"Two plus two equals five" (2 + 2 = 5) is a mathematically incorrect phrase used in the 1949
dystopia
A dystopia (from Ancient Greek δυσ- "bad, hard" and τόπος "place"; alternatively cacotopiaCacotopia (from κακός ''kakos'' "bad") was the term used by Jeremy Bentham in his 1818 Plan of Parliamentary Reform (Works, vol. 3, p. 493). ...
n novel ''
Nineteen Eighty-Four
''Nineteen Eighty-Four'' (also stylised as ''1984'') is a dystopian social science fiction novel and cautionary tale written by the English writer George Orwell. It was published on 8 June 1949 by Secker & Warburg as Orwell's ninth and final ...
'' by
George Orwell
Eric Arthur Blair (25 June 1903 – 21 January 1950), better known by his pen name George Orwell, was an English novelist, essayist, journalist, and critic. His work is characterised by lucid prose, social criticism, opposition to totalitar ...
. It appears as a possible statement of Ingsoc (
English Socialism) philosophy, like the
dogma
Dogma is a belief or set of beliefs that is accepted by the members of a group without being questioned or doubted. It may be in the form of an official system of principles or doctrines of a religion, such as Roman Catholicism, Judaism, Islam ...
"War is Peace", which the Party expects the citizens of
Oceania
Oceania (, , ) is a region, geographical region that includes Australasia, Melanesia, Micronesia, and Polynesia. Spanning the Eastern Hemisphere, Eastern and Western Hemisphere, Western hemispheres, Oceania is estimated to have a land area of ...
to believe is true. In writing his secret diary in the year 1984, the protagonist
Winston Smith Winston Smith may refer to:
People
* Winston Smith (artist) (born 1952), American artist
* Winston Smith (athlete) (born 1982), Olympic track and field athlete
* Winston Boogie Smith (born ), American man killed by law enforcement in 2021
* Winst ...
ponders if the Inner Party might declare that "two plus two equals five" is a fact. Smith further ponders whether or not belief in such a
consensus reality
Consensus reality is that which is generally agreed to be reality, based on a consensus view.
The appeal to consensus arises from the idea that humans do not fully understand or agree upon the nature of knowledge or ontology, often making it unce ...
makes the lie true.
About the falsity of "two plus two equals five", in
Room 101
The Ministry of Truth, the Ministry of Peace, the Ministry of Love, and the Ministry of Plenty are the four ministries of the government of Oceania in the 1949 dystopian novel ''Nineteen Eighty-Four'', by George Orwell.
The use of contradictory ...
, the interrogator
O'Brien tells the
thought criminal Smith that control over physical reality is unimportant to the Party, provided the citizens of Oceania subordinate their real-world perceptions to the political will of the Party; and that, by way of
doublethink
Doublethink is a process of indoctrination in which subjects are expected to simultaneously accept two conflicting beliefs as truth, often at odds with their own memory or sense of reality. Doublethink is related to, but differs from, hypocrisy. ...
: "Sometimes, Winston.
ometimes it is four fingers.Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once".
As a theme and as a subject in the arts, the
anti-intellectual
Anti-intellectualism is hostility to and mistrust of intellect, intellectuals, and intellectualism, commonly expressed as deprecation of education and philosophy and the dismissal of art, literature, and science as impractical, politically mo ...
slogan 2 + 2 = 5 pre-dates Orwell and has produced literature, such as ''Deux et deux font cinq'' (''Two and Two Make Five''), written in 1895 by
Alphonse Allais
Alphonse Allais (20 October 1854 – 28 October 1905) was a French writer, journalist and humorist.
Life
Allais was born in Honfleur, Calvados (department), Calvados. He died in Paris.
Work
He is the author of many collections of whimsical writ ...
, which is a collection of
absurdist short stories;
and the 1920
imagist
Imagism was a movement in early-20th-century Anglo-American poetry that favored precision of imagery and clear, sharp language. It is considered to be the first organized literary modernism, modernist literary movement in the English language. ...
art manifesto ''2 × 2 = 5'' by the poet
Vadim Shershenevich
Vadim Gabrielevich Shershenevich (russian: Вадим Габриэлевич Шершеневич; 25 January 1893 – 18 May 1942) was a Russian poet. He was highly prolific, working in more than one genre, moving from Symbolism to Futurism aft ...
, in the 20th century.
