View source for 2 + 2 = 5

{{Short description|Mathematically incorrect slogan}}
{{about||the book by Alphonse Allais|Deux et deux font cinq{{!}}''Deux et deux font cinq''|the Radiohead song|2 + 2 {{=}} 5 (song)|the documentary film|Orwell: 2+2{{=}}5}}
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{{Use British English|date=March 2012}}
{{Use dmy dates|date=July 2020}}
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[[File:Allais - Deux et deux font cinq (2+2=5).djvu|page=7|thumb|''Two Plus Two Make Five'' (1895), by [[Alphonse Allais]], is a collection of [[Absurdist fiction|absurdist]] short stories about [[anti-intellectualism]] as politics.]]

'''2 + 2 = 5''' or '''two plus two equals five''' is a mathematical [[falsehood]] which is used as an example of a simple [[logical error]] that is obvious to anyone familiar with basic [[arithmetic]].

The phrase has been used in various contexts since 1728, and is best known from the 1949 [[dystopia]]n novel ''[[Nineteen Eighty-Four]]'' by [[George Orwell]].

As a theme and as a subject in the arts, the [[Anti-intellectualism|anti-intellectual]] 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]], which is a collection of [[Absurdist fiction|absurdist]] short stories;<ref name="Allais 1895">{{Cite book|title=Deux et deux font cinq (2 + 2 = 5)|last=Allais|first=Alphonse|date=1895|publisher=Ollendorff|language=fr}}</ref> and the 1920 [[imagist]] art manifesto ''2 × 2 = 5'' by the poet [[Vadim Shershenevich]].<ref name="Шершеневич 1920">{{Cite book|title=2 × 2 = 5: листы имажиниста|last=Шершеневич|first=Вадим|date=1920|language=ru}}</ref>

== Self-evident truth and self-evident falsehood ==
{{main|Self-evidence}}

In establishing the mundane reality of the self-evident truth of 2 + 2 = 4, in ''De Neutralibus et Mediis Libellus'' (1652) [[Johann Wigand]] said: "That twice two are four; a man may not lawfully make a doubt of it, because that manner of knowledge is grauen [graven] into mannes [man's] nature."<ref name="Clarendon Press">{{cite book |last1=Wilson |first1=F. P. |year=1970 |title=The Oxford Dictionary of English Proverbs |edition=3rd |location=Oxford |publisher=Clarendon Press |page=849 |isbn=0198691181 }}</ref>

In the comedy-of-manners play ''[[Dom Juan|Dom Juan, or The Feast with the Statue]]'' (1665), by [[Molière]], the [[Libertinism|libertine]] [[protagonist]], Dom Juan, is asked in what [[values]] he believes, and answers that he believes "two plus two equals four".<ref>{{cite web |url=http://moliere-in-english.com/donjuan.html |title=Moliere Don Juan Adapted by Timothy Mooney |publisher=Moliere-in-english.com |access-date=1 February 2012 |archive-url=https://web.archive.org/web/20120301171143/http://moliere-in-english.com/donjuan.html |archive-date=1 March 2012 |url-status=dead }}</ref>

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]]'' (1728), by [[Ephraim Chambers]]: "Thus, a Proposition would be ''absurd'', that should affirm, that two and two make five; or that should deny 'em to make four."<ref>{{cite book |last1=Chambers |first1=Ephraim |year=1728 |title=Cyclopaedia; or, an Universal Dictionary of Arts and Sciences . . .Volume the First |url=https://upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Cyclopaedia%2C_Chambers_-_Volume_1.djvu/page56-2096px-Cyclopaedia%2C_Chambers_-_Volume_1.djvu.jpg |location=London |publisher=James and John Knapton et al. |page=11 |access-date=25 December 2016 }}</ref> In 1779, [[Samuel Johnson]] likewise said that "You may have a reason why two and two should make five, but they will still make but four."<ref name="Clarendon Press"/>

In the 19th century, in a personal letter to his future wife, [[Anne Isabella Byron, Baroness Byron|Anabella Milbanke]], [[Lord Byron]] 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."<ref>{{cite book|title=Alas! the Love of Women: 1813–1814|author-link=Lord Byron|last=Byron|first=George Gordon|year=1974|editor=Leslie A. Marchand|url=https://books.google.com/books?id=EnZ9c4KvQQEC&pg=PA159|orig-year=Written 1813–1814 |publisher=[[Harvard University Press|Belknap Press]]|page=159|isbn=9780674089426}}</ref>

