – 25 November 1998) was an American philosopher, known for his work on counterfactuals, mereology, the problem of induction, irrealism, and aesthetics. Life and career Goodman was born in Somerville, Ma ...
addressed these problems in an analytic style during the 1950s and 1960s. Since Goodman, aesthetics as a discipline for analytic philosophers has flourished. Arthur Danto argued for a "institutional definition of art" in the 1964 essay "The Artworld" in which Danto coined the term "artworld" (as opposed to the existing " art world", though they mean the same), by which he meant cultural context or "an atmosphere of
art theory Aesthetics (also spelled esthetics) is the branch of philosophy concerned with the nature of beauty and taste, which in a broad sense incorporates the philosophy of art.Slater, B. H.Aesthetics ''Internet Encyclopedia of Philosophy,'' , acces ...
". Rigorous efforts to pursue analyses of traditional aesthetic concepts were performed by Guy Sircello in the 1970s and 1980s, resulting in new analytic theories of love, sublimity, and beauty. In the opinion of Władysław Tatarkiewicz, there are six conditions for the presentation of art: beauty, form, representation, reproduction of reality, artistic expression, and innovation. However, one may not be able to pin down these qualities in a work of art. George Dickie was an influential philosopher of art. Dickie's student Noël Carroll is a leading philosopher of art.


Philosophy of language

Given the linguistic turn, it can be hard to separate logic, metaphysics, and the philosophy of language in analytic philosophy. Philosophy of language is a topic that has decreased in activity during the last four decades, as evidenced by the fact that few major philosophers today treat it as a primary research topic. While the debate remains fierce, it is still strongly influenced by those authors from the first half of the century, e.g. Frege, Russell, Wittgenstein, Austin, Tarski, and Quine.


Semantics

Saul Kripke Saul Aaron Kripke (; November 13, 1940 – September 15, 2022) was an American analytic philosophy, analytic philosopher and logician. He was Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emer ...
provided a
semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...
for modal logic. In his book '' Naming and Necessity'' (1980), Kripke challenges the descriptivist theory with a causal theory of reference. In it he introduced the term rigid designator. According to one author, "In the philosophy of language, ''Naming and Necessity'' is among the most important works ever." Ruth Barcan Marcus also challenged descriptivism. So did Keith Donnellan. Hilary Putnam used the Twin Earth thought experiment to argue for semantic externalism, or the view that the meanings of words are not psychological. Donald Davidson uses the thought experiment of Swampman to advocate for semantic externalism. Kripke in '' Wittgenstein on Rules and Private Language'' provides a rule-following paradox that undermines the possibility of our ever following rules in our use of language and, so, calls into question the idea of meaning. Kripke writes that this paradox is "the most radical and original skeptical problem that philosophy has seen to date". The
portmanteau In linguistics, a blend—also known as a blend word, lexical blend, or portmanteau—is a word formed by combining the meanings, and parts of the sounds, of two or more words together.
"Kripkenstein" has been coined as a term for a fictional person who holds the views expressed by Kripke's reading of Wittgenstein. Another influential philosopher, Pavel Tichý initiated Transparent Intensional Logic, an original theory of the logical analysis of
natural language A natural language or ordinary language is a language that occurs naturally in a human community by a process of use, repetition, and change. It can take different forms, typically either a spoken language or a sign language. Natural languages ...
s—the theory is devoted to the problem of saying exactly what it is that we learn, know, and can communicate when we come to understand what a sentence means.


Pragmatics

Paul Grice Herbert Paul Grice (13 March 1913 – 28 August 1988), usually publishing under the name H. P. Grice, H. Paul Grice, or Paul Grice, was a British philosopher of language who created the theory of implicature and the cooperative principle ( ...
and his maxims and theory of
implicature In pragmatics, a subdiscipline of linguistics, an implicature is something the speaker suggests or implies with an utterance, even though it is not literally expressed. Implicatures can aid in communicating more efficiently than by explicitly sayi ...
established the discipline of pragmatics.


