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==Mathematics ==
==Mathematics ==
There are four elementary arithmetic [[Operation (mathematics)|operations]] in mathematics: [[addition]] ('''+'''), [[subtraction]] ('''−'''), [[multiplication]] ('''×'''), and [[Division (mathematics)|division]] ('''÷''').{{Citation needed|date=August 2024}}
Four is the smallest [[composite number]], its proper [[divisor]]s being {{num|1}} and {{num|2}}.<ref>{{Cite book| last=Fiore | first=Gregory | url=https://books.google.com/books?id=moE01lKtPJcC&q=Four+is+the+smallest+composite+number,|title=Basic mathematics for college students: concepts and applications|date=1993-08-01|publisher=HarperCollins College | isbn=978-0-06-042046-8 |pages=162|language=en|quote=The smallest composite number is 4.}}</ref> Four is the sum and product of [[two]] with itself: <math>2+2=4=2\times 2</math>, the only non-zero number <math>b</math> such that <math>a+a=b=a\times a</math>. Four is also the smallest and only even squared [[prime number]] <math>2^{2}</math>. Also,


[[Lagrange's four-square theorem]] states that every positive integer can be written as the sum of at most four [[square number|square]]s.<ref>{{Citation|last=Spencer|first=Joel|title=Four Squares with Few Squares|year=1996|work=Number Theory: New York Seminar 1991–1995|pages=295–297|editor-last=Chudnovsky|editor-first=David V.|place=New York, NY|publisher=Springer US| language=en|doi=10.1007/978-1-4612-2418-1_22|isbn=978-1-4612-2418-1|editor2-last=Chudnovsky|editor2-first=Gregory V.|editor3-last=Nathanson|editor3-first=Melvyn B.}}</ref><ref>{{Cite book|last=Peterson|first=Ivars|url=https://books.google.com/books?id=4gWSAraVhtAC&q=7+for+instance+cannot+be+written+as+the+sum+of+three+squares.&pg=PA95|title=Mathematical Treks: From Surreal Numbers to Magic Circles|date=2002|publisher=MAA|isbn=978-0-88385-537-9|pages=95|language=en|quote=7 is an example of an integer that can't be written as the sum of three squares.}}</ref> Four is one of four [[Harshad number|all-Harshad number]]s. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. <math>4x=y^{2}-z^{2}</math>.
* In [[Knuth's up-arrow notation]], <math>2+2=2\times2=2^{2}=2\uparrow\uparrow 2=2\uparrow\uparrow\uparrow2=\;...\; = 4</math>, and so forth, for any number of up arrows.<ref>{{Cite book|last=Hodges|first=Andrew| url=https://books.google.com/books?id=HOcpgfiDu40C&q=2+%E2%86%91%E2%86%91+2&pg=PA249|title=One to Nine: The Inner Life of Numbers| date=2008-05-17|publisher=W. W. Norton & Company|isbn=978-0-393-06863-4|pages=249|language=en|quote=2 ↑↑ ... ↑↑ 2 is always 4}}</ref> By consequence, four is the only square one more than a prime number, specifically [[3|three]].
* The sum of the first four prime numbers [[2|two]] + [[3|three]] + [[5|five]] + [[7|seven]] is the only sum of four consecutive prime numbers that yields an [[Parity (mathematics)|odd]] prime number, [[17 (number)|seventeen]], which is the fourth [[super-prime]]. Four lies between the first proper pair of [[twin primes]], [[3|three]] and [[5|five]], which are the first two [[Fermat prime]]s, like [[17 (number)|seventeen]], which is the third. On the other hand, the [[Square (algebra)|square]] of four (<math>4^2</math>), equivalently the [[fourth power]] of two (<math>2^4</math>), is [[16 (number)|sixteen]]; the only number that has <math>a^{b}=b^{a}</math> as a form of [[factorization]].

There are four elementary arithmetic [[Operation (mathematics)|operations]] in mathematics: [[addition]] ('''+'''), [[subtraction]] ('''−'''), [[multiplication]] ('''×'''), and [[Division (mathematics)|division]] ('''÷''').

Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. <math>4x=y^{2}-z^{2}</math>.{{Citation needed|date=August 2024}} A number is a multiple of 4 if its last two digits are a multiple of 4 (for example, 1092 is a multiple of 4 because {{nowrap|1=92 = 4 × 23}}).<ref>{{Cite book|author=Kaplan Test Prep| url=https://books.google.com/books?id=D_rLDQAAQBAJ&q=last+two+digits+are+a+multiple+of+4&pg=PA289|title=SAT Subject Test Mathematics Level 1|date=2017-01-03|publisher=Simon and Schuster|isbn=978-1-5062-0922-7|pages=289|language=en|quote=An integer is divisible by 4 if the last two digits form a multiple of 4.}}</ref>

[[Lagrange's four-square theorem]] states that every positive integer can be written as the sum of at most four [[square number]]s.<ref>{{Citation|last=Spencer|first=Joel|title=Four Squares with Few Squares|year=1996|work=Number Theory: New York Seminar 1991–1995|pages=295–297|editor-last=Chudnovsky|editor-first=David V.|place=New York, NY|publisher=Springer US| language=en|doi=10.1007/978-1-4612-2418-1_22|isbn=978-1-4612-2418-1|editor2-last=Chudnovsky|editor2-first=Gregory V.|editor3-last=Nathanson|editor3-first=Melvyn B.}}</ref> Three are not always sufficient; {{num|7}} for instance cannot be written as the sum of three squares.<ref>{{Cite book|last=Peterson|first=Ivars|url=https://books.google.com/books?id=4gWSAraVhtAC&q=7+for+instance+cannot+be+written+as+the+sum+of+three+squares.&pg=PA95|title=Mathematical Treks: From Surreal Numbers to Magic Circles|date=2002|publisher=MAA|isbn=978-0-88385-537-9|pages=95|language=en|quote=7 is an example of an integer that can't be written as the sum of three squares.}}</ref>

Four is one of four [[Harshad number|all-Harshad number]]s.


A four-sided plane figure is a [[quadrilateral]] or quadrangle, sometimes also called a ''tetragon''. It can be further classified as a [[rectangle]] or ''oblong'', [[kite]], [[rhombus]], and [[square]].
A four-sided plane figure is a [[quadrilateral]] or quadrangle, sometimes also called a ''tetragon''. It can be further classified as a [[rectangle]] or ''oblong'', [[kite]], [[rhombus]], and [[square]].
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The [[four-color theorem]] states that a [[planar graph]] (or, equivalently, a flat [[map]] of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.<ref>{{cite book |first=Bryan |last=Bunch |title=The Kingdom of Infinite Number |location=New York |publisher=W. H. Freeman & Company |year=2000 |page=48}}</ref> Three colors are not, in general, sufficient to guarantee this.<ref>{{Cite book|last=Ben-Menahem|first=Ari|url=https://books.google.com/books?id=9tUrarQYhKMC&q=three+colors+map+not+enough&pg=PA2147|title=Historical Encyclopedia of Natural and Mathematical Sciences|date=2009-03-06|publisher=Springer Science & Business Media| isbn=978-3-540-68831-0|pages=2147|language=en|quote=(i.e. That there are maps for which three colors are not sufficient)}}</ref> The largest planar [[complete graph]] has four vertices.<ref>{{Cite book|last=Molitierno|first=Jason J.| url=https://books.google.com/books?id=2kvNBQAAQBAJ&q=largest+planar+complete+graph+has+four+vertices&pg=PA197| title=Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs|date=2016-04-19|publisher=CRC Press| isbn=978-1-4398-6339-8|pages=197|language=en|quote=... The complete graph on the largest number of vertices that is planar is K4 and that a(K4) equals 4.}}</ref>
The [[four-color theorem]] states that a [[planar graph]] (or, equivalently, a flat [[map]] of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.<ref>{{cite book |first=Bryan |last=Bunch |title=The Kingdom of Infinite Number |location=New York |publisher=W. H. Freeman & Company |year=2000 |page=48}}</ref> Three colors are not, in general, sufficient to guarantee this.<ref>{{Cite book|last=Ben-Menahem|first=Ari|url=https://books.google.com/books?id=9tUrarQYhKMC&q=three+colors+map+not+enough&pg=PA2147|title=Historical Encyclopedia of Natural and Mathematical Sciences|date=2009-03-06|publisher=Springer Science & Business Media| isbn=978-3-540-68831-0|pages=2147|language=en|quote=(i.e. That there are maps for which three colors are not sufficient)}}</ref> The largest planar [[complete graph]] has four vertices.<ref>{{Cite book|last=Molitierno|first=Jason J.| url=https://books.google.com/books?id=2kvNBQAAQBAJ&q=largest+planar+complete+graph+has+four+vertices&pg=PA197| title=Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs|date=2016-04-19|publisher=CRC Press| isbn=978-1-4398-6339-8|pages=197|language=en|quote=... The complete graph on the largest number of vertices that is planar is K4 and that a(K4) equals 4.}}</ref>


