Discrete Infinity of Language

The discrete infinity of language means unlimited productivity from the finite means as a major design feature of language (Irvine, 2014). Discreteness means that the boundary between linguistic symbols is clear. Since the linguistic symbols are discrete, the chain of linguistic symbols can be segmented part by part until the smallest linguistic symbols are assigned. For example, “You are hungry” can be divided into subject “you”, verb “are” and adjective “hungry”.

The order of the three linguistic symbols can be changed and the meaning of the new sentence will be totally different. If I change the order of the subject and verb, the new sentence will be “Are you hungry?” In this case, I am asking for a question instead of stating a fact. This is one significant difference between human beings and animals. The way that animals communicate with each other, such as the dance of bees and the sound of chimpanzees, etc. are continuous and can’t be syncopated. However, the linguistic symbols of human beings are discrete and they can be used repeatedly and repeatedly to combine with other linguistic symbols.

Consequently, they can express infinite thoughts with limited linguistic symbols.
Language is the essential mean of human communication and meaning-making and linguistic meaning emerges from a whole communication environment. Human beings can create and understand new context. Because of the discrete infinity of language, it’s necessary to combine the context to understand the meanings of language correctly. The same sentence in different environment or context can have significantly different meanings. For example, when “She is hot” is used in summer, it means the girl feels very hot about the weather. When “She is hot” is used in the beach, it may be a compliment to the girl’s appearance and stature. Consequently, not only the different combination of linguistic symbols can lead to infinite meanings, but also the different environment influences infinite meanings as well.

Although specific meanings are unlimited, they are bounded only by human-scale limits such as personal knowledge, time and memory (Irvine, 2014). This brings a new need for language, namely creativity. In the video presentation, Language and the human brain, Chomsky thinks that language is words, rules and interfaces. Among these, rules include syntax, morphology and phonology. One important quality is that rules focus on creativity, which means the ability to produce and understand new language. Rules allow for open-ended creativity, including the expression of unfamiliar meanings and the production of vast numbers of combination. That is consistent with the discrete infinity of language. Language has the potential and creativity to develop infinitely.

An extension of the discrete infinity of language is that ambiguous sentences imply different meanings from the same phase structure.

Journalists say that when a dog bites a man that is not news, but when a man bites a dog that is news (Pinker, 1994).

That’s an interesting case of the discrete infinity of language. In fact, ambiguous sentences are not rare both in spoken language and written language. And that reflects the miraculous of language. Even the change of the combination of different words can lead to totally different meanings.

1. Irvine, M. (2014). Introduction to Linguistics and Symbolic Systems: Key Concepts.
2. Pinker, S. (2007). The language instinct: How the mind creates language. New York: Harper Perennial Modern Classics.