Philosophy of mind and cognitive science

John Searle John Rogers Searle (; born July 31, 1932) is an American philosopher widely noted for contributions to the philosophy of language, philosophy of mind, and social philosophy. He began teaching at UC Berkeley in 1959 and was Willis S. and Mario ...
suggests that the obsession with the philosophy of language during the 20th century has been superseded by an emphasis on the
philosophy of mind Philosophy of mind is a branch of philosophy that deals with the nature of the mind and its relation to the Body (biology), body and the Reality, external world. The mind–body problem is a paradigmatic issue in philosophy of mind, although a ...
.


Physicalism

Motivated by the logical positivists' interest in verificationism,
logical behaviorism In the philosophy of mind, logical behaviorism (also known as analytical behaviorism) is the thesis that mental concepts can be explained in terms of behavioral concepts. Logical behaviorism was first stated by the Vienna Circle, especially Rudol ...
was the most prominent
theory of mind In psychology and philosophy, theory of mind (often abbreviated to ToM) refers to the capacity to understand other individuals by ascribing mental states to them. A theory of mind includes the understanding that others' beliefs, desires, intent ...
of analytic philosophy for the first half of the 20th century. Behaviorism later became much less popular, in favor of either type physicalism or functionalism. During this period, topics of the philosophy of mind were often related strongly to topics of
cognitive science Cognitive science is the interdisciplinary, scientific study of the mind and its processes. It examines the nature, the tasks, and the functions of cognition (in a broad sense). Mental faculties of concern to cognitive scientists include percep ...
, such as
modularity Modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a system into varying ...
or innateness.


= Behaviorism

= Behaviorists such as B. F. Skinner tended to opine either that statements about the mind were equivalent to ''statements about'' behavior and dispositions to behave in particular ways or that mental states were directly equivalent to behavior and dispositions to behave. Hilary Putnam criticized behaviorism by arguing that it confuses the symptoms of mental states with the mental states themselves, positing "super Spartans" who never display signs of pain. See also:


= Type identity

= Type physicalism or type identity theory identified mental states with brain states. Former students of Ryle at the
University of Adelaide The University of Adelaide is a public university, public research university based in Adelaide, South Australia. Established in 1874, it is the third-oldest university in Australia. Its main campus in the Adelaide city centre includes many Sa ...
J. J. C. Smart John Jamieson Carswell Smart (16 September 1920 – 6 October 2012) was a British-Australian philosopher who was appointed as an Emeritus Professor by the Australian National University. He worked in the fields of metaphysics, philosophy of sci ...
and Ullin Place argued for type physicalism.


= Functionalism

= Functionalism remains the dominant theory. Type identity was criticized using
multiple realizability In the philosophy of mind, multiple realizability is the thesis that the same mental property, state, or event can be implemented by different physical properties, states, or events. Philosophers of mind have used multiple realizability to argue ...
. Searle's
Chinese room The Chinese room argument holds that a computer executing a program cannot have a mind, understanding, or consciousness, regardless of how intelligently or human-like the program may make the computer behave. The argument was presented in a 19 ...
argument criticized functionalism and holds that while a computer can understand syntax, it could never understand semantics.


= Eliminativism

= The view of
eliminative materialism Eliminative materialism (also called eliminativism) is a materialist position in the philosophy of mind that expresses the idea that the majority of mental states in folk psychology do not exist. Some supporters of eliminativism argue that ...
is most closely associated with
Paul Paul may refer to: People * Paul (given name), a given name, including a list of people * Paul (surname), a list of people * Paul the Apostle, an apostle who wrote many of the books of the New Testament * Ray Hildebrand, half of the singing duo ...
and Patricia Churchland, who deny the existence of propositional attitudes, and with
Daniel Dennett Daniel Clement Dennett III (March 28, 1942 – April 19, 2024) was an American philosopher and cognitive scientist. His research centered on the philosophy of mind, the philosophy of science, and the philosophy of biology, particularly as those ...
, who is generally considered an eliminativist about
qualia In philosophy of mind, qualia (; singular: quale ) are defined as instances of subjective, conscious experience. The term ''qualia'' derives from the Latin neuter plural form (''qualia'') of the Latin adjective '' quālis'' () meaning "of what ...
and phenomenal aspects of consciousness.


