For it is no more fitting for what is established at the center and equally related to the extremes to move up rather than down or sideways. And it is impossible for it to make a move simultaneously in opposite directions. Therefore it is at rest of necessity. Testimonia A26.
This passage, reported to us by Aristotle in On Heavens, provides Anaxagoras's explanation of what holds the earth steady. This account marks the first known use of the famous principle of sufficient reason, which asserts that there is no effect without a cause, i.e. nothing changes unless there is a reason for it to change. Because, on Anaximander's view, the cosmos is perfectly symmetrical, and the earth is placed squarely in its center, there could not possibly be any reason for the earth to move in one direction rather than another. Therefore, the earth does not move. Anaximander was the only early philosopher, as far as we know, to correctly claim that the earth is not supported by anything material, such as water (Thales), a cushion of air (Anaximines), or a large column (Heraclitus).
Ethiopians say that their gods are flat-nosed and dark, Thracians that theirs are blue-eyes and red-haired. Fragment B16
This statement is one among several of Xenophanes' clever attempts to demonstrate the human tendency to project our own qualities onto our deities. The traditional theological conception, he claims, is based entirely on such projections and thus fails to hit on any theological truths. The truth, according to Xenophanes, is that there is a single god, unlike human beings in form or thought, who is unmoving, but all-seeing, all-hearing, and all-thinking, and who controls the world with his mind.
Eyes and ears are bad witnesses to people if they have barbarian souls. Fragment B107.
In this pithy statement Heraclitus provides one of his two vivid metaphors meant to illustrate the fundamental importance of understanding the logos. Without an understanding of the logos, or the divine law or plan within nature, observation is absolutely useless. To try to investigate nature without understanding the logos, is like trying to gain meaning from words without understanding the language to which they belong: all that you perceive, in both these cases, is meaningless noise. (A barbarian is literally just a person who does not understand Greek).
That which is there to be spoken of or thought of must be. Fragment B6
With this idea as his guiding principle, Parmenides effected a revolution in Presocratic thought. He maintained that one could only coherently speak about or think about being, rather than non-being, and using just this premise he deduced a picture of the nature of reality that completely contradicts everything experience tells us: he argued that reality is (1) eternal, (2) unchanging, (3) just one single thing, of a single, undifferentiated, qualitative type, and (4) unmoving. All later Greek philosophers, including Plato and Aristotle, had to contend with these arguments in putting forth their own theories of the nature of the world.
By convention sweet, by convention bitter; by convention hot, by convention cold; by convention color; but in reality: atoms and the void.
For those Post-Parmenidean Presocratics who refused to believe that the world is nothing like we experience it, the challenge lay in giving an account of the observable world, while not contradicting Parmenides' well-argued conclusions. The above statement sums up Democritus' resulting view on the nature of ultimate reality: the only truly real objects of the world, he is here claiming, are atoms and the void. The observable world, which arises from the arrangement and rearrangement of these atoms, is less real. Since only the atoms and the void are truly real, any change, plurality, etc. that we observe in our experience, is not a true violation of Parmenides' requirements for the real.