Self-evident truth and self-evident falsehood
In the 17th century, in the ''
Meditations on First Philosophy, in which the Existence of God and the Immortality of the Soul are Demonstrated'' (1641),
René Descartes
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathem ...
said that the standard of truth is self-evidence of clear and distinct ideas. Despite the logician Descartes' understanding of "self-evident truth", the philosopher Descartes considered that the self-evident truth of "two plus two equals four" might not exist beyond the human mind; that there might not exist correspondence between
abstract ideas and concrete
reality
Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary. The term is also used to refer to the ontological status of things, indicating their existence. In physical terms, r ...
.
In establishing the mundane reality of the self-evident truth of 2 + 2 = 4, in ''De Neutralibus et Mediis Libellus'' (1652)
Johann Wigand
Johann Wigand (Latin: Jo(h)annes Wigandus; c. 1523 – 21 October 1587) was a German Lutheran cleric, Protestant reformer and theologian. He served as Bishop of Pomesania.
Johann Wigand was born at Mansfeld in Saxony-Anhalt, Germany. He was ...
said: "That twice two are four; a man may not lawfully make a doubt of it, because that manner of knowledge is grauen
raven
A raven is any of several larger-bodied bird species of the genus ''Corvus''. These species do not form a single taxonomic group within the genus. There is no consistent distinction between "crows" and "ravens", common names which are assigned t ...
into mannes
an'snature."
In the comedy-of-manners play ''
Dom Juan, or The Feast with the Statue'' (1665), by
Molière
Jean-Baptiste Poquelin (, ; 15 January 1622 (baptised) – 17 February 1673), known by his stage name Molière (, , ), was a French playwright, actor, and poet, widely regarded as one of the greatest writers in the French language and world ...
, the
libertine
A libertine is a person devoid of most moral principles, a sense of responsibility, or sexual restraints, which they see as unnecessary or undesirable, and is especially someone who ignores or even spurns accepted morals and forms of behaviour ob ...
protagonist, Dom Juan, is asked in what
values
In ethics and social sciences, value denotes the degree of importance of something or action, with the aim of determining which actions are best to do or what way is best to live (normative ethics in ethics), or to describe the significance of dif ...
he believes, and answers that he believes "two plus two equals four".
In the 18th century, the self-evident falsehood of 2 + 2 = 5 was attested in the ''
Cyclopædia, or an Universal Dictionary of Arts and Sciences
''Cyclopædia: or, An Universal Dictionary of Arts and Sciences'' is an encyclopedia prepared by Ephraim Chambers and first published in 1728; six more editions appeared between 1728 and 1751 with a ''Supplement'' in 1753. The ''Cyclopædia'' ...
'' (1728), by
Ephraim Chambers
Ephraim Chambers ( – 15 May 1740) was an English writer and encyclopaedist, who is primarily known for producing the '' Cyclopaedia, or a Universal Dictionary of Arts and Sciences''.
Biography
Chambers was born in Milton near Kendal, Westmor ...
: "Thus, a Proposition would be ''absurd'', that should affirm, that two and two make five; or that should deny 'em to make four." In 1779,
Samuel Johnson
Samuel Johnson (18 September 1709 – 13 December 1784), often called Dr Johnson, was an English writer who made lasting contributions as a poet, playwright, essayist, moralist, critic, biographer, editor and lexicographer. The ''Oxford ...
likewise said that "You may have a reason why two and two should make five, but they will still make but four."
In the 19th century, in a personal letter to his future wife,
Anabella Milbanke,
Lord Byron
George Gordon Byron, 6th Baron Byron (22 January 1788 – 19 April 1824), known simply as Lord Byron, was an English romantic poet and Peerage of the United Kingdom, peer. He was one of the leading figures of the Romantic movement, and h ...
said: "I know that two and two make four—& should be glad to prove it, too, if I could—though I must say if, by any sort of process, I could convert 2 & 2 into ''five'', it would give me much greater pleasure."
In
Gilbert and Sullivan
Gilbert and Sullivan was a Victorian era, Victorian-era theatrical partnership of the dramatist W. S. Gilbert (1836–1911) and the composer Arthur Sullivan (1842–1900), who jointly created fourteen comic operas between 1871 and 1896, of which ...
's ''
Princess Ida
''Princess Ida; or, Castle Adamant'' is a comic opera with music by Arthur Sullivan and libretto by W. S. Gilbert. It was their eighth operatic collaboration of fourteen. ''Princess Ida'' opened at the Savoy Theatre on 5 January 1884, for a ru ...
'' (1884), the Princess comments that "The narrow-minded pedant still believes/That two and two make four! Why, we can prove,/We women—household drudges as we are –/That two and two make five—or three—or seven;/Or five-and-twenty, if the case demands!"
Politics, literature, propaganda
France
In the late 18th century, in the pamphlet ''
What is the Third Estate?
