. It provides one answer to the debate over commonality of experience. Basically the debate is "How do I know that what I experience is the same as what you experience?"
Wittgenstein simply proposed that language was the answer. A private language would not work. If we both spoke English words, but in my version scuba diving means taking a hot shower and to you it means swimming with a tank of air on your back we could quickly get confused. If everyone had their own definitions for all words communication would be impossible. Therefore the fact that language works at all is proof of commonality of experience. You hear yourself say scuba diving and I hear and understand (at least approximately) the same thing.
Another achievement of the private language argument is to provide a method of answering many philosophical questions. For example, take the question "what is beauty?" Definitely a philosophical question; you can see that the way the question is stated suggests that 'beauty' has some objective existence separate from objects in it's own right. However, using the private language theory we can say that the question merely refers to the word and its meaning. Thus, the answer to the question is simply: the meaning is however the word is used.
This approach is used in the Brain in a Vat essay. The question how can we tell if we are plugged into a virtual reality machine is answered by saying: what do we mean by reality? Reality is simply this, what we are experiencing now. Therefore even if machines feed our reality to us it is still reality.
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