Paintings are language

 A la Derrida, the sign represents a thing in its absence. Let's not obfuscate our meaning here. In order for a sign to exist, it must function in the absence of what is signfied. This is why dogs don't have language (but birds do). Dogs can only communicate that which is present. If they have to pee, they jump at the door. They communicate, but they can't say, "please open the door so that I may pee." There communication communicates something immediate. The equivalent of saying "this".

Humans are not the only species to produce language given Derrida's definition. Birds are capable of language processing, communicating that which is not immediately present, and so are dolphins. 

While there are already some balking at this approach, please remember that pictographs are language, even when they don't represent syllables. So, we are already at a point where we've admitted that pictures can be language. We can't really avoid admitting that.

So, now, paintings. Paintings are language and have been used linguistically to represent things that were not present from the first time we created paint. They were often used to illustrate stories and, once the story was told, stood in place of the story, representing it in its absence. Paintings are perhaps the first form of written language. We can establish through the derivation of the letter 'A' which, when you turn it upside down, looks like the head of an ox. 'Aleph' and 'Alpha' are also both on Semitic word alapu meaning 'ox'.

Ultimately, while we can say that words and paintings are different forms of expression, we can't say that they aren't both linguistic expressions. Linguists tend to focus on words and grammar. So, we're out on a bit of a limb here. But I don't deny the title of language to pictograms, so I won't deny it to paintings either.