A solid figure with four faces as well as four vertices is a [[tetrahedron]], which is the smallest possible number of faces and vertices a [[polyhedron]] can have.<ref>{{Cite book|last1=Grossnickle|first1=Foster Earl|url=https://books.google.com/books?id=Q2474oSAsc4C&q=4+is+the+smallest+possible+number+of+faces+(as+well+as+vertices)+of+a+polyhedron.|title=Discovering Meanings in Elementary School Mathematics|last2=Reckzeh|first2=John|date=1968|publisher=Holt, Rinehart and Winston|pages=337|isbn=9780030676451|language=en|quote=...the smallest possible number of faces that a polyhedron may have is four}}</ref> The regular tetrahedron, also called a 3-[[simplex]], is the simplest [[Platonic solid]].<ref>{{Cite book|last1=Grossnickle|first1=Foster Earl|url=https://books.google.com/books?id=Q2474oSAsc4C&q=4+is+the+smallest+possible+number+of+faces+(as+well+as+vertices)+of+a+polyhedron.|title=Discovering Meanings in Elementary School Mathematics|last2=Reckzeh|first2=John|date=1968|publisher=Holt, Rinehart and Winston|pages=337|isbn=9780030676451|language=en|quote=...face of the platonic solid. The simplest of these shapes is the tetrahedron...}}</ref> It has four [[regular triangle]]s as faces that are themselves at [[self-dual polytope|dual positions]] with the vertices of another tetrahedron.<ref>{{Cite book|last1=Hilbert|first1=David|url=https://books.google.com/books?id=7WY5AAAAQBAJ&q=self-dual+regular+polyhedron&pg=PA143|title=Geometry and the Imagination|last2=Cohn-Vossen |first2=Stephan |date=1999|publisher=American Mathematical Soc.|isbn=978-0-8218-1998-2|pages=143|language=en|quote=...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...}}</ref> Tetrahedra can be inscribed inside all other four Platonic solids, and [[Tessellation|tessellate space]] alongside the [[regular octahedron]] in the [[alternated cubic honeycomb]].
A solid figure with four faces as well as four vertices is a [[tetrahedron]], which is the smallest possible number of faces and vertices a [[polyhedron]] can have.<ref>{{Cite book|last1=Grossnickle|first1=Foster Earl|url=https://books.google.com/books?id=Q2474oSAsc4C&q=4+is+the+smallest+possible+number+of+faces+(as+well+as+vertices)+of+a+polyhedron.|title=Discovering Meanings in Elementary School Mathematics|last2=Reckzeh|first2=John|date=1968|publisher=Holt, Rinehart and Winston|pages=337|isbn=9780030676451|language=en|quote=...the smallest possible number of faces that a polyhedron may have is four}}</ref> The regular tetrahedron, also called a 3-[[simplex]], is the simplest [[Platonic solid]].<ref>{{Cite book|last1=Grossnickle|first1=Foster Earl|url=https://books.google.com/books?id=Q2474oSAsc4C&q=4+is+the+smallest+possible+number+of+faces+(as+well+as+vertices)+of+a+polyhedron.|title=Discovering Meanings in Elementary School Mathematics|last2=Reckzeh|first2=John|date=1968|publisher=Holt, Rinehart and Winston|pages=337|isbn=9780030676451|language=en|quote=...face of the platonic solid. The simplest of these shapes is the tetrahedron...}}</ref> It has four [[regular triangle]]s as faces that are themselves at [[self-dual polytope|dual positions]] with the vertices of another tetrahedron.<ref>{{Cite book|last1=Hilbert|first1=David|url=https://books.google.com/books?id=7WY5AAAAQBAJ&q=self-dual+regular+polyhedron&pg=PA143|title=Geometry and the Imagination|last2=Cohn-Vossen |first2=Stephan |date=1999|publisher=American Mathematical Soc.|isbn=978-0-8218-1998-2|pages=143|language=en|quote=...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...}}</ref> The tetrahedron is one of three [[Regular polyhedron|regular polyhedra]] that [[Tessellation|tessellate space]].{{Citation needed}}