In [[Gilbert and Sullivan]]'s ''[[Princess Ida]]'' (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!"<ref name="Bradley">{{cite book|last1=Bradley|first1=Ian|title=The Complete Annotated Gilbert and Sullivan|year=2016|publisher=Oxford|page=555}}</ref>

== Politics, literature, propaganda ==
=== France ===
[[File:Emmanuel Joseph Sieyès - crop.jpg|thumb|right|250px|In the political pamphlet "What is the Third Estate?" (1789), Emmanuel-Joseph Sieyès provided the humanist bases for the French Revolution (1789–1799).]]
In the late 18th century, in the pamphlet ''[[What is the Third Estate?]]'' (1789), about the [[Interpretivism (legal)|legalistic]] denial of political rights to the common-folk majority of France, [[Emmanuel Joseph Sieyès|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]] of the [[Estates General (France)|Estates-General]] for assigning disproportionate voting power to the political minorities of France—the [[Clergy]] (First Estate) and the [[French nobility]] (Second Estate)—in relation to the [[Estates of the realm#Third Estate|Third Estate]], the numeric and political majority of the citizens of France.<ref name="BakerBoyer1987">{{cite book|author1=Keith M. Baker|author2=John W. Boyer|author3=Julius Kirshner|title=University of Chicago Readings in Western Civilization, Volume 7: The Old Regime and the French Revolution|url=https://books.google.com/books?id=z5MelCA-zzIC&pg=PA154|date=15 May 1987|publisher=University of Chicago Press|isbn=978-0-226-06950-0|page=154}}</ref>

In the 19th century, in the novel ''[[Séraphîta]]'' (1834), about the nature of [[androgyny]], [[Honoré de Balzac]] said:
{{quote|Thus, you will never find, in all Nature, two identical objects; in the natural order, therefore, two and two can never make four, for, to attain that result, we must combine units that are exactly alike, and you know that it is impossible to find two leaves alike on the same tree, or two identical individuals in the same species of tree.

That axiom of your numeration, false in visible nature, is false likewise in the invisible universe of your abstractions, where the same variety is found in your ideas, which are the objects of the visible world extended by their interrelations; indeed, the differences are more striking there than elsewhere.<ref>{{Cite book|url=http://www.gutenberg.org/ebooks/1432|title=Seraphita by Honoré de Balzac}}</ref>}}

In the pamphlet "[[Napoléon le Petit]]" (1852), about the limitations of the [[Second French Empire]] (1852–1870), such as majority political support for the monarchist ''coup d'Ḗtat'', which installed [[Napoleon III]] (r. 1852–1870), and the French peoples' discarding from national politics the [[Liberalism|liberal values]] that informed the anti-monarchist Revolution, [[Victor Hugo]] 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."<ref name="Roderick T. Long">{{cite web|last=Long|first=Roderick T.|title=Victor Hugo on the Limits of Democracy|url=http://www.lewrockwell.com/long/long12.html|access-date=5 December 2011|archive-url=https://web.archive.org/web/20120115115619/http://www.lewrockwell.com/long/long12.html|archive-date=15 January 2012|url-status=dead}}</ref>

In [[The Plague (novel)|''The Plague'']] (1947), French philosopher [[Albert Camus]] declared that times came in history when those who dared to say that 2 + 2 = 4 rather than 2 + 2 = 5 were put to death.

