The Milesian philosophers—Thales, Anaximander, and Anaximines—set up a pattern of questions that all later Presocratic philosophers then tried to answer. The first and most fundamental of these was the question: what is the most basic or underlying substance of the world?
This question, the question of physis, can actually be broken down into two separate questions. The search for a physis is, first of all, a search for some substance out of which everything else in the world arose. In this sense, we might say that according to modern science the physis of the world is subatomic particles. Everything in the world, as far as we know, is built up out of these particles.
The search for a physis is also the search for a unifier within nature—either for some substance that is the most basic constituent of the world and of which everything else is somehow a variation, or else for some pattern through which all things in the world form a unity. For the Presocratics the physis was either one or the other of these—i.e. either some basic constituent or some lawlike pattern. To try once again to apply the physis problem to modern science, today we would probably say that the physis, in this second sense, is both a basic constituent (again the subatomic particles) and a lawlike pattern (the laws of quantum mechanics that govern the behavior of these subatomic particles).
Thales, as the first philosopher, was the first to treat the physis problem. According to Thales the physis of the world is water. But water was only Thales' physis in the first sense—as the substance out of which everything else arose. From the sparse fragments that remain to us of Thales' thought, it does not appear as if he considered the second part of the physis problem, the problem of a unifier within nature. Anaximander, a student of Thales, proposed a different physis. His physis was an infinite, indefinite substance, that he referred to as the "apeiron". The apeiron, like all the later candidates for physis, was meant to be a physis in both the above senses.
Anaximander's student Anaximines theorized that the physis was something he called "aer", an infinite substance, but not an indefinite one. Aer, is like a thick, misty air. For Xenophanes there were two physis, earth and water. Heraclitus was the first to propose that the unifier in nature was not some basic material constituent, but rather some structure, law, or plan within nature. He called this structure the "logos" and believed that it controlled the entire natural world.
For Parmenides there was only a single real thing in the world, the unified, unchanging, unmoving reality, and so there really was no need for a question of physis. The Pluralists, however, who tried to revive natural philosophy in Parmenides' wake, returned to the physis problem. According to Empedocles the physis were the four elements, for Anaxagoras the physis was an infinite number of homeomeric substances (i.e. substances without differentiated parts), and for the Atomists, the physis were tiny, indivisible, imperceptible atoms.
The second question that the Milesians posed, and that all later Presocratics tried to answer, is the plurality problem. The plurality problem asks how a single physis could give rise to the plurality of objects we observe in the world. Obviously, the question is based on the assumption made in the physis problem: that we can get the present cosmological structure in its full qualitative variety from a single fundamental substance (or, for Heraclitus, pattern or law).
Thales, as far as we know (again there is the problem of scarce fragments) did not treat the plurality problem, but starting from Anaxagoras the plurality problem became as central a concern to Presocratics as the question of physis. Anaxagoras was not only the first to treat this problem, but he also lay the framework through which many later philosophers would view it. According to Anaxagoras, the key to solving the plurality problem lay in the assumption of a basic polarity of opposites within the original physis (for him, the indefinite apeiron). These opposites (in particular, hot and cold) somehow separate off from the physis, through the eternal motion that the physis undergoes. The hot takes the form of fire, which in turn can coalesce into the sun and other heavenly bodies. The cold becomes dark mist (watery substance), which can then transform into air and earth once it is dried by the heat of fire.
Anaximines also solves the plurality problem by appealing to an eternal motion within his physis, but he makes a definite advance over his teacher by positing a detailed mechanism though which the elements become differentiated. His physis (aer) is transformed into everything else in the world through the processes of condensation and rarefaction. When aer rarifies it becomes fire, when it condenses it becomes wind, then water, then clouds, then earth, and then, finally, stone.
It is unclear how Xenophanes treated this problem (if he did at all), because we have very few fragments pertaining to his natural philosophy.
Heraclitus, like Anaxagoras, appeals to the idea of opposites inherent within nature in order to solve the plurality problem. According to Heraclitus's solution, though, there is really no such problem to begin with: the world begins as a plurality, a constant tension between opposites, which are also somehow unified through the logos.