Dualism

Finally, analytic philosophy has featured a certain number of philosophers who were dualists, and recently forms of
property dualism Property dualism describes a category of positions in the philosophy of mind which hold that, although the world is composed of just one kind of Substance theory, substance—Materialism, the physical kind—there exist two distinct kinds of pro ...
have had a resurgence; the most prominent representative is
David Chalmers David John Chalmers (; born 20 April 1966) is an Australian philosopher and cognitive scientist, specializing in philosophy of mind and philosophy of language. He is a professor of philosophy and neural science at New York University, as well ...
. Kripke also makes a notable argument for dualism.
Thomas Nagel Thomas Nagel (; born July 4, 1937) is an American philosopher. He is the University Professor of Philosophy and Law Emeritus at New York University, where he taught from 1980 until his retirement in 2016. His main areas of philosophical interest ...
's paper " What Is It Like to Be a Bat??" challenged the physicalist account of mind. So did Frank Jackson's
knowledge argument The knowledge argument (also known as Mary's Room, Mary the Colour Scientist, or Mary the super-scientist) is a philosophical thought experiment proposed by Frank Jackson in his article "Epiphenomenal Qualia" (1982), and extended in "What Mary Di ...
, which argues for
qualia In philosophy of mind, qualia (; singular: quale ) are defined as instances of subjective, conscious experience. The term ''qualia'' derives from the Latin neuter plural form (''qualia'') of the Latin adjective '' quālis'' () meaning "of what ...
.


Theories of consciousness

In recent years, a central focus of research in the philosophy of mind has been
consciousness Consciousness, at its simplest, is awareness of a state or object, either internal to oneself or in one's external environment. However, its nature has led to millennia of analyses, explanations, and debate among philosophers, scientists, an ...
and the
philosophy of perception The philosophy of perception is concerned with the nature of Perception, perceptual experience and the status of sense data, perceptual data, in particular how they relate to beliefs about, or knowledge of, the world.cf. http://plato.stanford.ed ...
. While there is a general consensus for the global neuronal workspace model of consciousness, there are many opinions as to the specifics. The best known theories are Searle's
naive realism Naivety (also spelled naïvety), naiveness, or naïveté is the state of being naive. It refers to an apparent or actual lack of experience and sophistication, often describing a neglect of pragmatism in favor of moral idealism. A ''naïve'' may ...
,
Fred Dretske Frederick Irwin "Fred" Dretske (; December 9, 1932 – July 24, 2013) was an American philosopher noted for his contributions to epistemology and the philosophy of mind. Life and career Born to Frederick and Hattie Dretske, Dretske first planned ...
and Michael Tye's
representationalism In the philosophy of perception and philosophy of mind, direct or naïve realism, as opposed to indirect or representational realism, are differing models that describe the nature of conscious experiences.Lehar, Steve. (2000)The Function of Con ...
,
Daniel Dennett Daniel Clement Dennett III (March 28, 1942 – April 19, 2024) was an American philosopher and cognitive scientist. His research centered on the philosophy of mind, the philosophy of science, and the philosophy of biology, particularly as those ...
's heterophenomenology, and the higher-order theories of either David M. Rosenthal—who advocates a higher-order thought (HOT) model—or David Armstrong and
William Lycan William G. Lycan ( ; born September 26, 1945) is an American philosopher and professor emeritus at University of North Carolina at Chapel Hill, where he was formerly the William Rand Kenan, Jr. Distinguished Professor. Since 2011, Lycan is also d ...
—who advocate a higher-order perception (HOP) model. An alternative higher-order theory, the higher-order global states (HOGS) model, is offered by Robert van Gulick.


