The scope of philosophy in the ancient understanding, and the writings of (at least some of) the ancient philosophers, were all intellectual endeavors. This included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics).
In the pre-Socratic period, ancient philosophers first articulated questions about the "arche" (the cause or first principle) of the universe. Western Philosophy is generally said to begin in the Greek cities of western Asia Minor (Ionia) with Thales of Miletus, who was active c. 585 BC and was responsible for the opaque dictum, "all is water." His most noted students were respectively Anaximander (all is apeiron (roughly, the unlimited)) and Anaximenes of Miletus ("all is air"). Pythagoras, from the island of Samos off the coast of Ionia, later lived at Croton in southern Italy (Magna Graecia). Pythagoreans hold that "all is number," giving formal accounts in contrast to the previous material of the Ionians. They also believe in metempsychosis, the transmigration of souls, or reincarnation.
A key figure in Greek philosophy is Socrates. Socrates studied under several Sophists but transformed Greek philosophy into a branch of philosophy that is still pursued today. It is said that following a visit to the Oracle of Delphi he spent much of his life questioning anyone in Athens who would engage him, in order to disprove the oracular prophecy that there would be no man wiser than Socrates. Socrates used a critical approach called the "elenchus" or Socratic method to examine people's views. He aimed to study human things: the good life, justice, beauty, and virtue. Although Socrates wrote nothing himself, some of his many disciples wrote down his conversations. He was tried for corrupting the youth and impiety by the Greek democracy. He was found guilty and sentenced to death. Although his friends offered to help him escape from prison, he chose to remain in Athens and abide by his principles. His execution consisting in drinking the poison hemlock and he died in 399 B.C.
Plato was a student of Socrates. Plato founded the Academy of Athens and wrote a number of dialogues, which applied the Socratic method of inquiry to examine philosophical problems. Some central ideas of Plato's dialogues are the immortality of the soul, the benefits of being just, that evil is ignorance, and the Theory of Forms. Forms are universal properties that constitute true reality and contrast with the changeable material things he called "becoming".
Aristotle was a pupil of Plato. Aristotle was perhaps the first truly systematic philosopher and scientist. He wrote about physics, biology, zoology, metaphysics, aesthetics, poetry, theater, music, rhetoric, politics and logic. Aristotelian logic was the first type of logic to attempt to categorize every valid syllogism. Aristotle tutored Alexander the Great. He in turn conquered much of the ancient world at a rapid pace. Hellenization and Aristotelian philosophy exercised considerable influence on almost all Western and Middle Eastern philosophers, including Greek, Roman, Christian, Jewish, and Islamic thinkers.