The smallest non-[[cyclic group]] has four elements; it is the [[Klein four-group]].<ref>{{Cite book|first=Jeremy|last=Horne|url=https://books.google.com/books?id=ZfYoDwAAQBAJ&pg=PA299|title=Philosophical Perceptions on Logic and Order|date=2017-05-19|publisher=IGI Global|isbn=978-1-5225-2444-1|pages=299|language=en|quote=The Klein four-group is the smallest noncyclic group,...|access-date=31 October 2022|archive-date=31 October 2022|archive-url=https://web.archive.org/web/20221031005437/https://books.google.com/books?id=ZfYoDwAAQBAJ&pg=PA299|url-status=live}}</ref> ''A{{sub|n}}'' [[alternating group]]s are not [[simple group|simple]] for values <math>n</math> ≤ <math>4</math>.
The smallest non-[[cyclic group]] has four elements; it is the [[Klein four-group]].<ref>{{Cite book|first=Jeremy|last=Horne|url=https://books.google.com/books?id=ZfYoDwAAQBAJ&pg=PA299|title=Philosophical Perceptions on Logic and Order|date=2017-05-19|publisher=IGI Global|isbn=978-1-5225-2444-1|pages=299|language=en|quote=The Klein four-group is the smallest noncyclic group,...|access-date=31 October 2022|archive-date=31 October 2022|archive-url=https://web.archive.org/web/20221031005437/https://books.google.com/books?id=ZfYoDwAAQBAJ&pg=PA299|url-status=live}}</ref> ''A{{sub|n}}'' [[alternating group]]s are not [[simple group|simple]] for values <math>n</math> ≤ <math>4</math>.
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They are defined as locally trivial [[fibration]]s that map <math>f : S^{2n-1} \rightarrow S^{n}</math> for values of <math>n=2,4,8</math> (aside from the trivial fibration mapping between two [[Point (geometry)|points]] and a [[circle]]).<ref>{{Cite book |last=Shokurov |first= A.V. |editor=Michiel Hazewinkel |editor-link=Michiel Hazewinkel |chapter=Hopf fibration |title=Encyclopedia of Mathematics |publisher=[[European Mathematical Society]] |location=Helsinki |chapter-url=https://encyclopediaofmath.org/wiki/Hopf_fibration |year=2002 |isbn=1402006098 |oclc=1013220521 |access-date=2023-04-30 |archive-date=1 May 2023 |archive-url=https://web.archive.org/web/20230501005558/https://encyclopediaofmath.org/wiki/Hopf_fibration |url-status=live }}</ref>
They are defined as locally trivial [[fibration]]s that map <math>f : S^{2n-1} \rightarrow S^{n}</math> for values of <math>n=2,4,8</math> (aside from the trivial fibration mapping between two [[Point (geometry)|points]] and a [[circle]]).<ref>{{Cite book |last=Shokurov |first= A.V. |editor=Michiel Hazewinkel |editor-link=Michiel Hazewinkel |chapter=Hopf fibration |title=Encyclopedia of Mathematics |publisher=[[European Mathematical Society]] |location=Helsinki |chapter-url=https://encyclopediaofmath.org/wiki/Hopf_fibration |year=2002 |isbn=1402006098 |oclc=1013220521 |access-date=2023-04-30 |archive-date=1 May 2023 |archive-url=https://web.archive.org/web/20230501005558/https://encyclopediaofmath.org/wiki/Hopf_fibration |url-status=live }}</ref>


In [[Knuth's up-arrow notation]], <math>2+2=2\times2=2^{2}=2\uparrow\uparrow 2=2\uparrow\uparrow\uparrow2=\;...\; = 4</math>, and so forth, for any number of up arrows.<ref>{{Cite book |last=Hodges |first=Andrew |url=https://books.google.com/books?id=HOcpgfiDu40C&q=2+%E2%86%91%E2%86%91+2&pg=PA249 |title=One to Nine: The Inner Life of Numbers |date=2008-05-17 |publisher=W. W. Norton & Company |isbn=978-0-393-06863-4 |pages=249 |language=en |quote=2 ↑↑ ... ↑↑ 2 is always 4}}</ref>
The [[1|unit]] (1) is the fourth distinct entry in the [[continued fraction]] for [[pi]] (<math>\pi</math>), by order of appearances of entries.<ref>{{Cite OEIS |A154883 |Distinct entries in continued fraction for Pi in the order of their appearance. |access-date=2024-06-16 }}</ref>