''What Is the Third Estate?'' (french: Qu'est-ce que le Tiers-État?) is a political pamphlet written in January 1789, shortly before the outbreak of the French Revolution, by the French writer and clergyman Abbé Emmanuel Joseph Sieyès (1748 ...
'' (1789), about the
legalistic denial of political rights to the common-folk majority of France,
Emmanuel-Joseph Sieyès, said: "Consequently, if it be claimed that, under the French constitution, 200,000 individuals, out of 26 million citizens, constitute two-thirds of the common will, only one comment is possible: It is a claim that two and two make five."
Using the illogic of "two and two make five", Sieyès mocked the
demagoguery
A demagogue (from Greek , a popular leader, a leader of a mob, from , people, populace, the commons + leading, leader) or rabble-rouser is a political leader in a democracy who gains popularity by arousing the common people against elites, ...
of the
Estates-General for assigning disproportionate voting power to the political minorities of France—the
Clergy
Clergy are formal leaders within established religions. Their roles and functions vary in different religious traditions, but usually involve presiding over specific rituals and teaching their religion's doctrines and practices. Some of the ter ...
(First Estate) and the
French nobility
The French nobility (french: la noblesse française) was a privileged social class in France from the Middle Ages until its abolition on June 23, 1790 during the French Revolution.
From 1808 to 1815 during the First Empire the Emperor Napoléo ...
(Second Estate)—in relation to the
Third Estate
The estates of the realm, or three estates, were the broad orders of social hierarchy used in Christendom (Christian Europe) from the Middle Ages to early modern Europe. Different systems for dividing society members into estates developed and ...
, the numeric and political majority of the citizens of France.
In the 19th century, in the novel ''
Séraphîta
''Séraphîta'' () is a French novel by Honoré de Balzac with themes of androgyny. It was published in the ''Revue de Paris'' in 1834. In contrast with the realism of most of the author's best known works, the story delves into the fantastic an ...
'' (1834), about the nature of
androgyny
Androgyny is the possession of both masculine and feminine characteristics. Androgyny may be expressed with regard to biological sex, gender identity, or gender expression.
When ''androgyny'' refers to mixed biological sex characteristics in ...
,
Honoré de Balzac
Honoré de Balzac ( , more commonly , ; born Honoré Balzac;Jean-Louis Dega, La vie prodigieuse de Bernard-François Balssa, père d'Honoré de Balzac : Aux sources historiques de La Comédie humaine, Rodez, Subervie, 1998, 665 p. 20 May 179 ...
said:
In the pamphlet "
Napoléon le Petit
''Napoléon le Petit'' (French; literally "Napoleon the Small") was an influential political pamphlet by Victor Hugo, published in 1852. It criticised the rule of Napoleon III and the politics of the Second French Empire for which he left Belgium, ...
" (1852), about the limitations of the
Second French Empire
The Second French Empire (; officially the French Empire, ), was the 18-year Empire, Imperial Bonapartist regime of Napoleon III from 14 January 1852 to 27 October 1870, between the French Second Republic, Second and the French Third Republic ...
(1852–1870), such as majority political support for the monarchist ''coup d'Ḗtat'', which installed
Napoleon III
Napoleon III (Charles Louis Napoléon Bonaparte; 20 April 18089 January 1873) was the first President of France (as Louis-Napoléon Bonaparte) from 1848 to 1852 and the last monarch of France as Emperor of the French from 1852 to 1870. A nephew ...
(r. 1852–1870), and the French peoples' discarding from national politics the
liberal values
Liberalism is a political and moral philosophy based on the rights of the individual, liberty, consent of the governed, political equality and equality before the law."political rationalism, hostility to autocracy, cultural distaste for c ...
that informed the anti-monarchist Revolution,
Victor Hugo
Victor-Marie Hugo (; 26 February 1802 – 22 May 1885) was a French Romantic writer and politician. During a literary career that spanned more than sixty years, he wrote in a variety of genres and forms. He is considered to be one of the great ...
said: "Now, get seven million, five hundred thousand votes to declare that two-and-two-make-five, that the straight line is the longest road, that the whole is less than its part; get it declared by eight millions, by ten millions, by a hundred millions of votes, you will not have advanced a step."
