I think it may be interesting for a few posters, particularly in regards to current philosophical thoughts they may read about ^^ Besides, I can answer questions, given that I am to again present a series of seminars on this subject this month. There had been a thread of mine on this subject, but many years ago, so it wouldn't be a good idea to just resurrect that.
So discussion can be generally on any subset of Greek philosophy in this time period (roughly, 7th century BC-4rth century BC), and tied subjects (eg more modern philosophy).
The three main types of ancient Greek philosophy are: Physical (to do with phenomena in the material world), Ethical (about theories on how to better live) and Dialectic (about notions and what it means to think).
As an OP I think it will be the best to just summarize how philosophy is argued to have started in ancient Greece (a good source, with historical value, is Diogenes Laertios' Lives of Philosophers), and why it was regarded as a distinct field than (say) mysticism or general thought.
-The main view in antiquity was that Greek philosophy differed from other civilization's similar studies, primarily due to it being an open field (not restricted to sects or other groups, such as Egyptian priests, Babylonian chaldeans, Persian magoi etc) and usually (but not in all cases; prominent exceptions include Pythagoras, the Eleans and to a smaller degree Plato) not featuring any theological elements.
-The first Greek philosopher was Thales, from Miletus. He also is the only philosopher who is part of the group of "the Seven Sages", and thus had one of his apofthegmata inscribed in the oracle at Delphoi (it read "Nothing in Excess", similar to a latter one by Aristotle). Thales was regarded in a similar way to how Einstein is regarded in current pop culture, being mentioned (eg) in plays by Aristophanes as a synonym for genius. More importantly, he is credited with providing the first theorem-based proof in mathematics, with his important theorem of analogy in intersecting lines. Another theorem of his is about angles in a circle, formed by points in the periphery.
Thales also presented solutions to more practical matters, using geometry. A method of calculating a ship's distance from the shore (without needing that much space in the shore either), as well as the calculation of the height of the larger pyramid at Giza (through shadows in a sun dial, and their analogy to the Pyramid's shadow) are two good examples of that.
Lastly, it is reported that he might have predicted an eclipse, which took place the day of a battle between Lydians and Persians.
The two students of Thales were Anaximander (also from Miletus) and Pythagoras. From Anaximander we get the notion of infinity - prior to him, the term was used in Greek only as an epithet, for example in Homer, to describe the vastness of the sea. From Pythagoras... we arrive at the very important first discovery of an irrational number (the diagonal of a square), apart from the eponymous theorem.
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