Philosophy of mathematics

Since the beginning, analytic philosophy has had an interest in the
philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...
.
Kurt Gödel Kurt Friedrich Gödel ( ; ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel profoundly ...
, a student of Hans Hahn of the Vienna Circle, produced his
incompleteness theorems Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies ...
showing that Russell and Whitehead's ''Principia Mathematica'' also failed to reduce arithmetic to logic. Gödel has been ranked as one of the four greatest logicians of all time, along with
Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...
, Frege, and Tarski.
Ernst Zermelo Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel set theory, Z ...
and
Abraham Fraenkel Abraham Fraenkel (; 17 February, 1891 – 15 October, 1965) was a German-born Israeli mathematician. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic ...
established
Zermelo Fraenkel Set Theory Ernst Friedrich Ferdinand Zermelo (; ; 27 July 187121 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics. He is known for his role in developing Zermelo–Fraenkel axiomatic se ...
. Quine developed his own system, dubbed
New Foundations In mathematical logic, New Foundations (NF) is a non-well-founded, finitely axiomatizable set theory conceived by Willard Van Orman Quine as a simplification of the theory of types of ''Principia Mathematica''. Definition The well-formed fo ...
. Physicist
Eugene Wigner Eugene Paul Wigner (, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his contributions to the theory of th ...
's seminal paper " The Unreasonable Effectiveness of Mathematics in the Natural Sciences" poses the question of why a formal pursuit like mathematics can have real utility. José Benardete argued for the reality of
infinity Infinity is something which is boundless, endless, or larger than any natural number. It is denoted by \infty, called the infinity symbol. From the time of the Ancient Greek mathematics, ancient Greeks, the Infinity (philosophy), philosophic ...
. Akin to the medieval debate on universals, between realists, idealists, and nominalists; the philosophy of mathematics has the debate between logicists or platonists, conceptualists or intuitionists, and formalists.


Platonism

Gödel was a platonist who postulated a special kind of mathematical intuition that lets us perceive mathematical objects directly. Quine and Putnam argued for platonism with the indispensability argument. Crispin Wright, along with Bob Hale, led a Neo-Fregean revival with his work ''Frege's Conception of Numbers as Objects''.


= Critics

= Structuralist
Paul Benacerraf Paul Joseph Salomon Benacerraf (; 26 March 1930 – 13 January 2025) was a French-born American philosopher working in the field of the philosophy of mathematics who taught at Princeton University his entire career, from 1960 until his retirement ...
has an epistemological objection to mathematical platonism.


Intuitionism

The intuitionists, led by L. E. J. Brouwer, are a constructivist school of mathematics that argues that mathematics is a
cognitive Cognition is the "mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of intellectual functions and processes such as: perception, attention, thought, ...
construct rather than a type of
objective truth The distinction between subjectivity and objectivity is a basic idea of philosophy, particularly epistemology Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowl ...
.


Formalism

The formalists, best exemplified by David Hilbert, considered mathematics to be merely the investigation of formal axiom systems. Hartry Field defended mathematical fictionalism.


Philosophy of religion

In ''Analytic Philosophy of Religion'', James Franklin Harris noted that: As with the study of ethics, early analytic philosophy tended to avoid the study of
religion Religion is a range of social system, social-cultural systems, including designated religious behaviour, behaviors and practices, morals, beliefs, worldviews, religious text, texts, sanctified places, prophecies, ethics in religion, ethics, or ...
, largely dismissing (as per the logical positivists) the subject as a part of
metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...
and therefore meaningless. The demise of logical positivism led to a renewed interest in the philosophy of religion, prompting philosophers not only to introduce new problems, but to re-study classical topics such as the
existence of God The existence of God is a subject of debate in the philosophy of religion and theology. A wide variety of arguments for and against the existence of God (with the same or similar arguments also generally being used when talking about the exis ...
, the nature of
miracle A miracle is an event that is inexplicable by natural or scientific lawsOne dictionary define"Miracle"as: "A surprising and welcome event that is not explicable by natural or scientific laws and is therefore considered to be the work of a divi ...
s, the
problem of evil The problem of evil is the philosophical question of how to reconcile the existence of evil and suffering with an Omnipotence, omnipotent, Omnibenevolence, omnibenevolent, and Omniscience, omniscient God.The Stanford Encyclopedia of Philosophy, ...
, the rationality of belief in God, concepts of the nature of God, and several others. The
Society of Christian Philosophers The Society of Christian Philosophers (SCP) was founded in 1978. The society is open to anyone interested in philosophy who considers himself or herself a Christian. Membership is not restricted to any particular "school" of philosophy or to any b ...
was established in 1978.


