Apeiron (ἄπειρον): a Greek word meaning unlimited, infinite, or indefinite from ἀ- a-, "without" and πεῖραρ peirar, "end, limit",the Ionic Greek form of πέρας peras, "end, limit, boundary".
Arche: (ἀρχή) is a Greek word with primary senses 'beginning', 'origin' or 'first cause' and 'power', 'sovereignty', 'domination' as extended meanings. This list is extended to 'ultimate underlying substance' and 'ultimate undemonstrable principle'.
'A theological-scientific mission to find the arche and apeiron.' That is my 1$ summary of the pre-Socratic movement. Interestingly enough it isn't too far from the truth. While barely anything on the pre-Socratics is left behind, there seems to be a lot of consensus as to the sort of methodology they upheld in trying to find the 'ultimate underlying substance'. The word philosopher seems to lack the robustness needed in a word to describe men like Thales and Anaximander. These men were more like mystical polymath-social engineers. People like to say that 'reason' as such sprung from nowhere in ancient Greece. Even Nietzsche seems to believe this. I would argue reason is something people use all the time, and what makes people philosophers -or at least good philosophers- is their ability to apply reason to problems of metaphysics, epistemology, and ethics. Unlike the Triebe (drive) of reason Nietzsche posits as being 'unleashed' by Socrates, I would say simply that philosophy became for the first time; philosophy as the manifestation of the relationship between fundamental human questions and a rational approach to the answers provided; the very same questions answered in mythology -'What am I?', 'Where do I come from'- are approached with a different methodology. But even then, what are we to say to that one rational ass hole in 6000 B.C. who lived in a cave and actually thought rationally about these questions before any Greek philosopher did. I have this dual frustration with the way people talk about the pre-Socratics. Firstly, the lack of information we have about the pre-Socratics is usually second-hand and that makes everything so vacuous. Secondly, I feel like we leave out all the undocumented history and attempt to make a conclusive historical narrative based on a fraction of all human activity.