==List of basic calculations==
==List of basic calculations==

Revision as of 14:46, 29 August 2024

← 3 4 5 →
−1 0 1 2 3 4 5 6 7 8 9
Cardinalfour
Ordinal4th
(fourth)
Numeral systemquaternary
Factorization22
Divisors1, 2, 4
Greek numeralΔ´
Roman numeral
Greek prefixtetra-
Latin prefixquadri-/quadr-
Binary1002
Ternary113
Senary46
Octal48
Duodecimal412
Hexadecimal416
ArmenianԴ
Arabic, Kurdish٤
Persian, Sindhi۴
Shahmukhi, Urdu۴
Ge'ez
Bengali, Assamese
Chinese numeral四,亖,肆
Devanagari
Telugu
Malayalam
Tamil
Hebrewד
Khmer
Thai
Kannada
Burmese
Babylonian numeral𒐘
Egyptian hieroglyph, Chinese counting rod||||
Maya numerals••••
Morse code.... _

4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is a square number, the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.

Evolution of the Hindu-Arabic digit

Two modern handwritten fours
Sculpted date "1481" in the Convent church of Maria Steinach in Algund, South Tirol, Italy. The upward loop signifies the number 4.

Brahmic numerals represented 1, 2, and 3 with as many lines. 4 was simplified by joining its four lines into a cross that looks like the modern plus sign. The Shunga would add a horizontal line on top of the digit, and the Kshatrapa and Pallava evolved the digit to a point where the speed of writing was a secondary concern. The Arabs' 4 still had the early concept of the cross, but for the sake of efficiency, was made in one stroke by connecting the "western" end to the "northern" end; the "eastern" end was finished off with a curve. The Europeans dropped the finishing curve and gradually made the digit less cursive, ending up with a digit very close to the original Brahmin cross.[1]

While the shape of the character for the digit 4 has an ascender in most modern typefaces, in typefaces with text figures the glyph usually has a descender, as, for example, in .

On the seven-segment displays of pocket calculators and digital watches, as well as certain optical character recognition fonts, 4 is seen with an open top: .[2]

Television stations that operate on channel 4 have occasionally made use of another variation of the "open 4", with the open portion being on the side, rather than the top. This version resembles the Canadian Aboriginal syllabics letter ᔦ. The magnetic ink character recognition "CMC-7" font also uses this variety of "4".[3]

Mathematics

There are four elementary arithmetic operations in mathematics: addition (+), subtraction (), multiplication (×), and division (÷).[citation needed]

Lagrange's four-square theorem states that every positive integer can be written as the sum of at most four squares.[4][5] Four is one of four all-Harshad numbers. Each natural number divisible by 4 is a difference of squares of two natural numbers, i.e. .

A four-sided plane figure is a quadrilateral or quadrangle, sometimes also called a tetragon. It can be further classified as a rectangle or oblong, kite, rhombus, and square.

Four is the highest degree general polynomial equation for which there is a solution in radicals.[6]

The four-color theorem states that a planar graph (or, equivalently, a flat map of two-dimensional regions such as countries) can be colored using four colors, so that adjacent vertices (or regions) are always different colors.[7] Three colors are not, in general, sufficient to guarantee this.[8] The largest planar complete graph has four vertices.[9]

A solid figure with four faces as well as four vertices is a tetrahedron, which is the smallest possible number of faces and vertices a polyhedron can have.[10] The regular tetrahedron, also called a 3-simplex, is the simplest Platonic solid.[11] It has four regular triangles as faces that are themselves at dual positions with the vertices of another tetrahedron.[12] The tetrahedron is one of three regular polyhedra that tessellate space.[citation needed]

The smallest non-cyclic group has four elements; it is the Klein four-group.[13] An alternating groups are not simple for values .