=== Russia ===
[[File:Yakov Guminer - Arithmetic of a counter-plan poster (1931).jpg|thumb|Soviet propaganda: The "Arithmetic of an Alternative Plan: 2 + 2 plus the Enthusiasm of the Workers = 5" exhorts the workers of the Soviet Union to realise five years of production in four years' time (Iakov Guminer, 1931).]]
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 [[Terrorism|political violence]] characterised much of the [[Ideology|ideological]] conflict among proponents of humanist [[democracy]] and defenders of [[tsarist autocracy]] in Russia.<ref>e.g. ''Novoe vremia'' newspaper ("New Times"), 31 October 1900.</ref> In ''The Reaction in Germany'' (1842), [[Mikhail Bakunin]] said that the political compromises of the French [[Positivism|Positivists]], at the start of the [[July Revolution]] (1830), confirmed their [[Juste milieu|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".<ref>{{cite book|last1=Bakunin|first1=Mikhail Aleksandrovich|title=Selected writings|year=1974|location=New York |publisher=Grove Press |others=distributed by Random House|isbn=9780394178738|url=https://books.google.com/books?id=jXpuAAAAIAAJ|language=en}}</ref><ref>{{cite web|url=https://archive.org/details/al_Michail_Bakunin_The_Reaction_in_Germany_From_the_Notebooks_of_a_Frenchman_a4|title=The Reaction in Germany From the Notebooks of a Frenchman|publisher=The Anarchist Library|year=1842|first=Michail|last=Bakunin|via=Internet Archive}}</ref><ref>{{cite book|last1=Meyers|first1=Jeffrey|title=Orwell: Life and Art|date=2010|publisher=University of Illinois Press|isbn=9780252090226|page=149|url=https://books.google.com/books?id=eUQ1Z12trIEC&pg=PA149|language=en}}</ref>

In ''[[Notes from Underground]]'' (1864), by [[Feodor Dostoevsky]], the anonymous protagonist accepts the falsehood of "two plus two equals five", and considers the implications ([[Ontology|ontological]] and [[Epistemology|epistemological]]) of rejecting the truth of "two times two makes four", and proposed that the [[intellectualism]] of [[free will]]—Man's inherent capability to choose or to reject logic and illogic—is the [[Cognition|cognitive ability]] 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."<ref>{{Cite web|url=http://www.classicreader.com/book/414/10/|title=Notes from the Underground: Part I: Chapter IX by Fyodor Dostoevsky|website=Classic Reader|access-date=2018-05-22}}</ref>

In the [[Vignette (literature)|literary vignette]] "Prayer" (1881), [[Ivan Turgenev]] 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'."<ref>Turgenev, Ivan ''Dream Tales and Poems'', p. 102</ref> In ''[[God and the State]]'' (1882), Bakunin dismissed [[deism]]: "Imagine a philosophical vinegar sauce of the most opposed systems, a mixture of [[Church Fathers|Fathers of the Church]], scholastic philosophers, [[Descartes]] and [[Blaise Pascal|Pascal]], [[Immanuel Kant|Kant]] and Scottish psychologists, all this a superstructure on the divine and innate ideas of [[Plato]], and covered up with a layer of [[Hegelian]] 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|personal god]]."<ref>{{cite book|title=The Communist Manifesto and Other Revolutionary Writings |publisher=[[Dover Publications]]|year=2003|isbn=0486424650|page=199|url=https://books.google.com/books?id=7bT1gfI3jjkC&pg=PA199}}</ref> Moreover, the slogan "two plus two equals five", is the title of the collection of [[Absurdist fiction|absurdist]] short stories ''Deux et deux font cinq'' (''Two and Two Make Five'', 1895), by [[Alphonse Allais]];<ref name="Allais 1895"/> and the title of the [[imagist]] art manifesto ''2 x 2 = 5'' (1920), by the poet [[Vadim Shershenevich]].<ref name="Шершеневич 1920"/>

In 1931, the artist {{ill|Yakov Guminer|ru|Гуминер, Яков Моисеевич}} 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 (Soviet Union)|first five-year plan]] (1928–1933) instead would be completed in 1932, in four years' time.<ref name='Stalin"1930"'>{{cite book|last1=Stalin|first1=Joseph|title=Political Report of the Central Committee to the Sixteenth Congress of the C.P.S.U.(B.)|date=June 1930|publisher=Pravda, No. 177|url=https://www.marxists.org/reference/archive/stalin/works/1930/aug/27.htm|access-date=10 October 2014}}</ref>

== George Orwell ==
[[File:George-orwell-BBC.jpg|thumb|right|upright|The anti-Nazi propagandist George Orwell, at the BBC during the Second World War (1939–1945)]]
{{See also|Doublespeak}}

