Mythology was at the root of seeking wisdom. Much like how religion is now, people believed in stories and characters in order to seek answers about the nature of the world around them. I suppose it could be considered a sort of socialization in which people learned the same stories to understand the difference between right and wrong. This imposes value judgments in ethics, which is an important branch of philosophy.
Likewise, theology also plays a large role in philosophy as a metaphysical answer to why the world is the way it is. The imposition of God or gods seeks to explain why we are here, and it is but one way to do so. Mythology ultimately gave rise to theology, which is one of the main topics that is debated between philosophers. One could also argue that it was the reason why Socrates was executed, which surely popularized philosophical thought to some extent because he was willing to die for the cause.
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There are nine Muses in classical mythology. Click on the link below to see their names and their domain.
primitive mythology is that such as peoples of prehistoric lands. eg belief that a god will heal them classical mythology is more complex, gods animals plants creatures can all be god like or god possesed
female deity of vengence
That is a rather broad question. Greek mythology somewhat played a role in shaping philosophy; however, there has always been a fine line between religion and philosophy, which has, and will, always be debated. An example of Greek mythology playing a role in the evolution of philosophy *directly* would be in the death of Socrates, who was convicted of corrupting the youth and impiety and put to death.
Supposedly she is the daughter of Gaea and Uranus according to The Wordsworth Classic Dictionary and The Dictionary of Classical Mythology.