In general, the age of the source is the most likely to be nearest the truth - symbolism and context allowed for. There is an inherent mistrust of Roman sources who tended to put their own spin on things. Similarly the fate of Socrates warned others like Plato not to rock the boat too much and the constant evolution of the Greek language makes identifying context difficult.
Chronological synchronisms can lead to a precise date but there are a number of these and they are of varying degrees of usefulness and reliability.
Seriation, i.e. archaeological sequences
Synchronisms with other chronologies
The Thera eruption(s)
Ancient Scriptures and Inscriptions
Folklore / Legend
The Atlantis story comes from Plato as told by Critias in the Timaeus and Critias Dialogues. Some argue the tale of Atlantis is just a fictional moralistic metaphor, and there is some evidence to justify this.
Whether the moral was given by Solon or Plato, or perhaps both, is open to question. There is no direct mention by Homer of Atlantis, although there are suggestions an Atlantean society had been in existence. Other ambiguous references from the Middle East, India, and Egypt, could easily relate to some other sunken island. Plato is the only one to mention Atlantis by name. Homer does however give us invaluable information about the life, times, and culture in ancient Greece and among Mediterranean peoples.
The following list is in chronological order rather than alphabetical:-
Homer c.800-600 BC, is an enigma. When the fact there is uncertainty as to whether Homer even existed is thrown into the mix, lines blur. It is one view that Homeric Poetry was akin to folklore and not directly attributable to one person, named Homer or otherwise. Very little can be verified. Homer, as a person, was most popularly cast as a blind bard from Ionia. Travelling minstrels and entertainers would entertain with such tales. No doubt they were subject to the Chinese Whispers treatment. Even Plato's account of Atlantis was heard 5th-hand at best.
Irrespective of that, Homer is responsible for two epic poems that are the central works of ancient Greek literature. The Iliad is set during the Trojan War, supposedly a ten-year* siege of the city of Troy by a coalition of Greeks. The Odyssey focuses on the ten-year* journey home of Odysseus, king of Ithaca, after the fall of Troy.
*Before 500 BC there was an anomaly with the Greek and Egyptian numerical systems which indicated a ten-fold exaggeration when translating. However, this applies to Plato (when Solon is the source) rather than Homer whose poems were of Greek origin.
Hesiod c.750-600 BC is considered by most as a contemporary of Homer and the oldest written source in 'modern' language. Two complete works have survived - Theogony and Works and Days. Theogony deals with the genealogy of the gods, Works and Days details the 'Five Ages of Man'. There was a lot more to Hesiod besides his Homeric dialect poetry. He was cited as a major source of farming techniques, economic thought and astronomy. Hesiod's genealogy has to be taken seriously when constructing a genealogy of ones own.
Solon 638-558 BC the secondary source of the Atlantis legend. He was told the story on a visit to Egypt. Atlantis aside, Solon was a very moralistic statesman who laid the foundations for democracy. He had a brother / family member / friend, Dropides, to whom he is said to have told the Atlantis story.
Herodotus 484-425 BC, is another source due to his Homeric references. If Plato is considered a little suspect in some ways, Herodotus gives even more reason for scepticism. Herodotus was called the 'father of history' by many, a phrase supposedly coined by Cicero. Yet despite numerous accolades, Herodotus, like Plato, had critics who ridiculed his work. Some of his contemporaries called him the father of lies. There is little doubt he travelled extensively, verified by geographical and historical facts he described in detail, and much information was gathered from folklore or wandering minstrels. Herodotus stated he only reported what was told to him (echoes of Plato in some respects), and there were some fanciful stories by consequence. Thucydides was a critic of Herodotus, not without cause.
Socrates c.470-399 BC left no writings and most of what we know is from accounts by the likes of Plato and Xenophon. Socrates was executed by being forced to take hemlock, his crimes supposedly impiety and corrupting the youth of Athens. Religion, as in other regions, was the main form of control over the masses. The ruling class wouldn't allow it to be undermined.
Thucydides 460-400 BC, was known as the 'father of scientific history' and whilst his need for accuracy is commendable, to completely overlook myth and legend is folly. It is a problem shared by scientists and atheists alike. They dismiss a whole book due to sporadic nonsense. Many of the collected folk tales were undoubtedly embellished but rather than discard them, we should look for the clues they hold. Another thing about Herodotus is his being a contemporary of Socrates, and he too seemed loathe to attribute acts to the Gods. However his 'reporting' style saved him sharing the same fate and may have been an inspiration for Plato.
Plato (or Aristocles) 424-347 BC There are many issues with Plato - not least his real name. The Timaeus and Critias dialogues are filled with anachronisms. He could be forgiven for implicating the deceased Socrates, considering the nature of the ruling class. Dropides told his son, Critias, the Atlantis story and he in turn told his grandson, also named Critias. This Critias is purported to be the one named in the Dialogues. Debates continue but it is quite irrelevant here as our chronology ends before this time. The fact is the story exists.
Parian Chronicle or Parian Marble is a stele giving a Greek chronology 1582 BC to 299 BC. It was found on the island of Paros in two sections, and sold to Thomas Howard, Earl of Arundel. The stele was deciphered by John Selden but the first of the sections subsequently disappeared. A third fragment comprising of the base was later found on Paros with entries from 336/35 to 299/98 BC. The stele was inscribed and erected c.263 BC and mixes historic events with what are generally considered myths. Other than a 20-25 year discrepancy with archaeological evidence, the stele appears to be a valid source of information.
Here, Greek Myths are treated in much the same way as ancient scriptures, art, pottery and other artefacts, the possibilities are explored objectively. The pleasing thing with the ancient Greeks is how they personified many of their deities. There are clues to actual people and places that can loosely be accounted for by 'known' historical / geological events. Conversely there is also a lot of nonsense (or superstitious misinterpretation of natural phenomena and the cause).
Of course it would be folly to believe or try to rationalise without at least a little evidence. Socrates tried to dispel the nonsensical areas of mythology but was 'encouraged to commit suicide' for it. Unfortunately all the work of Socrates is non-extant and Plato's accounts of it may be coloured by paranoia and a personal agenda.
Translations are from those generally accepted as most accurate. Being linguistically challenged with regard to Linear B and ancient Greek, it is necessary to accept these 'true translations' but I often feel context has been misconstrued.
Some translations are of text that is no longer extant and leaves the door open for more inaccuracy. Others are from fragments where later scholars attempted to fill in the blanks. Whilst extracts of generally accepted translations will be posted here, they are subject to closer scrutiny and are often given a slightly different slant. As stated, for the most part I regard contributions from Roman sources as deeply suspicious but one or two may have a little merit.
Geological and archaeological evidence is invaluable yet even here there is a failure to correlate data correctly. Text is open to (mis)interpretation just as is art. To fully appreciate and understand the context of scripture or imagery, a more holistic view is required.