logical argument An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectic ...

and mathematical proof, the therefore sign, , is generally used before a

logical consequence Logical consequence (also entailment) 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 logical argument is on ...

, such as the conclusion of a

syllogism A syllogism ( grc-gre, συλλογισμός, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. ...

. The symbol consists of three dots placed in an upright triangle and is read ''therefore''. While it is not generally used in formal writing, it is used in

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

and shorthand.

History

According to Cajori, '' A History of Mathematical Notations,'' Johann Rahn used both the ''therefore'' and ''because'' signs to mean "therefore"; in the German edition of ''Teutsche Algebra'' (1659) the ''therefore'' sign was prevalent with the modern meaning, but in the 1668 English edition Rahn used the ''because'' sign more often to mean "therefore". Other authors in the 18th century also used three dots in a triangle shape to signify "therefore", but as with Rahn, there wasn't much in the way of consistency as to how the triangle was oriented; ''because'' with its current meaning appears to have originated in the 19th century. In the 20th century, the three-dot notation for 'therefore' became very rare in continental Europe, but it remains popular in Anglophone countries.

Example of use

Used in a

: :All gods are immortal. : Zeus is a god. :∴ Zeus is immortal. and in mathematics : :

Other uses

In meteorology, the 'therefore' sign is used to indicate 'moderate rain' on a station model; the similar typographic symbol asterism (⁂, three

asterisk The asterisk ( ), from Late Latin , from Ancient Greek , ''asteriskos'', "little star", is a typographical symbol. It is so called because it resembles a conventional image of a heraldic star. Computer scientists and mathematicians often voc ...

s) indicates moderate snow.

Freemasonry

In Freemasonry traditions, the symbol is used to indicate a Masonic abbreviation (rather than the period mark used conventionally with some abbreviations). For example, "R∴W∴ John Smith" is an abbreviation for "Right Worshipful John Smith" (the term Right Worshipful is an honorific and indicates that Brother Smith is a Grand Lodge officer).

Unicode

The symbol has a Unicode code point at . See Unicode input for keyboard-entering methods.

Similar signs

The inverted form, , known as the because sign, is sometimes used as a shorthand form of "because". The character (visarga) in the Tamil script represents the āytam, a special sound of the Tamil language. An asterism, , is a typographic symbol consisting of three asterisks placed in a triangle. Its purpose is to "indicate minor breaks in text", to call attention to a passage, or to separate sub-chapters in a book. It is also used in meteorology to indicate 'moderate snowfall'. The graphically identical sign serves as a Japanese map symbol on the maps of the Geographical Survey Institute of Japan, indicating a tea plantation. On some maps, a version of the sign with thicker dots, , is used to signal the presence of a

national monument A national monument is a monument constructed in order to commemorate something of importance to national heritage, such as a country's founding, independence, war, or the life and death of a historical figure. The term may also refer to a spec ...

, historic site or ruins; it has its own Unicode code point. In Norwegian and Danish, a superficially similar symbol was formerly used as an explanatory symbol (''forklaringstegnet''). It can be typeset using the open o followed by a colon, thus: . It is used for the meaning "namely", ( i.e.), ( viz.) or similar.

References

{{DEFAULTSORT:Therefore Sign Typographical symbols Mathematical symbols Logic symbols Logical consequence