A private language seems to be a contradiction in terms. It can be claimed that a language is only meaningful as a form of social communication. A private language could not be used to communicate with another individual, so a private language could not be a language. However, language seems to represent thought, which is private. I argue that there are private languages that are just as common as it is to have a personal style of mathematical or logical symbolism. A private language could be intelligible by another individual if they learned the language.
A private language can be likened to ownership of property. For example, an owner can have his own language, as he has his own property. In this case, ownership can be described as a particular ordering. Furthermore, I'm reminded of the somewhat common colloquial expression - owning it - that is used sometimes in the arts and sports referring to the artistic rendering in all it's intricacies during a performance....
A particular arrangement of ownership that is not uncommon today is to have a manager run the activities of a property allocated toward production, i.e. a business. The manager attends to the objectives given to him by the owner, yet does not own it. The manager is only a custodian of the property and cannot change its ordering.
If an individual wants to communicate in the marketplace of thought, then they must have shared well-ordered terms and shared grammar. The standardization effect of the increase of making ideas more marketable can alter the particular grammatical scheme and well-ordering of a poem written in a private language or an object of sentimental value. In the marketplace, standardization reduces the spread between buyers and sellers. This is what is known as liquidity or marketability. An illiquid good may require a buyer to buy it higher and a seller to sell it low. Here, marketing can be compared to translation, where some arrangements do not translate that well.
The movie, 2001: A Space Odyssey, starts off with a scene where a man-ape tribe conquers another tribe after one of the man-apes figures out that a bone can be used as a tool or weapon. In other words, the man-ape conceived a way that the bone could be used in a different way, in effect the whereby man-ape developed his own scheme. In recent times, uncontacted tribes in the Amazon jungle can be seen in Youtube videos where they throw spears at planes. One might wonder how an uncontacted tribe would interpret a 2014 Ford Focus or a Coca-Cola bottle. The scheme would not be the same as someone from outside the uncontacted world.
Describing ownership of property as a private language can also inform us how ownership can incentivize individuals to develop systems of rights. For example, individuals exhibiting demonstrated preferences towards the division of labor, i.e. specialization. Labor refers to a particular scheme relationship to property. An individual would find their objectives more in reach if they could specialize and trade with each other, which leads the individuals that they traded with to right claims and yet again those that trade with them, ad infinitum. (I am a Humean when it comes to describing the development an ethical system. I argue that analytic relationships exist alongside a human nature explanation, such as self-interest or those provided by way of cognitive psychology and neuroscience.)
Rights claim refers to the claim on their own particular scheme in relation to property. Added to this is the analytic relationship of David Ricardo's Comparative Advantage in which due to this relationship individuals also discover advantages if they specialize. ...By way of a right claim individuals do not have to understand an owner's ordering of a property, as they do not have to understand their private language. The rights claim implies that they observe the owner's rights and yet are not required to understand their particular scheme.