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According to The Free Dictionary website, the term Shavian is defined as the following:
Of, relating to, or characteristic of George Bernard Shaw or his works.
Based solely off of this definition, the play "Pygmalion" is a Shavian play given it was written by Shaw. This alone is not a great definition of the characteristics of Shavian writing though.
Therefore, to characterize Shaw, and therefore Shavian writing, one must look at how and what Shaw's writings contained.
Shaw's writings are infused with his own wit and self-confidence. He educated himself in music and, therefore, was very fond of sound- as seen in the play "Pygmalion" given the teaching of proper speech.
Shaw's colorful language mirrors the "language" seen in music. The dialogue between characters seems to flow off of the tongue in the same way in which one would sing lyrics.
Shaw loved satire and seemed to find much humor in forcing people to look at the absurd ways in which conventional thinking led them. Shaw's discontent with conventional thinking almost caused him to be charged with treason after writing "Common Sense About the War". His wit and self-confidence seemed to be too much for those in charge of governmental dealings and they saw Shaw as bitter and simply cast him out.
Based upon these historical aspects of Shaw's life, one can characterize Shavian works as ones in which satire, wit, and author confidence are used to question the aspects of society which may seem too accepted.
Therefore, the play "Pygmalion" adheres to these characteristics given Shaw is poking fun at the social circles, manly confidence, and the 'assumptiveness' of society.