Russia
In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because
political violence
Political violence is violence which is perpetrated in order to achieve political goals. It can include violence which is used by a state against other states (war), violence which is used by a state against civilians and non-state actors (forced ...
characterised much of the
ideological
An ideology is a set of beliefs or philosophies attributed to a person or group of persons, especially those held for reasons that are not purely epistemic, in which "practical elements are as prominent as theoretical ones." Formerly applied prim ...
conflict among proponents of humanist
democracy
Democracy (From grc, δημοκρατία, dēmokratía, ''dēmos'' 'people' and ''kratos'' 'rule') is a form of government in which the people have the authority to deliberate and decide legislation (" direct democracy"), or to choose gov ...
and defenders of
tsarist autocracy
Tsarist autocracy (russian: царское самодержавие, transcr. ''tsarskoye samoderzhaviye''), also called Tsarism, was a form of autocracy (later absolute monarchy) specific to the Grand Duchy of Moscow and its successor states th ...
in Russia. In ''The Reaction in Germany'' (1842),
Mikhail Bakunin
Mikhail Alexandrovich Bakunin (; 1814–1876) was a Russian revolutionary anarchist, socialist and founder of collectivist anarchism. He is considered among the most influential figures of anarchism and a major founder of the revolutionary ...
said that the political compromises of the French
Positivists, at the start of the
July Revolution
The French Revolution of 1830, also known as the July Revolution (french: révolution de Juillet), Second French Revolution, or ("Three Glorious ays), was a second French Revolution after the first in 1789. It led to the overthrow of King ...
(1830), confirmed their
middle-of-the-road mediocrity: "The Left says, 2 times 2 are 4; the Right, 2 times 2 are 6; and the Juste-milieu says, 2 times 2 are 5".
In ''
Notes from Underground
''Notes from Underground'' ( pre-reform Russian: ; post-reform Russian: ; also translated as ''Notes from the Underground'' or ''Letters from the Underworld'') is a novella by Fyodor Dostoevsky, first published in the journal ''Epoch'' in 186 ...
'' (1864), by
Feodor Dostoevsky
Fyodor Mikhailovich Dostoevsky (, ; rus, Фёдор Михайлович Достоевский, Fyódor Mikháylovich Dostoyévskiy, p=ˈfʲɵdər mʲɪˈxajləvʲɪdʑ dəstɐˈjefskʲɪj, a=ru-Dostoevsky.ogg, links=yes; 11 November 18219 ...
, the anonymous protagonist accepts the falsehood of "two plus two equals five", and considers the implications (
ontological
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality.
Ontology addresses questions like how entities are grouped into categories and which of these entities exis ...
and
epistemological
Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics.
Episte ...
) of rejecting the truth of "two times two makes four", and proposed that the
intellectualism
Intellectualism is the mental perspective that emphasizes the use, the development, and the exercise of the intellect; and also identifies the life of the mind of the intellectual person. (Definition) In the field of philosophy, the term ''inte ...
of
free will
Free will is the capacity of agents to choose between different possible courses of action unimpeded.
Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actio ...
—Man's inherent capability to choose or to reject logic and illogic—is the
cognitive ability
Cognitive skills, also called cognitive functions, cognitive abilities or cognitive capacities, are brain-based skills which are needed in acquisition of knowledge, manipulation of information and reasoning. They have more to do with the mechanisms ...
that makes humanity human: "I admit that twice two makes four is an excellent thing, but, if we are to give everything its due, twice two makes five is sometimes a very charming thing, too."
In the
literary vignette "Prayer" (1881),
Ivan Turgenev
Ivan Sergeyevich Turgenev (; rus, links=no, Ива́н Серге́евич Турге́невIn Turgenev's day, his name was written ., p=ɪˈvan sʲɪrˈɡʲe(j)ɪvʲɪtɕ tʊrˈɡʲenʲɪf; 9 November 1818 – 3 September 1883 (Old Style dat ...
said that: "Whatever a man prays for, he prays for a miracle. Every prayer reduces itself to this: 'Great God, grant that twice two be not four'." In ''
God and the State
''God and the State'' (called by its author ''The Historical Sophisms of the Doctrinaire School of Communism'') is an unfinished manuscript by the Russian anarchist philosopher Mikhail Bakunin, published posthumously in 1882. The work criticises ...
'' (1882), Bakunin dismissed
deism
Deism ( or ; derived from the Latin ''deus'', meaning "god") is the Philosophy, philosophical position and Rationalism, rationalistic theology that generally rejects revelation as a source of divine knowledge, and asserts that Empirical evi ...
: "Imagine a philosophical vinegar sauce of the most opposed systems, a mixture of
Fathers of the Church, scholastic philosophers,
Descartes and
Pascal
Pascal, Pascal's or PASCAL may refer to:
People and fictional characters
* Pascal (given name), including a list of people with the name
* Pascal (surname), including a list of people and fictional characters with the name
** Blaise Pascal, Fren ...
,
Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German Philosophy, philosopher and one of the central Age of Enlightenment, Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemolo ...
and Scottish psychologists, all this a superstructure on the divine and innate ideas of
Plato
Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institution ...