Reformed epistemology

Analytic philosophy formed the basis for some sophisticated Christian arguments, such as those of the reformed epistemologists such as
Alvin Plantinga Alvin Carl Plantinga (born November 15, 1932) is an American analytic philosophy, analytic philosopher who works primarily in the fields of philosophy of religion, epistemology (particularly on issues involving theory of justification, epistemic ...
, William Alston, and Nicholas Wolterstorff. Plantinga was awarded the
Templeton Prize The Templeton Prize is an annual award granted to a living person, in the estimation of the judges, "whose exemplary achievements advance Sir John Templeton's philanthropic vision: harnessing the power of the sciences to explore the deepest ques ...
in 2017 and was once described by ''
Time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...
'' magazine as "America's leading orthodox
Protestant Protestantism is a branch of Christianity that emphasizes Justification (theology), justification of sinners Sola fide, through faith alone, the teaching that Salvation in Christianity, salvation comes by unmerited Grace in Christianity, divin ...
philosopher of God". His seminal work '' God and Other Minds'' (1967) argues that belief in God is a properly basic belief akin to the belief in other minds. Plantinga also developed a modal
ontological argument In the philosophy of religion, an ontological argument is a deductive philosophical argument, made from an ontological basis, that is advanced in support of the existence of God. Such arguments tend to refer to the state of being or existing. ...
in ''The Nature of Necessity'' (1974). Plantinga, J. L. Mackie, and Antony Flew debated the use of the ''Alvin Plantinga's free-will defense, free will defense'' as a way to solve the problem of evil. Plantinga's evolutionary argument against naturalism contends that there is a problem in asserting both evolution and naturalism. Plantinga further issued a trilogy on epistemology, and especially justification, ''Warrant: The Current Debate'', ''Warrant and Proper Function'', and ''Warranted Christian Belief.'' Alston defended divine command theory and applied the analytic philosophy of language to religious language. Robert Merrihew Adams also defended divine command theory, and worked on the relationship between faith and morality. William Lane Craig defends the Kalam cosmological argument in the The Kalām Cosmological Argument, book of the same name.


Analytic Thomism

Catholic philosophers in the analytic tradition—such as Elizabeth Anscombe, Peter Geach, Anthony Kenny, Alasdair MacIntyre, John Haldane (philosopher), John Haldane, Eleonore Stump, and others—developed an Analytical Thomism, analytic approach to Thomism.


Orthodox

Richard Swinburne wrote a trilogy of books, arguing for God, consisting of ''The Coherence of Theism'', ''The Existence of God (book), The Existence of God'', and ''Faith and Reason''.


Wittgenstein and religion

The analytic philosophy of religion has been preoccupied with Wittgenstein, as well as his interpretation of Søren Kierkegaard's philosophy of religion. Wittgenstein fought for the Austrian army in the First World War and came upon a copy of Leo Tolstoy's ''Gospel in Brief''. At that time, he underwent some kind of religious conversion. Using first-hand remarks (which were later published in ''Philosophical Investigations'', ''Culture and Value'', and other works), philosophers such as Peter Winch and Norman Malcolm developed what has come to be known as "contemplative philosophy", a Wittgensteinian school of thought rooted in the "Swansea University, Swansea school", and which includes Wittgensteinians such as Rush Rhees, Peter Winch, and D.Z. Phillips, among others. The name "contemplative philosophy" was coined by D. Z. Phillips in ''Philosophy's Cool Place'', which rests on an interpretation of a passage from Wittgenstein's ''Culture and Value''. This interpretation was first labeled "Wittgensteinian Fideism" by Kai Nielsen (philosopher), Kai Nielsen, but those who consider themselves members of the Swansea school have relentlessly and repeatedly rejected this construal as a caricature of Wittgenstein's position; this is especially true of Phillips. Responding to this interpretation, Nielsen and Phillips became two of the most prominent interpreters of Wittgenstein's philosophy of religion.


