Turned A (capital: Ɐ, lowercase: ɐ, math symbol ∀) is a letter and

symbol A symbol is a mark, Sign (semiotics), sign, or word that indicates, signifies, or is understood as representing an idea, physical object, object, or wikt:relationship, relationship. Symbols allow people to go beyond what is known or seen by cr ...

based upon the letter A.

Modern usage

* Lowercase ɐ (in Roman, or "two-storey" form) is used in the

International Phonetic Alphabet The International Phonetic Alphabet (IPA) is an alphabetic system of phonetic notation based primarily on the Latin script. It was devised by the International Phonetic Association in the late 19th century as a standard written representation ...

to identify the

near-open central vowel The near-open central vowel, or near-low central vowel, is a type of vowel sound, used in some spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is , a rotated lowercase double-story a. In English ...

. This is not to be confused with the ''turned

alpha Alpha (uppercase , lowercase ) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter ''aleph'' , whose name comes from the West Semitic word for ' ...

'' or ''turned script a'', ɒ, which is used in the IPA for the

open back rounded vowel The open back rounded vowel, or low back rounded vowel, is a type of vowel sound, used in some spoken languages. The symbol in the International Phonetic Alphabet that represents this sound is . It is called Latin turned alpha being a rotated v ...

. * The logical symbol ∀ has the same shape as a

sans-serif In typography and lettering, a sans-serif, sans serif (), gothic, or simply sans letterform is one that does not have extending features called "serifs" at the end of strokes. Sans-serif typefaces tend to have less stroke width variation than ...

capital turned A. It is used to represent

universal quantification In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by e ...

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 ...

, where it is typically read as "for all". It was first used in this way by

Gerhard Gentzen Gerhard Karl Erich Gentzen (24 November 1909 – 4 August 1945) was a German mathematician and logician. He made major contributions to the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. He died ...

in 1935, by analogy with

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 ...

's turned E notation for

existential quantification Existentialism is a family of philosophy, philosophical views and inquiry that explore the human individual's struggle to lead an Authenticity (philosophy), authentic life despite the apparent Absurdity#The Absurd, absurdity or incomprehensibili ...

and the later use of Peano's notation by

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 ...

Historical usage

File:Turned A in Edward Lhuyd, Archaeologia Britannica, 1707, p. 226.png , Turned a presented in Edward Lhuyd's ''Archaeologia Britannica'', 1707. File:Turned A in William Pryce, Archaeologia Cornu-Britannica, 1790, p. 1.png , Turned a in William Pryce's ''Archaeologia Cornu-Britannica'', 1790. Because of the relative ease of creating this letterform using traditional printing methods, it had frequent and varied historical uses. According to the principle of

acrophony Acrophony (; + 'sound') is the naming of letters of an alphabetic writing system so that a letter's name begins with the letter itself. For example, Greek letter names are acrophonic: the names of the letters α, β, γ, δ, are spelled with t ...

, the letter A originated from the Proto-Sinaitic alphabet as a symbol representing the head of an ox or cow (

aleph Aleph (or alef or alif, transliterated ʾ) is the first Letter (alphabet), letter of the Semitic abjads, including Phoenician alphabet, Phoenician ''ʾālep'' 𐤀, Hebrew alphabet, Hebrew ''ʾālef'' , Aramaic alphabet, Aramaic ''ʾālap'' � ...

), its orientation and original meaning having been lost over time. The turned A symbol restores the letter to a more easily recognizable

logographic In a written language, a logogram (from Ancient Greek 'word', and 'that which is drawn or written'), also logograph or lexigraph, is a written character that represents a semantic component of a language, such as a word or morpheme. Chinese c ...

representation of an ox's head. A

denarius The ''denarius'' (; : ''dēnāriī'', ) was the standard Ancient Rome, Roman silver coin from its introduction in the Second Punic War to the reign of Gordian III (AD 238–244), when it was gradually replaced by the ''antoninianus''. It cont ...

coin from the

Roman Republic The Roman Republic ( ) was the era of Ancient Rome, classical Roman civilisation beginning with Overthrow of the Roman monarchy, the overthrow of the Roman Kingdom (traditionally dated to 509 BC) and ending in 27 BC with the establis ...

has been found, struck with a (capital) turned A, in the collection of a Madrid-based numismatist; it is unclear whether this was intentional, or a printer's error for a V. It was used in the 18th century by Edward Lhuyd and

William Pryce William Pryce (baptised 1735–1790) was a British medical man, known as an antiquary, a promoter of the Cornish language and a writer on mining in Cornwall. Life He was the son of Dr. Samuel Pryce of Redruth in Cornwall, and Catherine Hill; W ...

as a phonetic character for the

Cornish language Cornish (Standard Written Form: or , ) is a Southwestern Brittonic language, Southwestern Brittonic language of the Celtic language family. Along with Welsh language, Welsh and Breton language, Breton, Cornish descends from Common Brittonic, ...

. In their books, both Ɐ and ɐ have been used. It was used in the 19th century by

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 ...

as a logical symbol for un-American. is used in the

Uralic Phonetic Alphabet Finno-Ugric transcription (FUT) or the Uralic Phonetic Alphabet (UPA) is a phonetic transcription or notational system used predominantly for the transcription and reconstruction of Uralic languages. It was first published in 1901 by Eemil Nesto ...

, a system developed in the early 20th century for transcribing

Uralic language The Uralic languages ( ), sometimes called the Uralian languages ( ), are spoken predominantly in Europe and North Asia. The Uralic languages with the most native speakers are Hungarian, Finnish, and Estonian. Other languages with speakers ab ...

s. However, as this system was not standardized across (nor within) languages, it has been supplanted in this use by the

Encodings

References

{{Common logical symbols Logic symbols A Phonetic transcription symbols

Modern usage

Historical usage

Encodings

See also

References