, and covered up with a layer of
Hegelian
Georg Wilhelm Friedrich Hegel (; ; 27 August 1770 – 14 November 1831) was a German philosopher. He is one of the most important figures in German idealism and one of the founding figures of modern Western philosophy. His influence extends a ...
immanence, accompanied, of course, by an ignorance, as contemptuous as it is complete, of natural science, and proving, just as two times two make five, the existence of a
personal god
A personal god, or personal goddess, is a deity who can be related to as a person, instead of as an impersonal force, such as the Absolute, "the All", or the "Ground of Being".
In the scriptures of the Abrahamic religions, God is described as b ...
." Moreover, the slogan "two plus two equals five", is the title of the collection of
absurdist short stories ''Deux et deux font cinq'' (''Two and Two Make Five'', 1895), by
Alphonse Allais
Alphonse Allais (20 October 1854 – 28 October 1905) was a French writer, journalist and humorist.
Life
Allais was born in Honfleur, Calvados (department), Calvados. He died in Paris.
Work
He is the author of many collections of whimsical writ ...
;
and the title of the
imagist
Imagism was a movement in early-20th-century Anglo-American poetry that favored precision of imagery and clear, sharp language. It is considered to be the first organized literary modernism, modernist literary movement in the English language. ...
art manifesto ''2 x 2 = 5'' (1920), by the poet
Vadim Shershenevich
Vadim Gabrielevich Shershenevich (russian: Вадим Габриэлевич Шершеневич; 25 January 1893 – 18 May 1942) was a Russian poet. He was highly prolific, working in more than one genre, moving from Symbolism to Futurism aft ...
.
In 1931, the artist supported Stalin's shortened production schedule for the economy of the Soviet Union with a propaganda poster that announced the "Arithmetic of an Alternative Plan: 2 + 2 plus the Enthusiasm of the Workers = 5" after Stalin's announcement, in 1930, that the
first five-year plan
The first five-year plan (russian: I пятилетний план, ) of the Union of Soviet Socialist Republics (USSR) was a list of economic goals, created by Communist Party General Secretary Joseph Stalin, based on his policy of socialism in ...
(1928–1933) instead would be completed in 1932, in four years' time.
George Orwell
George Orwell
Eric Arthur Blair (25 June 1903 – 21 January 1950), better known by his pen name George Orwell, was an English novelist, essayist, journalist, and critic. His work is characterised by lucid prose, social criticism, opposition to totalitar ...
used the idea of 2 + 2 = 5 in an essay of January 1939 in ''
The Adelphi
''The'' () is a grammatical article in English, denoting persons or things already mentioned, under discussion, implied or otherwise presumed familiar to listeners, readers, or speakers. It is the definite article in English. ''The'' is the m ...
''; "Review of ''Power: A New Social Analysis'' by
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
":
In propaganda work for the
BBC #REDIRECT BBC #REDIRECT BBC
Here i going to introduce about the best teacher of my life b BALAJI sir. He is the precious gift that I got befor 2yrs . How has helped and thought all the concept and made my success in the 10th board exam. ...
...
(1939–1945), Orwell applied the illogic of 2 + 2 = 5 to counter the reality-denying psychology of
, which he addressed in the essay "Looking Back on the Spanish War" (1943), indicating that:
In addressing Nazi
'' (1949), concerning the Party's philosophy of government for Oceania, Orwell said:
tweeted: "Theology is not #Mathematics. 2 + 2 in #Theology can make 5. Because it has to do with #God and real #life of #people...." In defence of the priest,
s stated that Spadaro's remark was referring to alleged contradictions among interpretations of the apostolic exhortation ''
'' (2016)—for divorced-remarried Catholics returning to the Church—and the doctrines of
. That a person can freely act in contradiction to Catholic doctrine if he or she felt that God allowed that action—despite the moral and theological contradictions inherent to the action. That Spadaro's "two plus two equal five" comments refer to the Church philosophy that
is insufficient for the full comprehension of God. That Spadaro was much like the
(becoming Catholic to marry a Catholic) is indifferent to ascertaining any aspect of
; Mottram attributes moral and theological contradictions to personal sinfulness.
Former mathematician Kareem Carr has said "when somebody says '2+2=5', I will always ask them for more details rather than dismissing them as an idiot because maybe they are talking about
chickens and turns out that is how chickens work!".