Metalogic - Overview - Formal Language

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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Famous quotes containing the words language and/or formal:

    Just as language has no longer anything in common with the thing it names, so the movements of most of the people who live in cities have lost their connexion with the earth; they hang, as it were, in the air, hover in all directions, and find no place where they can settle.
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    The manifestation of poetry in external life is formal perfection. True sentiment grows within, and art must represent internal phenomena externally.
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