Natural language Glossary


A natural language is a language such as English or Hindi, spoken by a group of human beings.


A natural language may have a written form as well as a spoken form, or parts of it may be written, or it may be entirely a spoken language without a writing system. There may also be many variants of a natural language, associated with different groups of speakers or used in different social situations. The grammar of a natural language is usually complex and may not be capable of a completely rigorous definition. Languages change over time, so a natural language is not definable as a fixed set of expressions.

In logic, we are mainly concerned with the use of language to make assertions. This includes the formulation of theories, conjectures, predictions, explanations, opinions and stories as well as simply stating facts. It is important to remember, however, that this is only a fragment of human linguistic activity. More of language is studied in philosophy as well as in the science of linguistics.

Natural languages contrast with the formal languages that are central to logic. The correspondence between logical formulae and natural language sentences is not exact.


  1. There are thousands of natural languages currently in use, and many more which were formerly used but now have no native speakers. The number is quite indeterminate because it is unclear how to count dialects, hybrid languages, pidgins and other variants. However, languages that can reasonably be estimated to have more than a quarter of a billion speakers include English, Mandarin, Hindi, Spanish, French, Arabic, Bengali and Russian.
  2. Artificially created languages based on natural ones include Esperanto. There might be good chances of defining a nice fit between part of that and formal logic, but the extra language classes it would require would make it not worth the effort!
  3. The fragments of natural languages (mostly English) used by mathematicians to write proofs are somewhere between the natural and formal. They have features of both language forms.

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