This is basically why art exists — painting, music, and poetry can point at things without having to name them. Language traps itself; other forms don't.
In Bhartrhari's Philosophy (and other Hindu philosophies) "Language" has a much broader definition which can encompass Art/Dance/Music/Painting/etc. Any medium of communication which can bring forth a "burst of meaning" (called Sphota) in one's consciousness is a language.
Natural Spoken language based on Sound (aka Sabda in Sanskrit) is considered the most fundamental since you can have languages without a written script/symbols/diagrams.
In Hindu philosophy, a "Language" is said to have four stages, only the last of which is the gross manifestation in the physical world;
1) Para - This is the latent undifferentiated potential which exists in everybody.
2) Pashyanti - This stage is where intuitive holistic meaning (of what you want to convey) exists.
3) Madhyama - This stage is where you have differentiated the thought/intention into an object and the means of representation for its communication.
4) Vaikhari - In spoken language, this is the manifest stage where you utter sentences according to established syntax/semantics to convey meaning.
Note that the first three stages are internal and only the last is the medium of expression in the physical world. It should now be obvious that the last can be any medium (eg. Dance/Painting/Music/Written-Language/Sign-Language/etc.) as long as the receiver "gets" the intended meaning.
PS: See also this comment of mine for further resources - https://news.ycombinator.com/item?id=49486845