away from substance and onto form. The numbers have no substance, yet they are the central concept because they govern the behavior of things. The substanceless numbers are in some sense more real than the substance itself, which merely provides a medium through which the number relationships can manifest themselves. This idea of the superiority of form was to become quite important in Greek thought, and at this very early juncture it provides an alternative formulation to the concept of nature set forth by the Ionians.
Reflection on the issues raised by postulating an underlying universal substance, when the world we observe shows a huge degree of variety, greatly influenced Greek thinking on nature. The question of Becoming, how the things of the world arise from an eternal unchanging Being, was answered in many different ways. Opposing views were proposed by two early giants of Greek philosophy, Heraclitus and Parmenides. For Heraclitus, change was the central feature of reality. All things are process and transformation, not static Being. There is an eternal principle, which he identifies as fire, but this principle itself is the principle of creation, destruction, and transformation. The true underlying order he calls Logos, but it’s not clear whether this is within the comprehension of humans. Parmenides, in contrast, maintains that all change is merely illusion and that static Being is the only true reality. The implications of this position are far-reaching: if all that we see is change, and change is an illusion, then everything that we infer from the evidence of the senses is unreliable opinion. The only truth that we can know comes from reason, not the senses. Hence, Parmenides does give us a physical theory of the Ionian kind, but he labels it as merely opinion. These two radical contrasting views were both incapable of leading to any further progress in formulating a concept of nature, but they stimulated thinking by clearly outlining the problem.
This problem of Becoming was addressed by the next generation of philosophers, who devised at least three distinct concepts of nature to solve it. The most direct solution was that of Anaxagoras, who believed that every distinguishable substance possessed its own elemental being. Thus, Being in general was divided into an infinite variety of eternal substances, eliminating the problem of how one substance could transform into another since no transformations occurred, only processes of mixing and replacing. The question now becomes identifying what guides these processes, and Anaxagoras proposed the existence of the Nous (mind, reason, purpose) as the animating principle that acts on the inert and mindless elements to form them into the world we know. In this way, Anaxagoras has now introduced a kind of teleological thinking into Greek nature philosophy, but left many problems by doing so (e.g. is the Nous material or immaterial? in what way does the Nous act? etc.). A much different kind of solution to the problem of Becoming was proposed by Empedocles. He limits the number of uncreated and indestructible elements to four, chosen on the basis of their contrasting properties: earth, water, air, and fire. These four elements are combined together and dissolved apart by the counteracting forces that he terms Love and Strife, which seem to be primarily mechanical in action (attraction and repulsion) despite their poetic names. An important innovation of Empedocles is the idea that any particular material (bone, for example) is characterized by a specific ratio of elements. This introduction of proportions and integer ratios exhibits the influence of Pythagoras. It is this Pythagorean influence that also tempers his tendency to view nature mechanistically. “There is, then, Empedocles concludes, some sort of archetypal intellect identified with Being […] its thoughts are ‘not to be uttered,’ but it is the fount from which Love draws the ratios and harmonies for its operations.”18 A third solution to the problem of Becoming, proposed by Leucippus, was to ascribe the unchanging Being to an infinite number of small indivisible bodies, the atoms. All change, then, was due to the movement of the atoms including their coming together into larger objects (or detaching as objects break apart or decay). The atoms exist in a void (which Parmenides had denied existence), and this solved the problem of how motion could occur. Unlike the somewhat similar ideas of Anaxagoras, the motions of the atoms are inherent properties of the atoms themselves and governed only by necessity, i.e. cause and unalterable rules. This rids the system of any hint of duality, but leaves Leucippus with an entirely materialistic concept of nature. We will look more closely at materialism in a later chapter.
Another line of thought accepted the conclusions of Parmenides and set out to defend these conclusions and explore their implications. The most famous member of this school was Zeno of Elea, with his well-known paradox proving that motion is impossible. But this line of thought proves sterile for the understanding of nature, ending in the sophistry of Gorgias (who proves that even Being does not exist). Since there is no point in studying nature, Gorgias and his fellow sophist Protagoras reduce philosophy to rhetoric. Their opponent Socrates is still concerned with a search for truth, but his interests are also in the affairs of humans such as ethics and politics. The concept of nature in this intellectual culture has become unimportant and irrelevant.
Meanwhile, other sources (outside philosophy) of study and information about the natural world were becoming more organized and important. Medicine, for example, was developing its own methodology and conclusions, sometimes independently of those considering nature as a whole and sometimes in concert with them. A good deal of empirical knowledge was acquired (bone and muscle anatomy, for example, and the course of certain diseases), but some of the medical theory (such as the four humors) seems to draw on more general cosmological ideas. The doctors and the philosophers were in agreement that rational necessity (rather than the whims of the gods) governed things, but methodologically the doctors were generally more interested in empirical observation given their agenda of curing the ill. Thus, although medicine did not have the explicit goal of developing a broad understanding of nature, it did indirectly influence the Greek concept of nature through its methods and point of view. Another influence was the development of mathematics, which was making steady progress and slowly becoming more independent of its philosophical roots. This process would later culminate in mathematics as a separate discipline with important applications in astronomy and statics. At about the time that the sophists were beginning to dominate the cultural discourse of Athens, Archytas of Tarentum was making important advances both in mathematics itself and in the Pythagorean program to unite philosophy, mathematics, and nature.
The humanistic concerns of Socrates are combined with the old questions about nature and the cosmos (including the role of mathematics) in the philosophy of Plato. Plato generalizes the Pythagorean idea of mathematical form governing the behavior of matter, and his ideal Forms (or Ideas) include ethical, physical, conceptual, esthetic, and other Forms as well as geometric and numerical Forms. The Forms are eternal and perfect, existing outside of time, space, and matter. Matter itself is formless and chaotic. The world as we know it, i.e. nature, is the result of the perfect Forms impressing themselves on the recalcitrant matter. Plato’s concept of nature, then, is that it is an imperfect imitation of the ideal Forms, involving change, growth, decay, and approximation. That which is intelligible in nature is merely a dim reflection of the pure intelligibility of the Forms themselves, and true knowledge can only be knowledge of these Forms. Thus, we can gain true knowledge only through the use of reason; study of the empirical world is useful, but only to gain clues providing grist for reason to work on. In Plato’s cosmology, an active principle (identified in the Timaeus as the Demiurge or Craftsman) is required to bring order to matter, using the patterns offered by the Forms. There are two crucial elements inherent in Plato’s vision of nature: the role of teleology and the role of mathematics. Because nature is a partial realization of perfect Forms, the world is filled with meaning and purpose, and much of the structure and action in the world exists to fulfill these purposes. Because the Forms are often mathematical, the manifestation of the Forms in visible nature gives rise to mathematical regularities there.
Aristotle modified Plato’s system in several significant ways. One important difference is that, although he agreed with Plato on the existence and importance of Forms, Aristotle identified the Forms inherently with the actual material things that manifested the Forms rather than some detached immaterial state. From this crucial difference, two corollary differences follow: First, the process of manifesting the Form becomes centrally important, and so teleology becomes one of the major components of Aristotle’s concept of nature. Second, the empirical study of the natural world played a much more prominent role in Aristotle’s thought than Plato’s. The emphases
