World Canonical Texts
I have started reading World Philosophies, 2nd edition (Ninian Smart 1999, re-edited by Oliver Leaman 2008). The book starts with and opening chapter and Indian philosophy (I'd blog on these a little later).
Some initial notes on pre-socratics:
A. Ionian school
Thales (Miletus, fl. ~580BCE) - water as underlying basis of the world; also mysteriously held that everything is full of gods
Anaximander (younger contemporary of Thales) - instead of water, it was apeiron or the limitless, which is beyond perception, and is not bounded in the way the four substances/forces of hot, cold, dry and wet are; believe in many cosmoses; humans came from animals, which first formed in the ocean before coming onto dry land (anticipation of evolutionary theory); naturalistic
Anaximenes (fl. 545BCE) - air as arche; air can rarefy into fire or condense into wind, water, earth and rock in successive stages
B. Pythagorean School
Pythagoras (c.570-490BCE, south Italy) - Cosmos a vast system of things whose inner nature was numerical (points 1; straight lines 2; minimal triangles 3; tetrahedrons, the minimum solid 4); cosmos seen as a (mathematical and musical) harmony (orderly and beautiful) in which (numerical) limit was imposed on the apeiron, causing the evolution of cosmos; believed in transmigration & rebirth; salvation by following a community devoted to sacred knowledge or philosophy
C. Heraclitus
Heraclitus (fl. 501BCE, Ephesis in Ionia) - the stuff of the cosmos to be fire; strife tears things apart as love brings them together; this dialectical interplay explains change, which is continuous; all things flow; postulating the Logos (reason, formula, word) according to which things regularly change
Cratylus (late 5th c., Heraclutius' disciple?) - "cannot step into the same river once"; world as extreme flux thus gave up speech
D. Parmenides (and followers)
Parmenides (b.c.515BCE, Elea, southern Italy) - Truth asserts that Being (the object of thought) is; contrast with the absurdity of non-being, and with the way of "seeming" which confusedly suppose that there are things which exist at one time and not at another (cosmology belongs here); homogeneity of space
Zeno (b.c. 490BCE, Parmenides' follower) - paradoxes to show the contradictory character of pluralism and motion
Melissus (5th c.; another follower of Parmenides) - the one being is infinite, both as to space and time; the world of sense-experience, in reporting change, registers contradictions and so is an illusion
E. Empedocles
Empedocles (1st part of the 5th c. BCE, Sicily) - all-rounded sage (politics, healing, science, poetry, religious); theory of 4 elements (earth, air, fire, water), the everlasting particles bodies which combined or uncombined under the influence of the two cosmic forces of love and hate; also postulated a soul, continually being reborn; a divine incorporeal being is governing the cosmos; not eating meat and beans like Pythagoreans.
F. Anaxagoras
Anaxagoras (?500-428 BCE, Clazomenae in Asia Minor, eventually settled in Athens) - postulated Nous as causing the initial mixture of elements of the cosmos to rotate; distinction between homogenous (e.g. gold) and differentiated substances
Leucippus (second part of the 5th c.) - atomic theory
Democritus (? 460-370, Abdera) - the laughing philosopher; extensive writings on the atomistic worldview; universe composed of a void with scattered in that void an infinite number of atomic (indivisible or uncuttable) entities; atoms are of an infinity of different shapes; materialist view of the soul (round atoms); rejected all notions of design in the cosmos; modified empiricism - need to go beyond the senses to understand the world (formed by atoms beyond sense perception); large number of worlds
G. Sophists & Socrates
Sophists - similar to early Confucianism (interest in education; virtue can be taught; concern with the performative; appeal to innate tendencies)
Protagoras (500-430BCE; b. Abdera, visited Athens) - shame is imparted to all humans; studied grammar
Gorgias (c.483-c.375BCE, from Sicily) - argued that nothing exists; there cannot be knowledge (of non-beings); if if there were knowledge, it could not be communicated, since each sign is different from that it is supposed to signify
Socrates (c.470-399 BCE, Athens) - used dialectical or conversational method to seek universal definitions of such attributes as courage or piety; virtue is knowledge
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So, Smart/Leaman mentions 16 philosophers in 7 sections. It is also clear that before the Sophists, there were no Skeptics or Relativists. Let's consider these 16 philosophers in 3 stages.
Stage 1: Ionian, 6th c. BCE
4 philosophers: Thales (water), Anaximander (apeiron, "evolutionary" cosmology), Anaximenes (air), Heraclitus (fire, change)
Ultimately, because all 4 are "naturalistic" and "materialistic", in our hexagon scheme all belong to the bottom right. However, at this early stage, these 4 theories can also be put in the hexagon scheme (without the far left and far right)
Anaximenes (air) Anaximander (apeiron)
Heraclitus (fire) Thales (water)
Stage 2: Southern Italy, fl. last 3rd of 6th c. and first 3rd of 5th c. BCE
3 philosophers: Pythagoras (slightly later than Anaxemenes, before Heraclitus), Parmenides, Empedocles (both after Heraclitus). These clearly known of the Ionians, but would try to argue for better positions against Heraclitus.