Philosophy of science

Science and the
philosophy of science Philosophy of science is the branch of philosophy concerned with the foundations, methods, and implications of science. Amongst its central questions are the difference between science and non-science, the reliability of scientific theories, ...
have also had increasingly significant roles in analytic metaphysics. The theory of special relativity has had a profound effect on the philosophy of time, and quantum physics is routinely discussed in the free will debate. The weight given to scientific evidence is largely due to commitments of philosophers to scientific realism and Naturalism (philosophy), naturalism. Others will see a commitment to using science in philosophy as scientism.


Confirmation theory

Carl Hempel advocated confirmation theory or Bayesian epistemology. He introduced the famous Raven paradox, raven's paradox.


Falsification

In reaction to what he considered excesses of logical positivism,
Karl Popper Sir Karl Raimund Popper (28 July 1902 – 17 September 1994) was an Austrian–British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the ...
, in ''The Logic of Scientific Discovery'', insisted on the role of falsifiability, falsification in the philosophy of science, using it to solve the demarcation problem.


Confirmation holism

The Duhem–Quine thesis, or problem of underdetermination, posits that no Hypothesis, scientific hypothesis can be understood in isolation, a viewpoint called confirmation holism.


Constructivism

In reaction to both the logical positivists and Popper, discussions of the philosophy of science during the last 40 years were dominated by social constructivism, social constructivist and cognitive relativism, cognitive relativist theories of science. Following Quine and Duhem, subsequent theories emphasized theory-ladenness. Thomas Samuel Kuhn, with his formulation of paradigm shifts, and Paul Feyerabend, with his epistemological anarchism, are significant for these discussions.


Biology

The philosophy of biology has also undergone considerable growth, particularly due to the considerable debate in recent years over the nature of evolution, particularly natural selection. Daniel Dennett and his 1995 book ''Darwin's Dangerous Idea'', which defends Neo-Darwinism, stand at the forefront of this debate.Lennox, James G., "Darwinism and Neo-Darwinism" in Sakar and Plutynski (eds.), ''A Companion to the Philosophy of Biology'' (Blackwell Publishing, 2008), p. 89. Jerry Fodor criticizes natural selection.


Notes


References


Sources

* Aristotle, ''Metaphysics (Aristotle), Metaphysics'' * * * Geach, P., ''Mental Acts'', London 1957 * * Kenny, A.J.P., ''Wittgenstein'', London 1973. * * * * Soames, Scott. ''Philosophical Analysis in the Twentieth Century: Volume 1, The Dawn of Analysis''. Princeton: Princeton University Press, 2003. * * Wittgenstein, ''
Tractatus Logico-Philosophicus The ''Tractatus Logico-Philosophicus'' (widely abbreviated and Citation, cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal ...
''


Further reading

* Th
London Philosophy Study Guide
offers many suggestions on what to read, depending on the student's familiarity with the subject

* Hirschberger, Johannes. ''A Short History of Western Philosophy'', ed. Clare Hay

* Hylton, Peter. ''Russell, Idealism, and the Emergence of Analytic Philosophy''. Oxford: Oxford University Press, 1990. * Passmore, John. ''A Hundred Years of Philosophy'', revised ed. New York: Basic Books, 1966. * Weitz, Morris, ed. ''Twentieth Century Philosophy: The Analytic Tradition''. New York: Free Press, 1966.


External links

* * {{DEFAULTSORT:Analytic Philosophy Analytic philosophy, 20th century in philosophy 21st century in philosophy Contemporary philosophy History of logic History of mathematics Intellectual history Philosophical schools and traditions Western culture