Originally, I thought language was any means of communication. So I would have said that the high-pitched sounds dolphins make and the meowing noises that my cat makes when she's hungry are all language. But apparently, language is a faculty unique to humans and it has to have certain levels of sophistication to be recognized as "real" language.
So I looked up the definition of language on the online Merriam-Webster Dictionary:
1 a: the words, their pronunciation, and the methods of combining them used and understood by a community b (1): audible, articulate, meaningful sound as produced by the action of the vocal organs (2): a systematic means of communicating ideas or feelings by the use of conventionalized signs, sounds, gestures, or marks having understood meanings (3): the suggestion by objects, actions, or conditions of associated ideas or feelings
And I wanted to discuss each of the definitions a little.
1a: This definition implies that language has to be verbal and widespread, or at least used in common by a significant number of people. According to this definition, sign language is not a language, and languages that are almost dying out (like those with just one or two speakers left) no longer qualify as language. This doesn't seems right. Vocalization of language is an important part of language. It's the most convenient way to communicate, in my opinion, because the response is immediate. However, deaf people who cannot speak have made up a beautiful, complex language that doesn't require sounds. So this definition doesn't seem to encompass the true meaning of language.
1b(1): Again, this definition also implies that language is verbal. The intent of this definition, I think, was to rule out animal sounds as language. Most people probably would agree that mooing, chirping, barking, etc. aren't "audible, articulate, meaningful" sounds.
1b(2): I like this definition the best so far because it doesn't require a verbal quality for language. If limiting language to human communication, I think it has the right amount of restrictions. Language has to be "systematic," "conventionalized," and "understood." It excludes animal sounds but includes all forms of language--written, verbal, and gestures.
1b(3): This definition refers to a different kind of language, I think. It's still a form of communication but more symbolic. A gift of roses would be a "suggestion" of attraction and language according to this definition.
1b(4): This one is close to my original definition of language. "Communication" and "animals" are the only two requirements.
1b(5): The important word in this definition is "rules." This definition would also exclude animal sounds, but it would include "scientific languages" like the symbols and equations used in chemistry and math. I think these should also qualify as languages. They are actually rather important languages because they are international. Most of the symbols are used uniformly throughout the world, which is amazing, if you think about it.
After my short analysis of the definition of language, I still think that language should mean any sounds, motions, or symbols that communicate meaning--even the simplest feelings like hunger. When my cat meows at us, we know that she wants food. When she purrs, we know that she's content. She expresses something, and we understand it. I think those two things (expression of emotions/thoughts & understanding of the expression) are the only two qualifications language has. Of course there are varying degrees of complexity in language, but as long as something is communicated between two or more living creatures, I'll call it "language."