There are four Hopf fibrations of hyperspheres:

They are defined as locally trivial fibrations that map for values of (aside from the trivial fibration mapping between two points and a circle).[14]

In Knuth's up-arrow notation, , and so forth, for any number of up arrows.[15]

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
4 × x 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 200 400 4000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4 ÷ x 4 2 1.3 1 0.8 0.6 0.571428 0.5 0.4 0.4 0.36 0.3 0.307692 0.285714 0.26 0.25
x ÷ 4 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
4x 4 16 64 256 1024 4096 16384 65536 262144 1048576 4194304 16777216 67108864 268435456 1073741824 4294967296
x4 1 16 81 256 625 1296 2401 4096 6561 10000 14641 20736 28561 38416 50625 65536

In religion

Buddhism

Biblical

Judaism

Hinduism

Islam

Taoism

Other

In politics

  • Four Freedoms: four fundamental freedoms that Franklin D. Roosevelt declared ought to be enjoyed by everyone in the world: Freedom of Speech, Freedom of Religion, Freedom from Want, Freedom from Fear.[57]
  • Gang of Four: Popular name for four Chinese Communist Party leaders who rose to prominence during China's Cultural Revolution, but were ousted in 1976 following the death of Chairman Mao Zedong. Among the four was Mao's widow, Jiang Qing. Since then, many other political factions headed by four people have been called "Gangs of Four".[58]

In computing

In science

In astronomy

In biology

In chemistry

  • Valency of carbon (that is basis of life on the Earth) is four. Also because of its tetrahedral crystal bond structure, diamond (one of the natural allotropes of carbon) is the hardest known naturally occurring material. It is also the valence of silicon, whose compounds form the majority of the mass of the Earth's crust.[73]
  • The atomic number of beryllium[74]
  • There are four basic states of matter: solid, liquid, gas, and plasma.[75]

In physics

In logic and philosophy

Four mugs
  • The symbolic meanings of the number four are linked to those of the cross and the square. "Almost from prehistoric times, the number four was employed to signify what was solid, what could be touched and felt. Its relationship to the cross (four points) made it an outstanding symbol of wholeness and universality, a symbol which drew all to itself". Where lines of latitude and longitude intersect, they divide the earth into four proportions. Throughout the world kings and chieftains have been called "lord of the four suns" or "lord of the four quarters of the earth",[79] which is understood to refer to the extent of their powers both territorially and in terms of total control of their subjects' doings.
  • The Square of Opposition, in both its Aristotelian version and its Boolean version, consists of four forms: A ("All S is R"), I ("Some S is R"), E ("No S is R"), and O ("Some S is not R").
  • In regard to whether two given propositions can have the same truth value, there are four separate logical possibilities: the propositions are subalterns (possibly both are true, and possibly both are false); subcontraries (both may be true, but not that both are false); contraries (both may be false, but not that both are true); or contradictories (it is not possible that both are true, and it is not possible that both are false).
  • Aristotle held that there are basically four causes in nature: the material, the formal, the efficient, and the final.[80]
  • The Stoics held with four basic categories, all viewed as bodies (substantial and insubstantial): (1) substance in the sense of substrate, primary formless matter; (2) quality, matter's organization to differentiate and individualize something, and coming down to a physical ingredient such as pneuma, breath; (3) somehow holding (or disposed), as in a posture, state, shape, size, action, and (4) somehow holding (or disposed) toward something, as in relative location, familial relation, and so forth.
  • Immanuel Kant expounded a table of judgments involving four three-way alternatives, in regard to (1) Quantity, (2) Quality, (3) Relation, (4) Modality, and, based thereupon, a table of four categories, named by the terms just listed, and each with three subcategories.
  • Arthur Schopenhauer's doctoral thesis was On the Fourfold Root of the Principle of Sufficient Reason.
  • Franz Brentano held that any major philosophical period has four phases: (1) Creative and rapidly progressing with scientific interest and results; then declining through the remaining phases, (2) practical, (3) increasingly skeptical, and (4) literary, mystical, and scientifically worthless—until philosophy is renewed through a new period's first phase. (See Brentano's essay "The Four Phases of Philosophy and Its Current State" 1895, tr. by Mezei and Smith 1998.)
  • C. S. Peirce, usually a trichotomist, discussed four methods for overcoming troublesome uncertainties and achieving secure beliefs: (1) the method of tenacity (policy of sticking to initial belief), (2) the method of authority, (3) the method of congruity (following a fashionable paradigm), and (4) the fallibilistic, self-correcting method of science (see "The Fixation of Belief", 1877); and four barriers to inquiry, barriers refused by the fallibilist: (1) assertion of absolute certainty; (2) maintaining that something is unknowable; (3) maintaining that something is inexplicable because absolutely basic or ultimate; (4) holding that perfect exactitude is possible, especially such as to quite preclude unusual and anomalous phenomena (see "F.R.L." [First Rule of Logic], 1899).
  • Paul Weiss built a system involving four modes of being: Actualities (substances in the sense of substantial, spatiotemporally finite beings), Ideality or Possibility (pure normative form), Existence (the dynamic field), and God (unity). (See Weiss's Modes of Being, 1958).
  • Karl Popper outlined a tetradic schema to describe the growth of theories and, via generalization, also the emergence of new behaviors and living organisms: (1) problem, (2) tentative theory, (3) (attempted) error-elimination (especially by way of critical discussion), and (4) new problem(s). (See Popper's Objective Knowledge, 1972, revised 1979.)
  • John Boyd (military strategist) made his key concept the decision cycle or OODA loop, consisting of four stages: (1) observation (data intake through the senses), (2) orientation (analysis and synthesis of data), (3) decision, and (4) action.[81] Boyd held that his decision cycle has philosophical generality, though for strategists the point remains that, through swift decisions, one can disrupt an opponent's decision cycle.
  • Richard McKeon outlined four classes (each with four subclasses) of modes of philosophical inquiry: (1) Modes of Being (Being); (2) Modes of Thought (That which is); (3) Modes of Fact (Existence); (4) Modes of Simplicity (Experience)—and, corresponding to them, four classes (each with four subclasses) of philosophical semantics: Principles, Methods, Interpretations, and Selections. (See McKeon's "Philosophic Semantics and Philosophic Inquiry" in Freedom and History and Other Essays, 1989.)
  • Jonathan Lowe (E.J. Lowe) argues in The Four-Category Ontology, 2006, for four categories: kinds (substantial universals), attributes (relational universals and property-universals), objects (substantial particulars), and modes (relational particulars and property-particulars, also known as "tropes"). (See Lowe's "Recent Advances in Metaphysics," 2001, Eprint)
  • Four opposed camps of the morality and nature of evil: moral absolutism, amoralism, moral relativism, and moral universalism.

