Aer was the physis according to Anaximines. He apparently conceived of air as a thick mist.
"Apeiron" is the Greek term for Anaximander's Unbounded. The Unbounded was Anaximander's physis. It was an infinite, eternal, and indefinite substance, without any properties of its own.
Arche is the Greek term for "first principle." Aristotle often referred to each Presocratic's physis as an "arche," but this terminology, because of the high level of sophistication it involves, is misleading when applied to the Presocratics.
The Eleatic philosophers were the followers of Parmenides of Elea. Zeno and Milessus are the two most famous Eleatics. The school of Elea was the first western school of thought to consider pure, abstract reason (as opposed to observation)as the sole criterion of truth. The theory they propounded, arrived at only through the use of pure reason, contradicted everything about our experience of the world.
Epistemology is the branch of philosophy concerned with human knowledge.
Empiricism is the theory that all knowledge arrives in the mind through sensory experience.
Homeomeric Substances -
Homeomeric substances are the most basic, most real components of the world according to Anaxagoras. They are substances without differentiated parts. So, for instance, bone or flesh would be a homeomeric substance, but a chair would not be.
According to Heraclitus there is a logos, or divine pattern, that guides and unifies all of nature. It is only by understanding the logos that we can make sense of our experiences and arrive at knowledge about the nature of the world.
Material Monism -
Material monism is the position that all objects in the world are variations on a single substance. All of the Milesian philosophers were probably material monists, though they differed about what substance comprised the building block of nature.
The branch of philosophy concerned with asking what there is in the world. Questions about physis are metaphysical questions, as are questions about the gods.
Microcosm/macrocosm principle -
A principle of reasoning drawn on heavily by early Greek thinkers. The microcosm/macrocosm principle uses observations about the human organism (or some other organism, or even human society) and draws inferences about the entire universe from these observations.
Thales, Anaxagoras, and Anaximines were the three Milesians. They are grouped together primarily because they were all from Miletus in Ionia and also because they are linked by student-teacher relations. They also, however, have strong similarities in their world systems, including a preoccupation with natural philosophy and a tendency toward material monism.
Natural Philosophy -
Natural philosophy is the branch of philosophy that covers all questions we would now call "scientific." It is concerned with observing natural phenomena and providing explanations to explain their occurrence. The attempt to give a cosmogony is an example of natural science, as is the attempt to give theories of origins of human life.
"Nous" is the Greek term for "mind." According to Anaxagoras, nous is the rational force within nature, guiding and ordering the cosmos.
The Parmenidean Real -
Parmenides threw all of philosophy into a crisis when he argued rigorously that the only possible reality was one that does not correlate at all with our sensory experience. All that exists, he claimed, is a single, continuous, spherical, eternal, unchanging, unmoving thing with no qualities or characteristics.
Aristotle referred to the Presocratic philosophers as "phusikoi," because of their preoccupation with identifying the physis of nature. We derive our modern term "physicist" from this word.
There are two senses in which something can be a physis. A physis can either be the substance out of which everything else in the world arose, or else it can be a unifier within nature. In other words, a physis is either a substance that is the most basic constituent of the world—of which everything else is somehow a variation, or else it is some pattern through which all things in the world form a unity. The Presocratics were particularly keen on identifying the physis of the world. See also apeiron, aer, logos.
The pluralists believed that there were multiple physis in the world. They were all reacting against the Eleatics, and so they claimed that each of their physis was, in fact, the Parmenidean Real.
Principle of Sufficient Reason -
The principle of sufficient reason asserts that there is no effect without a cause or no change without a reason for change. The principle is most closely linked to the philosopher G.W. Leibniz, who first gave it its explicit formulation as well as its name. It was first used, however, by Anaxagoras of Miletus, in arguing that the earth needs no material support.
Followers of the philosopher, mathematician, and religious cult leader Pythagoras. Pythagoreans made important advances in geometry (such as the discovery of the Pythagorean theorem) and also believed in the transmigration of souls. Their ideas had an influence on several of the Presocratic philosophers.