A *formal language* is an organized set of symbols the essential feature of which is that it can be precisely defined in terms of just the shapes and locations of those symbols. Such a language can be defined, then, without any reference to any meanings of any of its expressions; it can exist before any interpretation is assigned to it—that is, before it has any meaning. First order logic is expressed in some formal language. A formal grammar determines which symbols and sets of symbols are formulas in a formal language.

A formal language can be defined formally as a set *A* of strings (finite sequences) on a fixed alphabet α. Some authors, including Carnap, define the language as the ordered pair <α, *A*>. Carnap also requires that each element of α must occur in at least one string in *A*.

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**Formal Language**

... A

**formal language**is an organized set of symbols the essential feature being that it can be precisely defined in terms of just the shapes and locations ... Such a

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**Formal languages**are entirely syntactic in nature but may be given semantics that give meaning to the elements of the

**language**... set of possible formulas of a particular logic is a

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### Famous quotes containing the words language and/or formal:

“The necessity of poetry has to be stated over and over, but only to those who have reason to fear its power, or those who still believe that *language* is “only words” and that an old *language* is good enough for our descriptions of the world we are trying to transform.”

—Adrienne Rich (b. 1929)

“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce *formal* instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”

—David Elkind (20th century)