The Private Language Argument takes many different forms. With this in mind, it is very difficult to derive general conclusions regarding the possibility of a private language that would apply to every argument. While there are many different private language arguments, each one aims at the common conclusion that a private language is not possible. One of the goals of this work is to set the parameters for establishing the possibility of a private language, outside language describing sensations, by examining three different facets of language use. The three different facets I present are language describing sensations, the criteria for correctly using words and expressions, and Wittgenstein's paradox. With respect to language describing sensations, I apply this facet of language to the private language arguments of Rudolf Carnap, Otto Neurath, and Ludwig Wittgenstein. In Chapters 2 and 3, respectively, I effectively conclude that due to the nature of this kind of language, it is appropriately categorized as private. These conclusions drive a wedge between language describing sensations and language not describing sensations. It is here I conclude that a private language is possible with respect to language describing sensations. In Chapter 4, I examine Wittgenstein's requirements for the correct use of a word or phrase and conclude, with the help of A.J. Ayer, that Wittgenstein's criteria for correctly using a word or a phrase are too strong. Finally I examine the most difficult obstacle for an advocate of a private language, the Wittgensteinean-Kripkean paradox. I effectively conclude that the most problematic obstacle for an advocate of a private language is the Wittgensteinean-Kripkean paradox; the reader is left with the task to decide how vicious this paradox is. This work is best described as embryotic; the conclusions derived here are meant to set the framework and the parameter for a more well rounded discussion for the possibility of a private language.