A simple definition of language is a symbolic system of communication. Language can refer to spoken or written human language but also to forms of communication such as body language or even math or music. Language in this broad sense does not need to be restricted to human communication, but can also refer to auditory, physical and chemical communication between animals and even plants.
Many linguists have developed sets of properties that define or describe what constitutes a human language, and these lists vary from scholar to scholar. However, most seem to settle on six, rather than three, properties of human languages: displacement, arbitrariness, productivity, discreetness, duality and cultural transmission.
Displacement means that a language can refer to times and places other than the present. Most animal languages are believed to lack this property. For example, animals are able to convey messages to each other or us through body language, such as a dog wagging his tail, but this message implies that the dog is happy right now. He has no way of conveying that he was happy yesterday, or that he enjoyed that walk in the park last week.
Human languages have arbitrariness, meaning that the symbols we use have no direct connection to what they represent. The word home is not intrinsically tied in anyway to what a home is, rather the sounds that make up the word home were arbitrarily designated that meaning. Of course, there are instances where words are not entirely arbitrary, the obvious example being onomatopoeia, where words resemble the sound they refer to (for example, the word buzz).
Productivity refers to the ability of human language to grow and adapt with human learning and culture. It means we have the ability to develop new symbols or combinations of symbols (here we usually mean words and phrases) to represent new ideas or technologies. This allows us to communicate effectively even as we experience changes in the way we think or experience the world.
Discreetness is the property of each sound in the language being unique and having different meaning or interpretation. For example, the sounds made by the letters M and N are similar, but despite the similar sound, we know that the words mate and Nate have different meanings. In animal languages a general sound, such as a grunt or bark, may have a particular meaning, but different animals and even the same animal might not "pronounce" that symbolic sound using the exact same combinations of sounds every time. In human language specific combinations of sounds have specific meanings.
Duality is the nature of human language as comprised of a set of unique sounds, which alone are meaningless, but that are combined to form symbols with specific meanings. The letter L and the sound it makes has no meaning in itself. Neither do the sounds of I, F and E, but when we combine those particular sounds in that order we form the world LIFE, which does have symbolic meaning in English. Duality then is the merging of this set of meaningless sounds with a code of combinations that we have given meaning to.
And finally, human languages all must have cultural transmission, they must be passed from generation to generation. While we may have evolved to learn languages easily, the meanings of the sounds we make are not passed down in our genetics, we must learn the symbols from our parents or those around us. For a human language to effectively communicate, it must be shared among people so that they can understand one another and it must be taught to children so they can understand the symbology of their ancestors, communicate with one another, and use the same symbology to pass their knowledge on to new generations.
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