In Orwell's ''[[Nineteen Eighty-Four]]'', it appears as a possible statement of [[Ingsoc]] (English Socialism). The Party (i.e. a [[political party]]) slogan "War Is Peace, Freedom Is Slavery, Ignorance Is Strength" is a [[dogma]] which the Party expects the citizens of [[Nations of Nineteen Eighty-Four|Oceania]] to accept as true. Writing in his secret diary in the year 1984, the protagonist [[Winston Smith (Nineteen Eighty-Four)|Winston Smith]] ponders if the Inner Party might declare "two plus two equals five" as fact, as well as whether or not belief in such a [[consensus reality]] substantiates the lie.<ref name="Orwell 1949">{{cite book| last= Orwell| first= George |title= Nineteen Eighty-Four| year= 1949| chapter= Part Three, Chapter Two| url= http://www.george-orwell.org/1984/18.html| via= george-orwell.org| access-date= }}</ref> About the falsity of "two plus two equals five", in the [[Ministries_in_Nineteen_Eighty-Four#Ministry_of_Love|Ministry of Love]], the interrogator [[O'Brien (Nineteen Eighty-Four)|O'Brien]] tells the [[Thoughtcrime|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]]: "Sometimes, Winston. [Sometimes it is four fingers.] Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once".<ref name="Orwell 1949"/>

[[George Orwell]] used the idea of 2 + 2 = 5 in an essay of January 1939 in ''[[The Adelphi]]''; "Review of ''Power: A New Social Analysis'' by [[Bertrand Russell]]":<ref>{{Cite web|last=Orwell|first=George|date=January 1939|title=Review of Power: A New Social Analysis by Bertrand Russell|url=https://www.lehman.edu/faculty/rcarey/BRSQ/06may.orwell.htm|access-date=30 December 2020|website=}}</ref>

{{quote|It is quite possible that we are descending into an age in which two plus two will make five when the Leader says so.|author=|title=|source=|url=}}

In propaganda work for the [[BBC]] (British Broadcasting Corporation) during the [[World War II|Second World War]] (1939–1945), Orwell applied the illogic of 2 + 2 = 5 to counter the reality-denying psychology of [[Nazi propaganda]], which he addressed in the essay "Looking Back on the Spanish War" (1943), indicating that:

{{quote|Nazi theory, indeed, specifically denies that such a thing as "the truth" exists. There is, for instance, no such thing as "Science". There is only "German Science", "Jewish Science", etc. The implied objective of this line of thought is a nightmare world in which the Leader, or some ruling clique, controls not only the future, but ''the past''. If the Leader says of such and such an event, "It never happened"—well, it never happened. If he says that "two and two are five"—well, two and two are five. This prospect frightens me much more than bombs—and, after our experiences of the last few years [the [[The Blitz|Blitz]], 1940–41] that is not a frivolous statement.<ref name=lookingback>{{cite web|title=Looking Back on the Spanish War|author-link=George Orwell|last=Orwell|first=George|publisher=orwell.ru|url=http://orwell.ru/library/essays/Spanish_War/english/esw_1}}</ref>}}

In addressing Nazi [[anti-intellectualism]], Orwell's reference might have been [[Hermann Göring]]'s hyperbolic praise of [[Adolf Hitler]]: "If the [[Führer]] wants it, two and two makes five!"<ref>{{cite web|title=Hermann Göring|work=Museum of Tolerance Multimedia Learning Center|url=http://motlc.wiesenthal.com/text/x18/xr1883.html|access-date=18 February 2012|archive-url=https://web.archive.org/web/20041227105306/http://motlc.wiesenthal.com/text/x18/xr1883.html|archive-date=27 December 2004|url-status=dead}}</ref> In the political novel ''[[Nineteen Eighty-Four]]'' (1949), concerning the Party's philosophy of government for Oceania, Orwell said:

{{quote|In the end, the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four?  Or that the force of gravity works?  Or that the past is unchangeable?  If both the past and the external world exist only in the mind, and if the mind itself is controllable—what then?<ref>Orwell, George ''Nineteen Eighty-Four'' (1949), {{ISBN|0-452-28423-6}}</ref>}}

