I am having a little trouble distinguishing the difference between the Dionysian and Apollinian artists that Nietzsche talks about. Any way you could clarify?

You are certainly not alone in having a little trouble! These terms are used by Nietzsche in his Birth of Tragedy, which was his first published book. It is important to keep a few things in mind when reading this book. First, Nietzsche’s explicit intent was not to talk about the Greeks at all, but rather to talk about the contemporary European scene by way of a complex historical analogy with Greece. Thus, it is not even clear whether any particular artists that Nietzsche may have had in mind are to found in ancient Greece, or 19th Century Germany. Second, Nietzsche is employing a fairly conventional anthropological notion: that deities and myths are ideal representations of underlying cultural trends. Thus the Apollonian and Dionysian as concepts stand for trends or forces in Greek culture rather than specific cultural products. Third, Nietzsche is also not particularly interested in the Apollonian or Dionysian in themselves. He becomes interested only insofar as these two cultural forms work together in the specific phenomenon that is Greek tragic drama. Fourth, he is not even interested in tragedy as a genre, performances, or set of extant texts, but rather in that it deals with a set of metaphysical propositions (most of which are borrowed from Schopenhauer) and reveals in Greek culture (and perhaps in modern European culture) a capacity to understand and deal with the truth of this metaphysics. Nietzsche sees the Dionysian primarily in music and the Apollonian primarily in the plastic arts such as architecture or sculpture but, for the reasons we just suggested, he names few names. Shortly after writing this book, Nietzsche distances himself from both Schopenhauer and the artist he celebrated in the Birth of Tragedy (Richard Wagner). The concept of the Apollonian largely drops out of his philosophy leaving a substantially different notion of the Dionysian.

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