Hello Arnaud and welcome to Linguistics. Your question has been asked already, visit the link above. :)
– AlenannoApr 04 '13 at 11:26
I saw it, but I would like a very short answer to the question "is a language an association of a lexicon and a grammar ?".
– ArnaudApr 04 '13 at 11:27
The first answer in the question I linked provides a short definition in its first line.
– AlenannoApr 04 '13 at 11:30
I saw it, but I found it too indecisive. Is a language an association of a lexicon and a grammar ?
– ArnaudApr 04 '13 at 11:37
It's not indecisive, why do you say that? That's its definition. But if you want to analyze it the way you presented it, a language certainly includes lexicon and grammar, but saying that it's an association of those two is incomplete and inexact since it's not just made of those two. :)
– AlenannoApr 04 '13 at 11:58
If someone provided a short definition, would it be all right if it was decisive but incorrect? How about decisive and correct, but not short? You can't have all three.
– jlawlerApr 04 '13 at 13:56
What I mean by decisive is almost "mathematical". Speaking about a "complex system" is not a mathematical definition. If saying that this is an association of a lexicon and a grammar, what should we add ?
– ArnaudApr 04 '13 at 14:54
I have heard that, mathematically, a language is a set of strings (each string being a set whose members are ordered), and a grammar would be a set of rules that specifies which strings or kinds of strings are in the language and which are not. However, this is not a sufficient definition of natural language (examples of which include English, Chinese, Spanish, etc.). Natural languages are very complicated, so I don't see how one can devise a short definition of natural language.
– James GrossmannApr 04 '13 at 18:00
Oh very interesting ! So according to you, a lexicon and a grammar are sufficient ? You say that it is not sufficient for natural languages, but why ?
– ArnaudApr 04 '13 at 18:51
Because, unlike a purely formal language, natural language has to convey information regarding the world and not just information about the itself. It must also typically transmitted via an acoustic or visual code, which creates another set of complexities.
– James GrossmannApr 05 '13 at 05:35
Okay, so is a language an association of a grammar and a list of signs (visual and acoustic), each of us corresponding to an object of reality ?
– ArnaudApr 05 '13 at 14:32
Natural Language doesn't fit into this definition. We don't just associate signs with referents in one-to-one correspondence. We associate signs with meanings or concepts that each entail related meanings or concepts and define classes of things. We do not just talk about objects of reality--we can talk about states of affairs that may be real, hypothetical, or counterfactual. Please re-read the duplicate link.
– James GrossmannApr 06 '13 at 19:16