In technology

4 as a resin identification code, used in recycling

In music

In fiction

Other groups of four

See also

References

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  11. ^ Grossnickle, Foster Earl; Reckzeh, John (1968). Discovering Meanings in Elementary School Mathematics. Holt, Rinehart and Winston. p. 337. ISBN 9780030676451. ...face of the platonic solid. The simplest of these shapes is the tetrahedron...
  12. ^ Hilbert, David; Cohn-Vossen, Stephan (1999). Geometry and the Imagination. American Mathematical Soc. p. 143. ISBN 978-0-8218-1998-2. ...the tetrahedron plays an anomalous role in that it is self-dual, whereas the four remaining polyhedra are mutually dual in pairs...
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  16. ^ a b c Chwalkowski, Farrin (14 December 2016). Symbols in Arts, Religion and Culture: The Soul of Nature. Cambridge Scholars Publishing. p. 22. ISBN 978-1-4438-5728-4. The four main pilgrimages sites are: Lumbini, Bodh Gaya, Sarnath and Kusinara....four Noble Truths of Buddhism
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  19. ^ Chaudhuri, Saroj Kumar (2003). Hindu Gods and Goddesses in Japan. Vedams eBooks (P) Ltd. p. 20. ISBN 978-81-7936-009-5. The Buddhists adopted him as one of the four Devarajas or Heavenly Kings
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  23. ^ Jayatilleke, K. N. (16 October 2013). Early Buddhist Theory of Knowledge. Routledge. ISBN 978-1-134-54294-9. ...the states of the four arupajhanas.
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  91. ^ Baker, Felicity (2017). Houses of Hogwarts: Cinematic Guide. Scholastic Incorporated. ISBN 978-1-338-12861-1. ...the four houses of Hogwarts School of Witchcraft and Wizardry: Gryffindor, Ravenclaw, Hufflepuff, and Slytherin
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