Pythagoras has numbers as fundamental, though his school is not purely reductionist - it is more teleological, concerned about cosmic evolution, in fact, I can interpret him to be improving on Anaximander.
Parmenides (being) Pythagoras (math harmony)
[Heraclitus (change)] Empedocles (elements)
Stage 3: Converging to Athens, mid-3rd to last 3rd of 5th c. BCE
9 philosophers named, of which Zeno & Melissus continued from Parmenides, Cratylus continued from Heraclitus. Of the other 6, two are classified as Sophists (even though Protagoras is from the eastern side, Gorgias from Sicily), 3 are broadly materialist (Anaxagoras, plus two atomists, plus Socrates.
So in hexagon, I would put them:
Zeno, Melissus Anaxagoras (nous), Socrates (knowledge/virtue)
Gorgias (Skeptic) Protagoras (relativism)
Cratylus Leucippus, Democritus
I tentatively put Socrates at the top-right, which in the hexagon scheme leans towards principles/ideas as the ontological reality, while uses a dialectical method (in the Hegelian sense). But Socrates' belief in virtue as knowledge could make him a someone just generally tend "up" without easily putting him on the reductionistic (left) or the dialectical (right) side
Looking at the above 3 stages as one early phase of Greek philosophy, then the most prominent ones (leaning towards the Athenian period) occupying the spaces (excluding Socrates) are:
Parmenides Anaxagoras
Gorgias Protagoras
Heraclitus Democritus
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In this summary, only Xenophanes, about the time of Pythagoras, who held a Skeptic-like epistemology, is not included. In the Hexagon schematic, he would be prior to Gorgias on the far left.
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And of course, within the next 4 generations after Socrates, the picture will become
Socrates, Arcesilaus Plato (and Platonism)
Pyrrho (Skepticism) Aristotle (and his school)
Zeno of Citium (Stocism) Epicurus (and his school)
It is the slot occupied by Parmenides that is structurally left not satisfactorily filled.
I put middle Academic skepticism (e.g. Arcesilaus) in the slot for now - as a dogmatic position about impossibility of knowledge is itself a "reductionistic" attempt to simplify the world of multiplicity into a "principle/idea" - just like later dogmatic rationalism.
Note: I am made aware of John Cooper's (editor of complete Plato) 2012 book Pursuits of Wisdom: Six Ways of Life in Ancient Philosophy from Socrates to Plotnius. In the book blurb, it says: "Pursuits of Wisdom examines six central philosophies of living--Socratic, Aristotelian, Stoic, Epicurean, Skeptic, and the Platonist life of late antiquity." Of course, the point here is that John Cooper puts the Socratic way as different from the Platonists' way, thus more in line with the hexagon I draw in this section.
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The above gave the series:
Materialistic direction (bottom right):
Thales (water), Empedocles (elements), Leucippus, Democritus (atomic theory), Epicureanism
Direction of the primacy of change (bottom left): [ultimately, ancient Greek didn't get to the extreme positions like Buddhism or Berkeley's subjective idealism]
Heraclitus, Cratylus, Zeno of Citium (Stoicism)
Direction of reductionistic idea/principle (top left):
Anaximenes (air, still materialistic), Parmenides, Zeno/Melissus, (Socrates?), Academic Skepticism
Direction of dialectical noumenal cosmology (top right):
Anaximander, Pythagoras, Anaxagoras, (Socrates?), Plato (Platonism)
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Coda
By the generation of Arcesilaus (c. 315-240 BCE), Greek/Hellenistic philosophy has crystalized: Plato, Aristotle, Pyrrho, Epicurus, Zeno of Citium (Stoic), and Arcesilaus taking the path of Academic Skepticism.
In Smart/Leaman book chapter, the next philosopher mentioned with a date is Alcinoubinus of second century BCE (supposedly neo-platonic, but interestingly I can't find on Google / Wikipedia). The next set of authors mentioned are in mid-1st c. BCE, spurred by Roman conquest of the Greek East. Smart/Leaman mentioned Aenesidemus, Lucretius and Cicero. With a bit of web research I can add Posidonus (Stoic), Antiochus of Ascalon (platonic, mentioned in the Condensed Copleston), and Andronicus of Rhodes (editor of re-discovered texts of Aristotle and Theophrastus).
So in the early-to-mid 1st century BCE "Roman alignment" of Hellenistic philosophy, the hexogon stays the same with just new (some Roman) names)
Cicero (Academic Skeptic) Antiochus of Ascalon
Aenesidemus (Pyrrhonian Skeptic) Andronicus of Rhodes
Posidonius Lucretius