The 1951 British edition of the text, published by [[Secker & Warburg]], erroneously omitted the "5", thus rendering it simply as "2 + 2 =". This error, likely the result of a typesetting mistake, remained in all further editions of the text until the 1987 edition, whereafter a correction was made based on Orwell's original typescript.<ref>{{Cite book |last=Orwell |first=George |title=Nineteen Eighty-Four |contributor-last=Davison |contributor-first=Peter |contributor-link=Peter Davison (literary scholar) |date=2013 |publisher=Penguin Books |location=London |page=xix |contribution=A Note on the Text |orig-year=1989 |edition=Annotated |series=[[Penguin Classics|Penguin Modern Classics]] |isbn=978-0141391700}}</ref> This misprint did not exist in the American editions of the text, with British students of the text in the meanwhile misinterpreting Orwell's original intentions.<ref>{{Cite news |last=Thomas |first=Jo |date=1986-03-08 |title=New, Uncensored Edition of Orwell |url=https://www.nytimes.com/1986/03/08/books/new-uncensored-edition-of-orwell.html |access-date=2025-02-15 |work=The New York Times |language=en-US |issn=0362-4331}}</ref>

== Contemporary usage ==

[[File:2plus2havanagrafiti-IMG 20191212 123234734.jpg|thumb|Political graffiti in [[Havana]], Cuba questioning government policy perceived to be "2+2=5"]]
In ''[[The Cult of the Amateur|The Cult of the Amateur: How Today's Internet is Killing Our Culture]]'' (2007), the media critic [[Andrew Keen]] uses the slogan "two plus two equals five" to criticise the [[Wikipedia]] policy allowing any user to edit the [[encyclopedia]] — that the enthusiasm of the amateur for [[user generated content]], [[peer production]], and [[Web 2.0]] technology leads to an encyclopedia of [[common knowledge]], and not an encyclopedia of [[expert|expert knowledge]]; that the "[[wisdom of the crowd]]" will distort what society considers to be the [[truth]].<ref>{{cite book|last1=Keen|first1=Andrew|title=The Cult of the Amateur| year= 2007 |publisher= Doubleday |pages= 39–40, 44}}</ref>

In 2020, a [[social networking service|social media]] debate followed [[biostatistics]] PhD student Kareem Carr's statement, "If someone says 2+2=5, the correct response is, 'What are your definitions and axioms?' not a rant about the decline of Western civilization".<ref>{{Cite web|last1=Delbert|first1=Caroline|date=2020-08-07|title=Why Some People Think 2+2=5 ...and why they're right.|url=https://www.popularmechanics.com/science/math/a33547137/why-some-people-think-2-plus-2-equals-5/|access-date=2021-01-16|website=[[Popular Mechanics]]}}</ref>

== See also ==
* ''[[One Plus One Equals Three]]''
* [[1=2]]
* [[Indiana pi bill]]

== References ==
{{Reflist|colwidth=30em}}

== Further reading ==
* {{Citation |last=Euler |first=Houston |others=Reviewed by Andy Olson |year=1990 |title=The history of 2 + 2 = 5 |journal=Mathematics Magazine |volume=63 |number=5 |pages=338–339 |doi=10.2307/2690909|jstor=2690909 }}
* {{Citation |last1=Krueger |first1=L. E. |name-list-style=amp |first2=E. W. |last2=Hallford |year=1984 |title=Why 2 + 2 = 5 looks so wrong: On the odd-even rule in sum verification |journal=Memory & Cognition |volume=12 |issue=2 |pages=171–180 |pmid=6727639 |doi=10.3758/bf03198431|doi-access=free }}

== External links ==
* [https://archive.today/20130105041501/http://www.time.com/time/printout/0,8816,854746,00.html "Two Plus Two Equals Red"], ''Time'' Magazine, Monday, 30 Jun 1947
* Moore, Darcy (2020). [https://www.darcymoore.net/2020/03/07/22/ 2+2=]. Discusses the textual variation of the statement in Orwell's works
{{Nineteen Eighty-Four}}

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[[Category:Fictional elements introduced in 1949]]
[[Category:Nineteen Eighty-Four]]
[[Category:Mind control]]
[[Category:Communication of falsehoods]]
[[Category:Addition]]
[[Category:Quotations from literature]]
[[Category:1949 quotations]]
[[Category:Science fiction catchphrases]]
[[Category:Pseudomathematics]]