For Parmenides there is no plurality problem since there is no plurality. What exists is entirely unified. The pluralists, however, return to the problem of plurality. According to all of the pluralists, the plurality that we observe around us is explained as the result of mixtures between their physis: for Empedocles, everything is made out of certain proportions of the four elements, for Anaxagoras, everything is made out of certain ratios of homeomeric substances, and for the Atomists, all objects arise as the result of mixtures of atoms.
The final problem in the Milesian legacy is the maintenance problem. The maintenance problem asks how the universe can retain its current orderly structure—what keeps the world acting in orderly patterns and maintaining its recognizable constancy?
Again, Anaxagoras is the first philosopher we know of to have treated this problem. According to Anaxagoras the world maintains itself through a system much like human law courts. Though opposites are constantly struggling for dominance, nature pays out retributions and penalties to keep the opposites in line, maintaining their proper balance. There is a certain natural equilibrium or balance to the world, a kind of lawfulness within nature, and nature is always striving to maintain this equilibrium. Nature, in other words, is self- regulating. Anaximinies appears to agree with this view of an inherent equilibrium within nature, or, at least, we have no evidence that he disagreed. For Heraclitus, though, the picture is much more turbulent. Instead of occasional strife, which is constantly reigned in to a peaceful equilibrium, for Heraclitus the equilibrium within nature actually is a state of constant and universal strife between opposites. The logos, the pattern or law underlying all of nature, is responsible for maintaining this stormy equilibrium.
For Parmenides, the problem of maintenance dissolves because there is no change at all in the world, but the pluralists revive the question. For Empedocles, it is the two corporeal motive forces, love and strife, that maintain order in the world, whereas for Anaxagoras that role is played by mind or nous, a rationality that controls all of nature. For the Atomists there was no need to posit any force that imposes order on the world, because they believed that order was the result of physical necessity.
The Milesians and the pluralists were primarily interested in natural philosophy—in the topics that we today would call physics, cosmology, and biology. Xenophanes, Heraclitus, and Parmenides, however, also had another preoccupation. They were interested in epistemology, or the study of knowledge.
Xenophanes was the first to raise epistemological questions. He was a strong critic of the poets and of traditional belief. He urged his readers not to trust authority but to arrive at their beliefs through personal investigation. He believed in empiricism—that is, in deriving all beliefs through experience and observation. (The Milesians were also empiricists, but they simply took their empiricism for granted and apparently did not reflect on, or write about, it.) Xenophanes' reliance on empiricism led him to draw some strong conclusions about the limits of human knowledge. He argued, in fact, that we cannot have any knowledge when it comes to the important realms of religion and science; the gods, the question of physis, and the developing cosmos are all outside the range of our experience. Since we cannot observe these phenomena, argued the empiricist Xenophanes, we cannot have any knowledge regarding them. All that we can have are beliefs. This distinction between knowledge and belief has become one of the most important themes in philosophy.
Both Heraclitus and Parmenides attempted to escape Xenophanes' skeptical conclusions by recommending methods of inquiry that go beyond experience. Heraclitus developed his idea of the logos, the pattern or law that underlies all of nature. The logos of the world, he claimed, has a counterpart logos in our souls, which enables us to decode and understand nature. In other words, we should not try to arrive at knowledge through mere observation, rather we should try to rationally understand the structure of the world, using our own internal faculty of reason. To try to arrive at knowledge without understanding the logos, he claims, is like trying to decipher speech without understanding the language.
Parmenides also stresses the importance of pure reason in arriving at knowledge. In fact, he believed that human beings should ignore their sensory experience of the world entirely. Whereas Heraclitus claimed that observation needed only to be tempered by rational insight in order to lead to knowledge, Parmenides believed that any observation at all was bound to lead to untruths. Using only his faculty of reason, he arrives at a picture of the world that is wholly unlike anything we could possibly arrive at through observation. The world as it really is, on this picture, is nothing like the world that we can observe. The only way to arrive at knowledge, then, is to reason logically. Observation has nothing at all to do with the enterprise.